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Journal articles on the topic 'Topological frustration'

Author: Grafiati

Published: 23 November 2024

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1

De Filippi, Federico Raffaele, Antonio Francesco Mello, Daniel Sacco Shaikh, Maura Sassetti, Niccolò Traverso Ziani, and Michele Grossi. "Few-Body Precursors of Topological Frustration." Symmetry 16, no. 8 (August 20, 2024): 1078. http://dx.doi.org/10.3390/sym16081078.

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Spin 1/2 quantum spin chains represent the prototypical model for coupled two-level systems. Consequently, they offer a fertile playground for both fundamental and technological applications ranging from the theory of thermalization to quantum computation. Recently, it has been shown that interesting phenomena are associated to the boundary conditions imposed on the quantum spin chains via the so-called topological frustration. In this work, we analyze the effects of such frustration on a few-spin system, with a particular focus on the strong even–odd effects induced in the ground-state energy. We then implement a topologically frustrated quantum spin chain on a quantum computer to show that our predictions are visible on current quantum hardware platforms.

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2

Villain-Guillot, S., R. Dandoloff, A. Saxena, and A. R. Bishop. "Topological solitons and geometrical frustration." Physical Review B 52, no. 9 (September 1, 1995): 6712–22. http://dx.doi.org/10.1103/physrevb.52.6712.

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3

Hayami, Satoru, and Yukitoshi Motome. "Topological spin crystals by itinerant frustration." Journal of Physics: Condensed Matter 33, no. 44 (August 19, 2021): 443001. http://dx.doi.org/10.1088/1361-648x/ac1a30.

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4

McLenaghan, I. R., and D. Sherrington. "A model for variable topological frustration." Journal of Physics C: Solid State Physics 20, no. 11 (April 20, 1987): 1701–11. http://dx.doi.org/10.1088/0022-3719/20/11/013.

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5

Long, M. W. "Topological frustration can lead to superconductivity." Journal of Physics: Condensed Matter 3, no. 33 (August 19, 1991): 6387–402. http://dx.doi.org/10.1088/0953-8984/3/33/016.

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6

Yao, Zhenwei. "Topological vacancies in spherical crystals." Soft Matter 13, no. 35 (2017): 5905–10. http://dx.doi.org/10.1039/c7sm01599b.

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Understanding geometric frustration of ordered phases in two-dimensional condensed matter on curved surfaces is closely related to a host of scientific problems in condensed matter physics and materials science.

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7

Mishra, Shantanu, Doreen Beyer, Kristjan Eimre, Shawulienu Kezilebieke, Reinhard Berger, Oliver Gröning, Carlo A. Pignedoli, et al. "Topological frustration induces unconventional magnetism in a nanographene." Nature Nanotechnology 15, no. 1 (December 9, 2019): 22–28. http://dx.doi.org/10.1038/s41565-019-0577-9.

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8

Straley, Joseph P. "Effect of topological frustration on the freezing temperature." Physical Review B 34, no. 1 (July 1, 1986): 405–9. http://dx.doi.org/10.1103/physrevb.34.405.

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9

Gosavi, Shachi, Leslie L. Chavez, Patricia A. Jennings, and José N. Onuchic. "Topological Frustration and the Folding of Interleukin-1β." Journal of Molecular Biology 357, no. 3 (March 2006): 986–96. http://dx.doi.org/10.1016/j.jmb.2005.11.074.

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10

Imaoka, Hitoshi, and Yasuhiro Kasai. "Topological Expression for Frustration in Antiferromagnetic Triangular Ising Model." Journal of the Physical Society of Japan 65, no. 3 (March 15, 1996): 725–31. http://dx.doi.org/10.1143/jpsj.65.725.

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11

GAFVELIN, G. "Topological ?frustration? in multispanning E. coli inner membrane proteins." Cell 77, no. 3 (May 1994): 401–12. http://dx.doi.org/10.1016/0092-8674(94)90155-4.

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12

Morais Smith, C., T. Drose, R. Besseling, and P. Kes. "Plastic depinning in artificial vortex channels: Competition between bulk and boundary nucleation." Journal de Physique IV 12, no. 9 (November 2002): 179. http://dx.doi.org/10.1051/jp4:20020389.

