Статті в журналах: "Topologically-ordered phases"

1

Lee, In-Hwan, Hoang-Anh Le, and S. R. Eric Yang. "Mutual Information and Correlations across Topological Phase Transitions in Topologically Ordered Graphene Zigzag Nanoribbons." Entropy 25, no. 10 (October 15, 2023): 1449. http://dx.doi.org/10.3390/e25101449.

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Graphene zigzag nanoribbons, initially in a topologically ordered state, undergo a topological phase transition into crossover phases distinguished by quasi-topological order. We computed mutual information for both the topologically ordered phase and its crossover phases, revealing the following results: (i) In the topologically ordered phase, A-chirality carbon lines strongly entangle with B-chirality carbon lines on the opposite side of the zigzag ribbon. This entanglement persists but weakens in crossover phases. (ii) The upper zigzag edge entangles with non-edge lines of different chirality on the opposite side of the ribbon. (iii) Entanglement increases as more carbon lines are grouped together, regardless of the lines’ chirality. No long-range entanglement was found in the symmetry-protected phase in the absence of disorder.

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2

Hussien, Musa A. M., and Aniekan Magnus Ukpong. "Electrodynamics of Topologically Ordered Quantum Phases in Dirac Materials." Nanomaterials 11, no. 11 (October 30, 2021): 2914. http://dx.doi.org/10.3390/nano11112914.

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First-principles calculations of the electronic ground state in tantalum arsenide are combined with tight-binding calculations of the field dependence of its transport model equivalent on the graphene monolayer to study the emergence of topologically ordered quantum states, and to obtain topological phase diagrams. Our calculations include the degrees of freedom for nuclear, electronic, and photonic interactions explicitly within the quasistatic approximation to the time-propagation-dependent density functional theory. This field-theoretic approach allows us to determine the non-linear response of the ground state density matrix to the applied electromagnetic field at distinct quantum phase transition points. Our results suggest the existence of a facile electronic switch between trivial and topologically ordered quantum states that may be realizable through the application of a perpendicular electric or magnetic field alongside a staggered-sublattice potential in the underlying lattice. Signatures of the near field electrodynamics in nanoclusters show the formation of a quantum fluid phase at the topological quantum phase transition points. The emergent carrier density wave transport phase is discussed to show that transmission through the collective excitation mode in multilayer heterostructures is a unique possibility in plasmonic, optoelectronic, and photonic applications when atomic clusters of Dirac materials are integrated within nanostructures, as patterned or continuous surfaces.

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3

GROVER, TARUN. "ENTANGLEMENT ENTROPY AND STRONGLY CORRELATED TOPOLOGICAL MATTER." Modern Physics Letters A 28, no. 05 (February 6, 2013): 1330001. http://dx.doi.org/10.1142/s0217732313300012.

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Topological ordered phases are gapped states of matter that are characterized by non-local entanglement in their ground state wave functions instead of a local order parameter. In this paper, we review some of the basic results on the entanglement structure of topologically ordered phases. In particular, we focus on the notion and uses of "topological entanglement entropy" in two and higher dimensions, and also briefly review the relation between entanglement spectrum and the spectrum of the physical edge states for chiral topological states. Furthermore, we discuss a curvature expansion for the entanglement entropy which sharpens the nonlocality of topological entanglement entropy.

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4

Spanton, Eric M., Alexander A. Zibrov, Haoxin Zhou, Takashi Taniguchi, Kenji Watanabe, Michael P. Zaletel, and Andrea F. Young. "Observation of fractional Chern insulators in a van der Waals heterostructure." Science 360, no. 6384 (March 1, 2018): 62–66. http://dx.doi.org/10.1126/science.aan8458.

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Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices C=−1, ±2, and ±3. Some of these phases, in C=−1 and C=2 bands, are characterized by fractional Hall conductance—that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.

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5

Daniel, Austin K., Rafael N. Alexander, and Akimasa Miyake. "Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices." Quantum 4 (February 10, 2020): 228. http://dx.doi.org/10.22331/q-2020-02-10-228.

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What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by this observation, we analyze the computational capability of SPTO cluster phases on all vertex-translative 2D Archimedean lattices. There are four subsystem symmetries here called ribbon, cone, fractal, and 1-form symmetries, and the former three are fundamentally in one-to-one correspondence with three classes of Clifford quantum cellular automata. We conclude that nine out of the eleven Archimedean lattices support universal cluster phases protected by one of the former three symmetries, while the remaining lattices possess 1-form symmetries and have a different capability related to error correction.

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6

Jacobsen, Brad, Karl Saunders, Leo Radzihovsky, and John Toner. "Two New Topologically Ordered Glass Phases of Smectics Confined in Anisotropic Random Media." Physical Review Letters 83, no. 7 (August 16, 1999): 1363–66. http://dx.doi.org/10.1103/physrevlett.83.1363.

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7

Saunders, Karl, Brad Jacobsen, Leo Radzihovsky, and John Toner. "Topologically ordered phases of smectics confined in anisotropic random media: smectic Bragg glasses." Journal of Physics: Condensed Matter 12, no. 8A (February 17, 2000): A215—A220. http://dx.doi.org/10.1088/0953-8984/12/8a/326.