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We study the depinning transition of a driven chain-like system in the presence of frustration and quenched disorder. The analysis is motivated by recent transport experiments on artificial vortex-flow channels in superconducting thin films. We start with a London description of the vortices and then map the problem onto a generalized Frenkel-Kontorova model and its continuous equivalent, the sine-Gordon model. In the absence of disorder, frustration reduces the depinning threshold in the commensurate phase, which nearly vanishes in the incommensurate regime. Depinning of the driven frustrated chain occurs via unstable configurations that are localized at the boundaries of the sample and evolve into topological defects which move freely through the entire sample. In the presence of disorder, topological defects can also be generated in the bulk. Further, disorder leads to pinning of topological defects. We find that weak disorder effectively reduces the depinning threshold in the commensurate phase, but increases the threshold in the incommensurate phase.

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13

Norbiato, Federico, Flavio Seno, Antonio Trovato, and Marco Baiesi. "Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures." International Journal of Molecular Sciences 21, no. 1 (December 27, 2019): 213. http://dx.doi.org/10.3390/ijms21010213.

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Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.

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14

Mishra, Shantanu, Doreen Beyer, Kristjan Eimre, Shawulienu Kezilebieke, Reinhard Berger, Oliver Gröning, Carlo A. Pignedoli, et al. "Publisher Correction: Topological frustration induces unconventional magnetism in a nanographene." Nature Nanotechnology 15, no. 1 (December 17, 2019): 81. http://dx.doi.org/10.1038/s41565-019-0621-9.

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15

Hafner, J., and M. Krajči´. "Localized modes and topological frustration in rational approximants to quasicrystals." Physical Review B 47, no. 2 (January 1, 1993): 1084–87. http://dx.doi.org/10.1103/physrevb.47.1084.

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16

dos Santos, Roberto J. V., and M. L. Lyra. "Temperature-dependent “frustration”: A thermodynamic rather than a topological effect." Physica A: Statistical Mechanics and its Applications 182, no. 1-2 (March 1992): 133–44. http://dx.doi.org/10.1016/0378-4371(92)90234-h.

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17

Kurumaji, Takashi, Taro Nakajima, Max Hirschberger, Akiko Kikkawa, Yuichi Yamasaki, Hajime Sagayama, Hironori Nakao, Yasujiro Taguchi, Taka-hisa Arima, and Yoshinori Tokura. "Skyrmion lattice with a giant topological Hall effect in a frustrated triangular-lattice magnet." Science 365, no. 6456 (August 8, 2019): 914–18. http://dx.doi.org/10.1126/science.aau0968.

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Geometrically frustrated magnets can host complex spin textures, leading to unconventional electromagnetic responses. Magnetic frustration may also promote topologically nontrivial spin states such as magnetic skyrmions. Experimentally, however, skyrmions have largely been observed in noncentrosymmetric lattice structures or interfacial symmetry-breaking heterostructures. Here, we report the emergence of a Bloch-type skyrmion state in the frustrated centrosymmetric triangular-lattice magnet Gd2PdSi3. We observed a giant topological Hall response, indicating a field-induced skyrmion phase, which is further corroborated by the observation of in-plane spin modulation probed by resonant x-ray scattering. Our results may lead to further discoveries of emergent electrodynamics in magnetically frustrated centrosymmetric materials.

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18

Zhang, Zhao. "Bicolor loop models and their long range entanglement." Quantum 8 (February 29, 2024): 1268. http://dx.doi.org/10.22331/q-2024-02-29-1268.

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Quantum loop models are well studied objects in the context of lattice gauge theories and topological quantum computing. They usually carry long range entanglement that is captured by the topological entanglement entropy. I consider generalization of the toric code model to bicolor loop models and show that the long range entanglement can be reflected in three different ways: a topologically invariant constant, a sub-leading logarithmic correction to the area law, or a modified bond dimension for the area-law term. The Hamiltonians are not exactly solvable for the whole spectra, but admit a tower of area-law exact excited states corresponding to the frustration free superposition of loop configurations with arbitrary pairs of localized vertex defects. The continuity of color along loops imposes kinetic constraints on the model and results in Hilbert space fragmentation, unless plaquette operators involving two neighboring faces are introduced to the Hamiltonian.