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8

Oreg, Yuval, and Felix von Oppen. "Majorana Zero Modes in Networks of Cooper-Pair Boxes: Topologically Ordered States and Topological Quantum Computation." Annual Review of Condensed Matter Physics 11, no. 1 (March 10, 2020): 397–420. http://dx.doi.org/10.1146/annurev-conmatphys-031218-013618.

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Recent experimental progress introduced devices that can combine topological superconductivity with Coulomb-blockade effects. Experiments with these devices have already provided additional evidence for Majorana zero modes in proximity-coupled semiconductor wires. They also stimulated numerous ideas for how to exploit interactions between Majorana zero modes generated by Coulomb charging effects in networks of Majorana wires. Coulomb effects promise to become a powerful tool in the quest for a topological quantum computer as well as for driving topological superconductors into topologically ordered insulating states. Here, we present a focused review of these recent developments, including discussions of recent experiments, designs of topological qubits, Majorana-based implementations of universal quantum computation, and topological quantum error correction. Motivated by the analogy between a qubit and a spin-1/2 degree of freedom, we also review how coupling between Cooper-pair boxes leads to emergent topologically ordered insulating phases.

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9

Wen, Xiao-Gang. "A theory of 2+1D bosonic topological orders." National Science Review 3, no. 1 (November 24, 2015): 68–106. http://dx.doi.org/10.1093/nsr/nwv077.

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Abstract In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new ‘topological’ phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase—topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems).

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10

Wen, Xiao-Gang. "Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons." ISRN Condensed Matter Physics 2013 (March 27, 2013): 1–20. http://dx.doi.org/10.1155/2013/198710.

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We review the progress in the last 20–30 years, during which we discovered that there are many new phases of matter that are beyond the traditional Landau symmetry breaking theory. We discuss new “topological” phenomena, such as topological degeneracy that reveals the existence of those new phases—topologically ordered phases. Just like zero viscosity defines the superfluid order, the new “topological” phenomena define the topological order at macroscopic level. More recently, we found that at the microscopical level, topological order is due to long-range quantum entanglements. Long-range quantum entanglements lead to many amazing emergent phenomena, such as fractional charges and fractional statistics. Long-range quantum entanglements can even provide a unified origin of light and electrons; light is a fluctuation of long-range entanglements, and electrons are defects in long-range entanglements.

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11

Sims, Christopher. "Simulation of Higher-Dimensional Discrete Time Crystals on a Quantum Computer." Crystals 13, no. 8 (July 30, 2023): 1188. http://dx.doi.org/10.3390/cryst13081188.

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The study of topologically ordered states has given rise to a growing interest in symmetry-protected states in quantum matter. Recently, this theory has been extended to quantum many-body systems, which demonstrate ordered states at low temperatures. An example of this is the discrete time crystal (DTC), which has been demonstrated in a real quantum computer and in driven systems. These states are periodic in time and are protected from disorder to a certain extent. In general, DTCs can be classified into two phases: the stable many-body localization (MBL) state and the disordered thermal state. This work demonstrates the by generalizing DTCs to two dimensions, where there was an decrease in the thermal noise and an increase in the operating range of the MBL range in the presence of disorder.

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12

Safi, Taqiyyah S., Chung-Tao Chou, Justin T. Hou, Jiahao Han, and Luqiao Liu. "Spin-generation in magnetic Weyl semimetal Co₂MnGa across varying degree of chemical order." Applied Physics Letters 121, no. 9 (August 29, 2022): 092404. http://dx.doi.org/10.1063/5.0102039.

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Recently discovered magnetic Weyl semimetals (MWSM), with enhanced Berry curvature stemming from the topology of their electronic band structure, have gained much interest for spintronics applications. In this category, Co2MnGa, a room temperature ferromagnetic Heusler alloy, has garnered special interest as a promising material for topologically driven spintronic applications. However, until now, the structural-order dependence of spin current generation efficiency through the spin Hall effect has not been fully explored in this material. In this paper, we study the evolution of magnetic and transport properties of Co2MnGa thin films from the chemically disordered B2 to ordered L21 phase. We also report on the change in spin generation efficiency across these different phases, using heterostructures of Co2MnGa and ferrimagnet Co xTb1− x with perpendicular magnetic anisotropy. We measured large spin Hall angles in both the B2 and L21 phases, and within our experimental limits, we did not observe the advantage brought by the MWSM ordering in generating a strong spin Hall angle over the disordered phases, which suggests more complicated mechanisms over the intrinsic, Weyl-band structure-determined spin Hall effect in these material stacks.

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13

Kapfer, M., P. Roulleau, M. Santin, I. Farrer, D. A. Ritchie, and D. C. Glattli. "A Josephson relation for fractionally charged anyons." Science 363, no. 6429 (January 24, 2019): 846–49. http://dx.doi.org/10.1126/science.aau3539.

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Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the fractional quantum Hall effect (FQHE). Their dynamics are of utmost importance for topological quantum phases and possible decoherence-free quantum information approaches, but observing these dynamics experimentally is challenging. Here, we report on a dynamical property of anyons: the long-predicted Josephson relation fJ = e*V/h for charges e* = e/3 and e/5, where e is the charge of the electron and h is Planck’s constant. The relation manifests itself as marked signatures in the dependence of photo-assisted shot noise (PASN) on voltage V when irradiating contacts at microwaves frequency fJ. The validation of FQHE PASN models indicates a path toward realizing time-resolved anyon sources based on levitons.

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14

Ojovan, Michael I., and Robert F. Tournier. "On Structural Rearrangements Near the Glass Transition Temperature in Amorphous Silica." Materials 14, no. 18 (September 11, 2021): 5235. http://dx.doi.org/10.3390/ma14185235.

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The formation of clusters was analyzed in a topologically disordered network of bonds of amorphous silica (SiO2) based on the Angell model of broken bonds termed configurons. It was shown that a fractal-dimensional configuron phase was formed in the amorphous silica above the glass transition temperature Tg. The glass transition was described in terms of the concepts of configuron percolation theory (CPT) using the Kantor-Webman theorem, which states that the rigidity threshold of an elastic percolating network is identical to the percolation threshold. The account of configuron phase formation above Tg showed that (i) the glass transition was similar in nature to the second-order phase transformations within the Ehrenfest classification and that (ii) although being reversible, it occurred differently when heating through the glass–liquid transition to that when cooling down in the liquid phase via vitrification. In contrast to typical second-order transformations, such as the formation of ferromagnetic or superconducting phases when the more ordered phase is located below the transition threshold, the configuron phase was located above it.

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15

Kesselring, Markus S., Fernando Pastawski, Jens Eisert, and Benjamin J. Brown. "The boundaries and twist defects of the color code and their applications to topological quantum computation." Quantum 2 (October 19, 2018): 101. http://dx.doi.org/10.22331/q-2018-10-19-101.

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The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.

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16

Seepersad, Carolyn Conner, Janet K. Allen, David L. McDowell, and Farrokh Mistree. "Robust Design of Cellular Materials With Topological and Dimensional Imperfections." Journal of Mechanical Design 128, no. 6 (January 9, 2006): 1285–97. http://dx.doi.org/10.1115/1.2338575.

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A paradigm shift is underway in which the classical materials selection approach in engineering design is being replaced by the design of material structure and processing paths on a hierarchy of length scales for multifunctional performance requirements. In this paper, the focus is on designing mesoscopic material topology—the spatial arrangement of solid phases and voids on length scales larger than microstructures but smaller than the characteristic dimensions of an overall product. A robust topology design method is presented for designing materials on mesoscopic scales by topologically and parametrically tailoring them to achieve properties that are superior to those of standard or heuristic designs, customized for large-scale applications, and less sensitive to imperfections in the material. Imperfections are observed regularly in cellular material mesostructure and other classes of materials because of the stochastic influence of feasible processing paths. The robust topology design method allows us to consider these imperfections explicitly in a materials design process. As part of the method, guidelines are established for modeling dimensional and topological imperfections, such as tolerances and cracked cell walls, as deviations from intended material structure. Also, as part of the method, robust topology design problems are formulated as compromise Decision Support Problems, and local Taylor-series approximations and strategic experimentation techniques are established for evaluating the impact of dimensional and topological imperfections, respectively, on material properties. Key aspects of the approach are demonstrated by designing ordered, prismatic cellular materials with customized elastic properties that are robust to dimensional tolerances and topological imperfections.

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17

Li, Sai, Wei Tao, Ke Gao, Naveed Athir, Fanzhu Li, Yulong Chen, Jun Liu, Liqun Zhang, and Mesfin Tsige. "Phase manipulation of topologically engineered AB-type multi-block copolymers." RSC Advances 9, no. 72 (2019): 42029–42. http://dx.doi.org/10.1039/c9ra07734k.

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18

Bais, F. A., and J. K. Slingerland. "Condensate-induced transitions between topologically ordered phases." Physical Review B 79, no. 4 (January 26, 2009). http://dx.doi.org/10.1103/physrevb.79.045316.

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19

Eric Yang, S. R., Hoang Anh Le, In-Hwan Lee та Young Heon Kim. "Phase diagram and crossover phases of topologically ordered graphene zigzag nanoribbons: role of localization eﬀects". Journal of Physics: Condensed Matter, 28 березня 2024. http://dx.doi.org/10.1088/1361-648x/ad38f9.

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Abstract We computed the phase diagram of zigzag graphene nanoribbons as a function of on-site repulsion, doping, and disorder strength. The topologically ordered phase undergoes topological phase transitions into crossover phases, which are new disordered phases with non-universal topological entanglement entropy that exhibits signiﬁcant variance. We explored the nature of non-local correlations in both the topologically ordered and crossover phases. In the presence of localization eﬀects, strong on-site repulsion and/or doping weaken non-local correlations between the opposite zigzag edges of the topologically ordered phase. In one of the crossover phases, both e-/2 solitonic fractional charges and spin-charge separation were absent; however, charge-transfer correlations between the zigzag edges were possible. Another crossover phase contains solitonic e-/2 fractional charges but lacks charge transfer correlations. We also observed properties of non-topological, strongly disordered, and strongly repulsive phases. Each phase on the phase diagram exhibits a diﬀerent zigzag-edge structure. Additionally, we investigated the tunneling of solitonic fractional charges under an applied voltage between the zigzag edges of undoped topologically ordered zigzag ribbons, and found that it may lead to a zero-bias tunneling anomaly. Keywords: Topological order, Topological phase transition, Semions

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20

Watanabe, Haruki, Meng Cheng, and Yohei Fuji. "Ground state degeneracy on torus in a family of ZN toric code." Journal of Mathematical Physics 64, no. 5 (May 1, 2023). http://dx.doi.org/10.1063/5.0134010.