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19

Vyazovskaya, Alexandra Yu, Evgeniy K. Petrov, Yury M. Koroteev, Mihovil Bosnar, Igor V. Silkin, Evgueni V. Chulkov, and Mikhail M. Otrokov. "Superlattices of Gadolinium and Bismuth Based Thallium Dichalcogenides as Potential Magnetic Topological Insulators." Nanomaterials 13, no. 1 (December 22, 2022): 38. http://dx.doi.org/10.3390/nano13010038.

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Using relativistic spin-polarized density functional theory calculations we investigate magnetism, electronic structure and topology of the ternary thallium gadolinium dichalcogenides TlGdZ2 (Z= Se and Te) as well as superlattices on their basis. We find TlGdZ2 to have an antiferromagnetic exchange coupling both within and between the Gd layers, which leads to frustration and a complex magnetic structure. The electronic structure calculations reveal both TlGdSe2 and TlGdTe2 to be topologically trivial semiconductors. However, as we show further, a three-dimensional (3D) magnetic topological insulator (TI) state can potentially be achieved by constructing superlattices of the TlGdZ2/(TlBiZ2)n type, in which structural units of TlGdZ2 are alternated with those of the isomorphic TlBiZ2 compounds, known to be non-magnetic 3D TIs. Our results suggest a new approach for achieving 3D magnetic TI phases in such superlattices which is applicable to a large family of thallium rare-earth dichalcogenides and is expected to yield a fertile and tunable playground for exotic topological physics.

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20

Karube, Kosuke, Jonathan S. White, Daisuke Morikawa, Charles D. Dewhurst, Robert Cubitt, Akiko Kikkawa, Xiuzhen Yu, et al. "Disordered skyrmion phase stabilized by magnetic frustration in a chiral magnet." Science Advances 4, no. 9 (September 2018): eaar7043. http://dx.doi.org/10.1126/sciadv.aar7043.

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Magnetic skyrmions are vortex-like topological spin textures often observed to form a triangular-lattice skyrmion crystal in structurally chiral magnets with the Dzyaloshinskii-Moriya interaction. Recently, β-Mn structure–type Co-Zn-Mn alloys were identified as a new class of chiral magnet to host such skyrmion crystal phases, while β-Mn itself is known as hosting an elemental geometrically frustrated spin liquid. We report the intermediate composition system Co7Zn7Mn6 to be a unique host of two disconnected, thermal-equilibrium topological skyrmion phases; one is a conventional skyrmion crystal phase stabilized by thermal fluctuations and restricted to exist just below the magnetic transition temperature Tc, and the other is a novel three-dimensionally disordered skyrmion phase that is stable well below Tc. The stability of this new disordered skyrmion phase is due to a cooperative interplay between the chiral magnetism with the Dzyaloshinskii-Moriya interaction and the frustrated magnetism inherent to β-Mn.

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21

Gao, Meng, Ping Li, Zhengding Su, and Yongqi Huang. "Topological frustration leading to backtracking in a coupled folding–binding process." Physical Chemistry Chemical Physics 24, no. 4 (2022): 2630–37. http://dx.doi.org/10.1039/d1cp04927e.

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22

Knezevic, M., and J. Vannimenus. "Topological frustration and quasicompact phase in a model of interacting polymers." Journal of Physics A: Mathematical and General 20, no. 15 (October 21, 1987): L969—L973. http://dx.doi.org/10.1088/0305-4470/20/15/007.

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23

Norcross, Todd S., and Todd O. Yeates. "A Framework for Describing Topological Frustration in Models of Protein Folding." Journal of Molecular Biology 362, no. 3 (September 2006): 605–21. http://dx.doi.org/10.1016/j.jmb.2006.07.054.

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24

Hills, Ronald D., and Charles L. Brooks. "Subdomain Competition, Cooperativity, and Topological Frustration in the Folding of CheY." Journal of Molecular Biology 382, no. 2 (October 2008): 485–95. http://dx.doi.org/10.1016/j.jmb.2008.07.007.

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25

Nencka‐Ficek, H. "Topological closure as the necessary condition for frustration or phase transitions." Journal of Mathematical Physics 26, no. 7 (July 1985): 1597–99. http://dx.doi.org/10.1063/1.526924.