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Topologically ordered phases in 2 + 1 dimensions are generally characterized by three mutually related features: fractionalized (anyonic) excitations, topological entanglement entropy, and robust ground state degeneracy that does not require symmetry protection or spontaneous symmetry breaking. Such a degeneracy is known as topological degeneracy and can be usually seen under the periodic boundary condition regardless of the choice of the system sizes L1 and L2 in each direction. In this work, we introduce a family of extensions of the Kitaev toric code to N level spins (N ≥ 2). The model realizes topologically ordered phases or symmetry-protected topological phases depending on the parameters in the model. The most remarkable feature of topologically ordered phases is that the ground state may be unique, depending on L1 and L2, despite that the translation symmetry of the model remains unbroken. Nonetheless, the topological entanglement entropy takes the nontrivial value. We argue that this behavior originates from the nontrivial action of translations permuting anyon species.

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21

Hermele, Michael. "String flux mechanism for fractionalization in topologically ordered phases." Physical Review B 90, no. 18 (November 18, 2014). http://dx.doi.org/10.1103/physrevb.90.184418.

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22

Ebisu, Hiromi, and Bo Han. "Z2 topologically ordered phases on a simple hyperbolic lattice." Physical Review Research 4, no. 4 (November 14, 2022). http://dx.doi.org/10.1103/physrevresearch.4.043099.

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23

Christian, Jessica, David Green, Peter Huston, and David Penneys. "A lattice model for condensation in Levin-Wen systems." Journal of High Energy Physics 2023, no. 9 (September 11, 2023). http://dx.doi.org/10.1007/jhep09(2023)055.

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Abstract Levin-Wen string-net models provide a construction of (2+1)D topologically ordered phases of matter with anyonic localized excitations described by the Drinfeld center of a unitary fusion category. Anyon condensation is a mechanism for phase transitions between (2+1)D topologically ordered phases. We construct an extension of Levin-Wen models in which tuning a parameter implements anyon condensation. We also describe the classification of anyons in Levin-Wen models via representation theory of the tube algebra, and use a variant of the tube algebra to classify low-energy localized excitations in the condensed phase.

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24

Xiang, Liang, Wenjie Jiang, Zehang Bao, Zixuan Song, Shibo Xu, Ke Wang, Jiachen Chen, et al. "Long-lived topological time-crystalline order on a quantum processor." Nature Communications 15, no. 1 (October 17, 2024). http://dx.doi.org/10.1038/s41467-024-53077-9.

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AbstractTopologically ordered phases of matter elude Landau’s symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to periodically driven systems gives rise to exotic new phenomena that are forbidden in thermal equilibrium. Here, we report the observation of signatures of such a phenomenon—a prethermal topologically ordered time crystal—with programmable superconducting qubits arranged on a square lattice. By periodically driving the superconducting qubits with a surface code Hamiltonian, we observe discrete time-translation symmetry breaking dynamics that is only manifested in the subharmonic temporal response of nonlocal logical operators. We further connect the observed dynamics to the underlying topological order by measuring a nonzero topological entanglement entropy and studying its subsequent dynamics. Our results demonstrate the potential to explore exotic topologically ordered nonequilibrium phases of matter with noisy intermediate-scale quantum processors.

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25

Mesaros, Andrej, Yong Baek Kim, and Ying Ran. "Changing topology by topological defects in three-dimensional topologically ordered phases." Physical Review B 88, no. 3 (July 30, 2013). http://dx.doi.org/10.1103/physrevb.88.035141.

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26

Devakul, Trithep, Yizhi You, F. J. Burnell, and Shivaji Sondhi. "Fractal Symmetric Phases of Matter." SciPost Physics 6, no. 1 (January 16, 2019). http://dx.doi.org/10.21468/scipostphys.6.1.007.

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We study spin systems which exhibit symmetries that act on a fractal subset of sites, with fractal structures generated by linear cellular automata. In addition to the trivial symmetric paramagnet and spontaneously symmetry broken phases, we construct additional fractal symmetry protected topological (FSPT) phases via a decorated defect approach. Such phases have edges along which fractal symmetries are realized projectively, leading to a symmetry protected degeneracy along the edge. Isolated excitations above the ground state are symmetry protected fractons, which cannot be moved without breaking the symmetry. In 3D, our construction leads additionally to FSPT phases protected by higher form fractal symmetries and fracton topologically ordered phases enriched by the additional fractal symmetries.

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27

Hu, Peng-Sheng, Yi-Han Zhou, and Zhao Liu. "Floquet fractional Chern insulators and competing phases in twisted bilayer graphene." SciPost Physics 15, no. 4 (October 10, 2023). http://dx.doi.org/10.21468/scipostphys.15.4.148.

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We study the many-body physics in twisted bilayer graphene coupled to periodic driving of a circularly polarized light when electron-electron interactions are taken into account. In the limit of high driving frequency \OmegaΩ, we use Floquet theory to formulate the system by an effective static Hamiltonian truncated to the order of \Omega^{-2}Ω−2, which consists of a single-electron part and the screened Coulomb interaction. We numerically simulate this effective Hamiltonian by extensive exact diagonalization in the parameter space spanned by the twist angle and the driving strength. Remarkably, in a wide region of the parameter space, we identify Floquet fractional Chern insulator states in the partially filled Floquet valence bands. We characterize these topologically ordered states by ground-state degeneracy, spectral flow, and entanglement spectrum. In regions of the parameter space where fractional Chern insulator states are absent, we find topologically trivial charge density waves and band-dispersion-induced Fermi liquids which strongly compete with fractional Chern insulator states.

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28

Sagi, Eran, Ady Stern, and David F. Mross. "Composite Weyl semimetal as a parent state for three-dimensional topologically ordered phases." Physical Review B 98, no. 20 (November 15, 2018). http://dx.doi.org/10.1103/physrevb.98.201111.

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29

Ebisu, Hiromi, Rohit R. Kalloor, Alexei M. Tsvelik, and Yuval Oreg. "Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands." Physical Review B 102, no. 16 (October 8, 2020). http://dx.doi.org/10.1103/physrevb.102.165112.

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30

Cabo-Bizet, Alejandro. "Quantum phases of 4d SU(N) $$ \mathcal{N} $$ = 4 SYM." Journal of High Energy Physics 2022, no. 10 (October 7, 2022). http://dx.doi.org/10.1007/jhep10(2022)052.

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Abstract It is argued that 4d SU(N) $$ \mathcal{N} $$ N = 4 SYM has an accumulation line of zero-temperature topologically ordered phases. Each of these phases corresponds to N bound states charged under electromagnetic $$ {\mathbb{Z}}_N^{(1)} $$ ℤ N 1 one-form symmetries. Each of the N bound states is made of two Dyonic flux components each of them extended over a two dimensional surface. They are localized at the fixed loci of a rotational action, and are argued to correspond to conformal blocks (or primaries) of an SU(N)1 WZNW model on a two-torus.

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31

Gao, He, Guoqiang Xu, Xue Zhou, Shuihua Yang, Zhongqing Su, and Cheng-Wei Qiu. "Topological Anderson phases in heat transport." Reports on Progress in Physics, August 9, 2024. http://dx.doi.org/10.1088/1361-6633/ad6d88.

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Abstract Topological Anderson phases (TAPs) offer intriguing transitions from ordered to disordered systems in photonics and acoustics. However, achieving these transitions often involves cumbersome structural modifications to introduce disorders in parameters, leading to limitations in flexible tuning of topological properties and real-space control of TAPs. Here, we exploit disordered convective perturbations in a fixed heat transport system. Continuously tunable disorder-topology interactions are enabled in thermal dissipation through irregular convective lattices. In the presence of a weak convective disorder, the trivial diffusive system undergos topological Anderson phase transition, characterized by the emergence of topologically protected corner modes. Further increasing the strength of convective perturbations, a second phase transition occurs converting from TAP to Anderson phase. Our work elucidates the pivotal role of disorders in topological heat transport and provides a novel recipe for manipulating thermal behaviors in diverse topological platforms.

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32

Zhang, Qi, Wen-Tao Xu, Zi-Qi Wang, and Guang-Ming Zhang. "Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions." Communications Physics 3, no. 1 (November 13, 2020). http://dx.doi.org/10.1038/s42005-020-00479-y.

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AbstractNegative signs in many-body wavefunctions play an important role in quantum mechanics because interference relies on cancellation between amplitudes of opposite signs. The ground-state wavefunction of double semion model contains negative signs that cannot be removed by any local transformation. Here we study the quantum effects of these intrinsic negative signs. By proposing a generic double semion wavefunction in tensor network representation, we show that its norm can be mapped to the partition function of a triangular lattice Ashkin-Teller model with imaginary interactions. We use numerical tensor-network methods to solve this non-Hermitian model with parity-time symmetry and determine a global phase diagram. In particular, we find a dense loop phase described by non-unitary conformal field theory and a parity-time-symmetry breaking phase characterized by the zeros of the partition function. Therefore, our work establishes a connection between the intrinsic signs in the topological wavefunction and non-unitary phases in the parity-time-symmetric non-Hermitian statistical model.

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33

Cong, Iris, Nishad Maskara, Minh C. Tran, Hannes Pichler, Giulia Semeghini, Susanne F. Yelin, Soonwon Choi, and Mikhail D. Lukin. "Enhancing detection of topological order by local error correction." Nature Communications 15, no. 1 (February 20, 2024). http://dx.doi.org/10.1038/s41467-024-45584-6.

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AbstractThe exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations. We subsequently apply it to an experimental realization, providing new insights into a quantum spin liquid created on a Rydberg-atom simulator. Finally, we extend LED to generic topological phases, including those with non-abelian order.