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26

Copenhagen, Katherine, Gema Malet-Engra, Weimiao Yu, Giorgio Scita, Nir Gov, and Ajay Gopinathan. "Frustration-induced phases in migrating cell clusters." Science Advances 4, no. 9 (September 2018): eaar8483. http://dx.doi.org/10.1126/sciadv.aar8483.

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Certain malignant cancer cells form clusters in a chemoattractant gradient, which can spontaneously show three different phases of motion: translational, rotational, and random. Guided by our experiments on the motion of two-dimensional clusters in vitro, we developed an agent-based model in which the cells form a cohesive cluster due to attractive and alignment interactions. We find that when cells at the cluster rim are more motile, all three phases of motion coexist, in agreement with our observations. Using the model, we show that the transitions between different phases are driven by competition between an ordered rim and a disordered core accompanied by the creation and annihilation of topological defects in the velocity field. The model makes specific predictions, which we verify with our experimental data. Our results suggest that heterogeneous behavior of individuals, based on local environment, can lead to novel, experimentally observed phases of collective motion.

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27

Fang, Fang, Richard Clawson, and Klee Irwin. "The Curled Up Dimension in Quasicrystals." Crystals 11, no. 10 (October 14, 2021): 1238. http://dx.doi.org/10.3390/cryst11101238.

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Most quasicrystals can be generated by the cut-and-project method from higher dimensional parent lattices. In doing so they lose the periodic order their parent lattice possess, replaced with aperiodic order, due to the irrationality of the projection. However, perfect periodic order is discovered in the perpendicular space when gluing the cut window boundaries together to form a curved loop. In the case of a 1D quasicrystal projected from a 2D lattice, the irrationally sloped cut region is bounded by two parallel lines. When it is extrinsically curved into a cylinder, a line defect is found on the cylinder. Resolving this geometrical frustration removes the line defect to preserve helical paths on the cylinder. The degree of frustration is determined by the thickness of the cut window or the selected pitch of the helical paths. The frustration can be resolved by applying a shear strain to the cut-region before curving into a cylinder. This demonstrates that resolving the geometrical frustration of a topological change to a cut window can lead to preserved periodic order.

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28

Ostoréro, J., A. Mauger, M. Guillot, A. Derory, M. Escorne, and A. Marchand. "Influence of topological frustration on the magnetic properties of the normal oxyspinelCdFe2O4." Physical Review B 40, no. 1 (July 1, 1989): 391–95. http://dx.doi.org/10.1103/physrevb.40.391.

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29

Lee, Ji Young, Li Duan, Tyler M. Iverson, and Ruxandra I. Dima. "Exploring the Role of Topological Frustration in Actin Refolding with Molecular Simulations." Journal of Physical Chemistry B 116, no. 5 (January 30, 2012): 1677–86. http://dx.doi.org/10.1021/jp209340y.

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30

Shenoy, Subodh R. "Topological disorder hierarchically trapped at frustration sites: Physical picture for a glass." Physical Review B 35, no. 16 (June 1, 1987): 8652–56. http://dx.doi.org/10.1103/physrevb.35.8652.

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31

Araki, Takeaki, Marco Buscaglia, Tommaso Bellini, and Hajime Tanaka. "Memory and topological frustration in nematic liquid crystals confined in porous materials." Nature Materials 10, no. 4 (March 20, 2011): 303–9. http://dx.doi.org/10.1038/nmat2982.

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32

Hall, Douglas M., and Gregory M. Grason. "How geometric frustration shapes twisted fibres, inside and out: competing morphologies of chiral filament assembly." Interface Focus 7, no. 4 (June 16, 2017): 20160140. http://dx.doi.org/10.1098/rsfs.2016.0140.

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Chirality frustrates and shapes the assembly of flexible filaments in rope-like, twisted bundles and fibres by introducing gradients of both filament shape (i.e. curvature) and packing throughout the structure. Previous models of chiral filament bundle formation have shown that this frustration gives rise to several distinct morphological responses, including self-limiting bundle widths, anisotropic domain (tape-like) formation and topological defects in the lateral inter-filament order. In this paper, we employ a combination of continuum elasticity theory and discrete filament bundle simulations to explore how these distinct morphological responses compete in the broader phase diagram of chiral filament assembly. We show that the most generic model of bundle formation exhibits at least four classes of equilibrium structure—finite-width, twisted bundles with isotropic and anisotropic shapes, with and without topological defects, as well as bulk phases of untwisted, columnar assembly (i.e. ‘frustration escape’). These competing equilibrium morphologies are selected by only a relatively small number of parameters describing filament assembly: bundle surface energy, preferred chiral twist and stiffness of chiral filament interactions, and mechanical stiffness of filaments and their lateral interactions. Discrete filament bundle simulations test and verify continuum theory predictions for dependence of bundle structure (shape, size and packing defects of two-dimensional cross section) on these key parameters.