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34

Cho, Gil Young, Jeffrey C. Y. Teo, and Shinsei Ryu. "Conflicting symmetries in topologically ordered surface states of three-dimensional bosonic symmetry protected topological phases." Physical Review B 89, no. 23 (June 3, 2014). http://dx.doi.org/10.1103/physrevb.89.235103.

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35

Wiedmann, Raymond, Lea Lenke, Matthias R. Walther, Matthias Mühlhauser, and Kai Phillip Schmidt. "Quantum critical phase transition between two topologically ordered phases in the Ising toric code bilayer." Physical Review B 102, no. 21 (December 17, 2020). http://dx.doi.org/10.1103/physrevb.102.214422.

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36

Wang, Ke, and T. A. Sedrakyan. "Universal finite-size scaling around tricriticality between topologically ordered, symmetry-protected topological, and trivial phases." Physical Review B 101, no. 3 (January 10, 2020). http://dx.doi.org/10.1103/physrevb.101.035410.

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37

Huang, Hsin-Yuan, Richard Kueng, Giacomo Torlai, Victor V. Albert, and John Preskill. "Provably efficient machine learning for quantum many-body problems." Science 377, no. 6613 (September 23, 2022). http://dx.doi.org/10.1126/science.abk3333.

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Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

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38

Cassella, G., P. d’Ornellas, T. Hodson, W. M. H. Natori, and J. Knolle. "An exact chiral amorphous spin liquid." Nature Communications 14, no. 1 (October 20, 2023). http://dx.doi.org/10.1038/s41467-023-42105-9.

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AbstractTopological insulator phases of non-interacting particles have been generalized from periodic crystals to amorphous lattices, which raises the question whether topologically ordered quantum many-body phases may similarly exist in amorphous systems? Here we construct a soluble chiral amorphous quantum spin liquid by extending the Kitaev honeycomb model to random lattices with fixed coordination number three. The model retains its exact solubility but the presence of plaquettes with an odd number of sides leads to a spontaneous breaking of time reversal symmetry. We unearth a rich phase diagram displaying Abelian as well as a non-Abelian quantum spin liquid phases with a remarkably simple ground state flux pattern. Furthermore, we show that the system undergoes a finite-temperature phase transition to a conducting thermal metal state and discuss possible experimental realisations.

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39

Ebisu, Hiromi, and Bo Han. "Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs." SciPost Physics 14, no. 5 (May 11, 2023). http://dx.doi.org/10.21468/scipostphys.14.5.106.

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We study unusual gapped topological phases where they admit \mathbb{Z}_NℤN fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by \bigl[N\times \prod_{i}\text{gcd}(N, p_i)\bigr]^2[N×∏igcd(N,pi)]2, where p_ipi’s are invariant factors of the Laplacian that are greater than one and gcd stands for the greatest common divisor. We also discuss braiding statistics between quasiparticle excitations.

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40

Chen, Chuan, Peng Rao, and Inti Sodemann. "Berry phases of vison transport in Z2 topologically ordered states from exact fermion-flux lattice dualities." Physical Review Research 4, no. 4 (October 4, 2022). http://dx.doi.org/10.1103/physrevresearch.4.043003.

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41

Wu, Han, Lei Chen, Paul Malinowski, Bo Gyu Jang, Qinwen Deng, Kirsty Scott, Jianwei Huang, et al. "Reversible non-volatile electronic switching in a near-room-temperature van der Waals ferromagnet." Nature Communications 15, no. 1 (March 28, 2024). http://dx.doi.org/10.1038/s41467-024-46862-z.

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AbstractNon-volatile phase-change memory devices utilize local heating to toggle between crystalline and amorphous states with distinct electrical properties. Expanding on this kind of switching to two topologically distinct phases requires controlled non-volatile switching between two crystalline phases with distinct symmetries. Here, we report the observation of reversible and non-volatile switching between two stable and closely related crystal structures, with remarkably distinct electronic structures, in the near-room-temperature van der Waals ferromagnet Fe5−δGeTe2. We show that the switching is enabled by the ordering and disordering of Fe site vacancies that results in distinct crystalline symmetries of the two phases, which can be controlled by a thermal annealing and quenching method. The two phases are distinguished by the presence of topological nodal lines due to the preserved global inversion symmetry in the site-disordered phase, flat bands resulting from quantum destructive interference on a bipartite lattice, and broken inversion symmetry in the site-ordered phase.

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42

Bauer, Andreas, Jens Eisert, and Carolin Wille. "A unified diagrammatic approach to topological fixed point models." SciPost Physics Core 5, no. 3 (July 25, 2022). http://dx.doi.org/10.21468/scipostphyscore.5.3.038.

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We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories, but is formalised and unified in terms of tensor networks. In contrast to existing tensor network ansatzes for the study of ground states of topologically ordered phases, the tensor networks in our formalism represent discrete path integrals in Euclidean space-time. This language is more directly related to the Hamiltonian defining the model than other approaches, via a Trotterization of the respective imaginary time evolution. We introduce our formalism by simple examples, and demonstrate its full power by expressing known families of models in 2+1 dimensions in their most general form, namely string-net models and Kitaev quantum doubles based on weak Hopf algebras. To elucidate the versatility of our formalism, we also show how fermionic phases of matter can be described and provide a framework for topological fixed point models in 3+1 dimensions.