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33

Yan, Li, Yingfang Li, Sakander Hayat, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran, Sarfraz Ahmad, and Mohammad Reza Farahani. "On Degree-Based and Frustration Related Topological Indices of Single-Walled Titania Nanotubes." Journal of Computational and Theoretical Nanoscience 13, no. 11 (November 1, 2016): 9027–32. http://dx.doi.org/10.1166/jctn.2016.6080.

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34

Bachmann, Sven, Wojciech De Roeck, Brecht Donvil, and Martin Fraas. "Stability of invertible, frustration-free ground states against large perturbations." Quantum 6 (September 8, 2022): 793. http://dx.doi.org/10.22331/q-2022-09-08-793.

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A gapped ground state of a quantum spin system has a natural length scale set by the gap. This length scale governs the decay of correlations. A common intuition is that this length scale also controls the spatial relaxation towards the ground state away from impurities or boundaries. The aim of this article is to take a step towards a proof of this intuition. We assume that the ground state is frustration-free and invertible, i.e. it has no long-range entanglement. Moreover, we assume the property that we are aiming to prove for one specific kind of boundary condition; namely open boundary conditions. This assumption is also known as the "local topological quantum order" (LTQO) condition. With these assumptions we can prove stretched exponential decay away from boundaries or impurities, for any of the ground states of the perturbed system. In contrast to most earlier results, we do not assume that the perturbations at the boundary or the impurity are small. In particular, the perturbed system itself can have long-range entanglement.

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35

Tranquada, John M. "Topological Doping and Superconductivity in Cuprates: An Experimental Perspective." Symmetry 13, no. 12 (December 8, 2021): 2365. http://dx.doi.org/10.3390/sym13122365.

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Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

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36

Ge, Yang, Jianlong Ji, Zhizhong Shen, Qiang Zhang, Aoqun Jian, Qianqian Duan, Chao Wang, Jun Jiang, Wendong Zhang, and Shengbo Sang. "First principles study of magnetism induced by topological frustration of bowtie-shaped graphene nanoflake." Carbon 127 (February 2018): 432–36. http://dx.doi.org/10.1016/j.carbon.2017.11.005.

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37

Hong, Sungyeon, Michael A. Klatt, Gerd Schröder-Turk, Nicolas François, and Mohammad Saadatfar. "Dynamical arrest of topological defects in 2D hyperuniform disk packings." EPJ Web of Conferences 249 (2021): 15002. http://dx.doi.org/10.1051/epjconf/202124915002.

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We investigate collective motions of points in 2D systems, orchestrated by Lloyd algorithm. The algorithm iteratively updates a system by minimising the total quantizer energy of the Voronoi landscape of the system. As a result of a tradeoff between energy minimisation and geometric frustration, we find that optimised systems exhibit a defective landscape along the process, where strands of 5- and 7-coordinated dislocations are embedded in the hexatic phase. In particular, dipole defects, each of which is the simplest possible pair of a pentagon and a heptagon, come into the picture of dynamical arrest, as the system freezes down to a disordered hyperuniform state. Moreover, we explore the packing fractions of 2D disk packings associated to the obtained hyperuniform systems by considering the maximum inscribed disks in their Voronoi cells.

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38

Azzoni, C. B., M. C. Mozzati, A. Paleari, V. Massarottib, D. Capsonib, and M. Binib. "Magnetic Order in Li-Mn Spinels." Zeitschrift für Naturforschung A 53, no. 8 (August 1, 1998): 693–98. http://dx.doi.org/10.1515/zna-1998-0809.

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Abstract Magnetic measurements were carried out on different samples of Lithium-Manganese spinel LiMn2O4 , great care having been taken to avoid the presence of spurious magnetic phases, such as Mn3O4 . Susceptibility data, showing deviations from paramagnetic behaviour at about 40 K, were analyzed in terms of local magnetic interactions, taking into account the structural and transport properties of these com-pounds. The magnetic response of pure and stoichiometric samples suggests that the onset of a longrange magnetic ordering is hindered by the topological frustration of the antiferromagnetic octahedral sublattice of the spinel.

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39

Romaguera, Arnau, Xiaodong Zhang, Ruyong Li, Oscar Fabelo, and José Luis García-Muñoz. "Magnetic properties of highly ordered single crystals with layered YBaCuFeO₅ structure." EPJ Web of Conferences 286 (2023): 05005. http://dx.doi.org/10.1051/epjconf/202328605005.

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In the layered perovskites YBaCuFeO5 (YBCFO) magnetic frustration stabilizes incommensurate spiral order up to unexpectedly high temperatures (TS). The level of frustration and hence TS depend directly on the fraction (nd) of B-site (Cu/Fe) chemical disorder in the samples. We report a neutron investigation on the magnetic transitions in two YBaCuFeO5 single crystals (one pure and the second slightly doped with Mn), grown by floating-zone methods, that present very low Fe/Cu cation disorder (nd→0). The low density of antiferromagnetic Fe2O9 bipyramid units in these crystals precludes the stabilization of a frustrated topological network, which is at the origin of the non-collinear (helicoidal) magnetic order. Instead, the ground state is substituted by two competing commensurate collinear magnetic phases, the majority one (k1) attributed to the perfectly ordered YBCFO perovskite (nd=0). A second type of collinear magnetic domains (k3) develop for samples with disorder below a critical threshold (0<nd< n0). Only in YBCFO samples with Cu/Fe disorder above the critical threshold a long-range helicoidal or spiral magnetic state can be formed.

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40

Muttathukattil, Aswathy N., Prashant Chandra Singh, and Govardhan Reddy. "Role of Disulfide Bonds and Topological Frustration in the Kinetic Partitioning of Lysozyme Folding Pathways." Journal of Physical Chemistry B 123, no. 15 (March 26, 2019): 3232–41. http://dx.doi.org/10.1021/acs.jpcb.9b00739.

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41

BENOIT, J., R. DANDOLOFF, and A. SAXENA. "HEISENBERG SPINS ON A CYLINDER SECTION." International Journal of Modern Physics B 14, no. 19n20 (August 10, 2000): 2093–100. http://dx.doi.org/10.1142/s0217979200001242.

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Classical Heisenberg spins in the continuum limit (i.e. the nonlinear σ-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated microtubules and cylindrical membranes. The corresponding rigid cylinder model exhibits topological soliton configurations with geometrical frustration due to the finite length of the cylinder section. Assuming small and smooth deformations allows to find shapes of the elastic support by relaxing the rigidity constraint: an inhomogeneous Lamé equation arises. Finally, this leads to a novel geometric effect: a global shrinking of the cylinder section with swellings.

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42

Chen, X., T. Z. Ji, L. Sun, B. F. Miao, Y. T. Millev, and H. F. Ding. "General nature of the step-induced frustration at ferromagnetic/antiferromagnetic interfaces: topological origin and quantitative understanding." New Journal of Physics 21, no. 12 (December 18, 2019): 123045. http://dx.doi.org/10.1088/1367-2630/ab5cbd.

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43

Zhang, Wenjuan, Zachariah Addison, and Nandini Trivedi. "Orbital frustration and topological flat bands." Physical Review B 104, no. 23 (December 9, 2021). http://dx.doi.org/10.1103/physrevb.104.235202.

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44

Schmidt, Kai Phillip. "Persisting topological order via geometric frustration." Physical Review B 88, no. 3 (July 16, 2013). http://dx.doi.org/10.1103/physrevb.88.035118.

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45

Drisko, Jasper, Thomas Marsh, and John Cumings. "Topological frustration of artificial spin ice." Nature Communications 8, no. 1 (January 13, 2017). http://dx.doi.org/10.1038/ncomms14009.

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46

Maiellaro, Alfonso, Francesco Romeo, and Roberta Citro. "Effects of geometric frustration in Kitaev chains." European Physical Journal Plus 136, no. 6 (June 2021). http://dx.doi.org/10.1140/epjp/s13360-021-01592-9.