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43

Mukherjee, Anirban, and Siddhartha Lal. "Superconductivity from repulsion in the doped 2D electronic Hubbard model: an entanglement perspective." Journal of Physics: Condensed Matter, April 12, 2022. http://dx.doi.org/10.1088/1361-648x/ac66b3.

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Abstract We employ the momentum space entanglement renormalization group (MERG) scheme developed in Refs.([1,2]) for the study of various insulating, superconducting and normal phases of the doped and the undoped 2D Hubbard model on a square lattice found recently by us ([3,4]). At each MERG step, disentanglement of particular degrees of freedom, transforms the tensor network representation of the many-particle states. The MERG reveals distinct holographic entanglement features for the normal metallic, topologically ordered insulating quantum liquid and Ne\'{e}l antiferromagnetic symmetry-broken ground states of the 2D Hubbard model at half-filling, clarifying the essence of the entanglement phase transitions that separates the three phases. An MERG analysis of the quantum critical point of the hole-doped 2D Hubbard model reveals the evolution of the many-particle entanglement of the quantum liquid ground state with hole-doping, as well as how the collapse of Mottness is concomitant with the emergence of d-wave superconductivity.

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44

Charpentier, Sophie, Luca Galletti, Gunta Kunakova, Riccardo Arpaia, Yuxin Song, Reza Baghdadi, Shu Min Wang, et al. "Induced unconventional superconductivity on the surface states of Bi2Te3 topological insulator." Nature Communications 8, no. 1 (December 2017). http://dx.doi.org/10.1038/s41467-017-02069-z.

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Abstract Topological superconductivity is central to a variety of novel phenomena involving the interplay between topologically ordered phases and broken-symmetry states. The key ingredient is an unconventional order parameter, with an orbital component containing a chiral p x + ip y wave term. Here we present phase-sensitive measurements, based on the quantum interference in nanoscale Josephson junctions, realized by using Bi2Te3 topological insulator. We demonstrate that the induced superconductivity is unconventional and consistent with a sign-changing order parameter, such as a chiral p x + ip y component. The magnetic field pattern of the junctions shows a dip at zero externally applied magnetic field, which is an incontrovertible signature of the simultaneous existence of 0 and π coupling within the junction, inherent to a non trivial order parameter phase. The nano-textured morphology of the Bi2Te3 flakes, and the dramatic role played by thermal strain are the surprising key factors for the display of an unconventional induced order parameter.

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45

Wilhelm, Patrick, Thomas Lang, Mathias Scheurer, and Andreas Läuchli. "Non-coplanar magnetism, topological density wave order and emergent symmetry at half-integer filling of moiré Chern bands." SciPost Physics 14, no. 3 (March 20, 2023). http://dx.doi.org/10.21468/scipostphys.14.3.040.

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Twisted double- and mono-bilayer graphene are graphene-based moiré materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moiré scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, “rotating” the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number |C|=1, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems.

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46

Crépel, Valentin, Nicolas Regnault, and Raquel Queiroz. "Chiral limit and origin of topological flat bands in twisted transition metal dichalcogenide homobilayers." Communications Physics 7, no. 1 (May 7, 2024). http://dx.doi.org/10.1038/s42005-024-01641-6.

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AbstractThe observation of zero field fractional quantum Hall analogs in twisted transition metal dichalcogenides (TMDs) asks for a deeper understanding of what mechanisms lead to topological flat bands in two-dimensional heterostructures, and what makes TMDs an excellent platform for topologically ordered phases, surpassing twisted bilayer graphene. To this aim, we explore the chiral limits of massive Dirac theories applicable to C3-symmetric moiré materials, and show their relevance for both bilayer graphene and TMD homobilayers. In the latter, the Berry curvature of valence bands leads to relativistic corrections of the moiré potential that promote band flattening, and permit a limit with exactly flat bands with nonzero Chern number. The relativistic corrections enter as a layer-orbit coupling, analogous to spin-orbit coupling for relativistic Dirac fermions, which we show is non-negligible on the moiré scale. The Berry curvature of the TMD monolayers therefore plays an essential role in the flattening of moiré Chern bands in these heterostructures.

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47

Moradi, Heidar, Seyed Faroogh Moosavian, and Apoorv Tiwari. "Topological holography: Towards a unification of Landau and beyond-Landau physics." SciPost Physics Core 6, no. 4 (October 16, 2023). http://dx.doi.org/10.21468/scipostphyscore.6.4.066.

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We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with a global symmetry in one lower dimension. The global symmetry naturally serves as an input for the topological order. In particular, we holographically construct a String Operator Algebra (SOA) which is the building block of symmetric quantum systems with a given symmetry G in one lower dimension. This exposes a vast web of dualities which act on the space of G-symmetric quantum systems. The SOA facilitates the classification of gapped phases as well as their corresponding order parameters and fundamental excitations, while dualities help to navigate and predict various corners of phase diagrams and analytically compute universality classes of phase transitions. A novelty of the approach is that it treats conventional Landau and unconventional topological phase transitions on an equal footing, thereby providing a holographic unification of these seemingly-disparate domains of understanding. We uncover a new feature of gapped phases and their multi-critical points, which we dub fusion structure, that encodes information about which phases and transitions can be dual to each other. Furthermore, we discover that self-dual systems typically posses emergent non-invertible, i.e., beyond group-like symmetries. We apply these ideas to 1+1d1+1d quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in 2+1d2+1d. We predict the phase diagrams of various concrete spin models, and analytically compute the full conformal spectra of non-trivial quantum phase transitions, which we then verify numerically.

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48

Sati, Hisham, and Urs Schreiber. "Anyonic topological order in twisted equivariant differential (TED) K-theory." Reviews in Mathematical Physics, December 6, 2022. http://dx.doi.org/10.1142/s0129055x23500010.

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While the classification of noninteracting crystalline topological insulator phases by equivariant K-theory has become widely accepted, its generalization to anyonic interacting phases — hence to phases with topologically ordered ground states supporting topological braid quantum gates — has remained wide open. On the contrary, the success of K-theory with classifying noninteracting phases seems to have tacitly been perceived as precluding a K-theoretic classification of interacting topological order; and instead a mix of other proposals has been explored. However, only K-theory connects closely to the actual physics of valence electrons; and self-consistency demands that any other proposal must connect to K-theory. Here, we provide a detailed argument for the classification of symmetry protected/enhanced [Formula: see text]-anyonic topological order, specifically in interacting 2d semi-metals, by the twisted equivariant differential (TED) K-theory of configuration spaces of points in the complement of nodal points inside the crystal’s Brillouin torus orbi-orientifold. We argue, in particular, that: (1) topological 2d semi-metal phases modulo global mass terms are classified by the flat differential twisted equivariant K-theory of the complement of the nodal points; (2) [Formula: see text]-electron interacting phases are classified by the K-theory of configuration spaces of [Formula: see text] points in the Brillouin torus; (3) the somewhat neglected twisting of equivariant K-theory by “inner local systems” reflects the effective “fictitious” gauge interaction of Chen, Wilczeck, Witten and Halperin (1989), which turns fermions into anyonic quanta; (4) the induced [Formula: see text]-anyonic topological order is reflected in the twisted Chern classes of the interacting valence bundle over configuration space, constituting the hypergeometric integral construction of monodromy braid representations. A tight dictionary relates these arguments to those for classifying defect brane charges in string theory [H. Sati and U. Schreiber, Anyonic defect branes in TED-K-theory, arXiv:2203.11838], which we expect to be the images of momentum-space [Formula: see text]-anyons under a nonperturbative version of the AdS/CMT correspondence.

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49

Huston, Peter, Fiona Burnell, Corey Jones, and David Penneys. "Composing topological domain walls and anyon mobility." SciPost Physics 15, no. 3 (September 4, 2023). http://dx.doi.org/10.21468/scipostphys.15.3.076.

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Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a framework for decomposing stacks of multiple domain walls into superselection sectors — i.e., into fundamental domain wall types that cannot be mixed by any local operators. Such a decomposition can be understood using an alternate framework in the case that the topological order is anomaly-free, in the sense that it can be realized by a commuting projector lattice model. By placing these Witt equivalences in the context of a 3-category of potentially anomalous (2+1)D topological orders, we develop a framework for computing the decomposition of parallel topological domain walls into indecomposable superselection sectors, extending the previous understanding to topological orders with non-trivial anomaly. We characterize the superselection sectors in terms of domain wall particle mobility, which we formalize in terms of tunnelling operators. The mathematical model for the 3-category of topological orders is the 3-category of fusion categories enriched over a fixed unitary modular tensor category.

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50

Barkeshli, Maissam, and Meng Cheng. "Relative anomalies in (2+1)D symmetry enriched topological states." SciPost Physics 8, no. 2 (February 18, 2020). http://dx.doi.org/10.21468/scipostphys.8.2.028.

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Certain patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. An important question is to determine how to compute this anomaly, which means determining which SPT hosts a given symmetry-enriched topological order at its surface. While special cases are known, a general method to compute the anomaly has so far been lacking. In this paper we propose a general method to compute relative anomalies between different symmetry fractionalization classes of a given (2+1)D topological order. This method applies to all types of symmetry actions, including anyon-permuting symmetries and general space-time reflection symmetries. We demonstrate compatibility of the relative anomaly formula with previous results for diagnosing anomalies for \mathbb{Z}_2^{T}ℤ2T space-time reflection symmetry (e.g. where time-reversal squares to the identity) and mixed anomalies for U(1) \times \mathbb{Z}_2^{T}U(1)×ℤ2T and U(1) \rtimes \mathbb{Z}_2^{T}U(1)⋊ℤ2T symmetries. We also study a number of additional examples, including cases where space-time reflection symmetries are intertwined in non-trivial ways with unitary symmetries, such as \mathbb{Z}_4^{T}ℤ4T and mixed anomalies for \mathbb{Z}_2 \times \mathbb{Z}_2^{T}ℤ2×ℤ2T symmetry, and unitary \mathbb{Z}_2 \times \mathbb{Z}_2ℤ2×ℤ2 symmetry with non-trivial anyon permutations.

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