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AbstractWe study the topological phase transitions of a Kitaev chain frustrated by the addition of a single long-range hopping. In order to study the topological properties of the resulting legged-ring geometry (Kitaev tie model), we generalize the transfer matrix approach through which the emergence of Majorana edge modes is analyzed. We find that geometric frustration gives rise to a topological phase diagram in which non-trivial phases alternate with trivial ones at varying the range of the hopping and the chemical potential. Robustness to disorder of non-trivial phases is also proven. Moreover, geometric frustration effects persist when translational invariance is restored by considering a multiple-tie system. These findings shed light on an entire class of experimentally realizable topological systems with long-range couplings.

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Marić, Vanja, Fabio Franchini, Domagoj Kuić, and Salvatore Marco Giampaolo. "Resilience of the topological phases to frustration." Scientific Reports 11, no. 1 (March 22, 2021). http://dx.doi.org/10.1038/s41598-021-86009-4.

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AbstractRecently it was highlighted that one-dimensional antiferromagnetic spin models with frustrated boundary conditions, i.e. periodic boundary conditions in a ring with an odd number of elements, may show very peculiar behavior. Indeed the presence of frustrated boundary conditions can destroy the local magnetic orders presented by the models when different boundary conditions are taken into account and induce novel phase transitions. Motivated by these results, we analyze the effects of the introduction of frustrated boundary conditions on several models supporting (symmetry protected) topological orders, and compare our results with the ones obtained with different boundary conditions. None of the topological order phases analyzed are altered by this change. This observation leads naturally to the conjecture that topological phases of one-dimensional systems are in general not affected by topological frustration.

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Marić, Vanja, Salvatore Marco Giampaolo, and Fabio Franchini. "Quantum phase transition induced by topological frustration." Communications Physics 3, no. 1 (December 2020). http://dx.doi.org/10.1038/s42005-020-00486-z.

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AbstractIn quantum many-body systems with local interactions, the effects of boundary conditions are considered to be negligible, at least for sufficiently large systems. Here we show an example of the opposite. We consider a spin chain with two competing interactions, set on a ring with an odd number of sites. When only the dominant interaction is antiferromagnetic, and thus induces topological frustration, the standard antiferromagnetic order (expressed by the magnetization) is destroyed. When also the second interaction turns from ferro to antiferro, an antiferromagnetic order characterized by a site-dependent magnetization which varies in space with an incommensurate pattern, emerges. This modulation results from a ground state degeneracy, which allows to break the translational invariance. The transition between the two cases is signaled by a discontinuity in the first derivative of the ground state energy and represents a quantum phase transition induced by a special choice of boundary conditions.

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Marić, Vanja, Gianpaolo Torre, Fabio Franchini, and Salvatore Marco Giampaolo. "Topological Frustration can modify the nature of a Quantum Phase Transition." SciPost Physics 12, no. 2 (February 24, 2022). http://dx.doi.org/10.21468/scipostphys.12.2.075.

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Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. We show that topological frustration can change the nature of a second order quantum phase transition separating two different ordered phases. Even more remarkably, frustration is triggered simply by a suitable choice of boundary conditions in a 1D chain. While with every other BC each of two phases is characterized by its own local order parameter, with frustration no local order can survive. We construct string order parameters to distinguish the two phases, but, having proved that topological frustration is capable of altering the nature of a system's phase transition, our results pose a clear challenge to the current understanding of phase transitions in complex quantum systems.

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Torre, Gianpaolo, Jovan Odavić, Pierre Fromholz, Salvatore Marco Giampaolo, and Fabio Franchini. "Long-range entanglement and topological excitations." SciPost Physics Core 7, no. 3 (August 5, 2024). http://dx.doi.org/10.21468/scipostphyscore.7.3.050.

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Topological order comes in different forms, and its classification and detection is an important field of modern research. In this work, we show that the Disconnected Entanglement Entropy, a measure originally introduced to identify topological phases, is also able to unveil the long-range entanglement (LRE) carried by a single, fractionalized excitation. We show this by considering a quantum, delocalized domain wall excitation that can be introduced into a system by inducing geometric frustration in an antiferromagnetic spin chain. Furthermore, we show that the LRE of such systems is resilient against a quantum quench and the introduction of disorder, as it happens in traditional symmetry-protected topological phases. All these evidences establish the existence of a new phase induced by frustration with topological features despite not being of the usual type.

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