Artykuły w czasopismach: „Quantum Spin-orbital Liquid State”

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Katayama, Naoyuki, Kenta Kimura, Yibo Han, Joji Nasu, Natalia Drichko, Yoshiki Nakanishi, Mario Halim i in. "Absence of Jahn−Teller transition in the hexagonal Ba3CuSb2O9 single crystal". Proceedings of the National Academy of Sciences 112, nr 30 (13.07.2015): 9305–9. http://dx.doi.org/10.1073/pnas.1508941112.

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With decreasing temperature, liquids generally freeze into a solid state, losing entropy in the process. However, exceptions to this trend exist, such as quantum liquids, which may remain unfrozen down to absolute zero owing to strong quantum entanglement effects that stabilize a disordered state with zero entropy. Examples of such liquids include Bose−Einstein condensation of cold atoms, superconductivity, quantum Hall state of electron systems, and quantum spin liquid state in the frustrated magnets. Moreover, recent studies have clarified the possibility of another exotic quantum liquid state based on the spin–orbital entanglement in FeSc2S4. To confirm this exotic ground state, experiments based on single-crystalline samples are essential. However, no such single-crystal study has been reported to date. Here, we report, to our knowledge, the first single-crystal study on the spin–orbital liquid candidate, 6H-Ba3CuSb2O9, and we have confirmed the absence of an orbital frozen state. In strongly correlated electron systems, orbital ordering usually appears at high temperatures in a process accompanied by a lattice deformation, called a static Jahn−Teller distortion. By combining synchrotron X-ray diffraction, electron spin resonance, Raman spectroscopy, and ultrasound measurements, we find that the static Jahn−Teller distortion is absent in the present material, which indicates that orbital ordering is suppressed down to the lowest temperatures measured. We discuss how such an unusual feature is realized with the help of spin degree of freedom, leading to a spin–orbital entangled quantum liquid state.

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Nirmala, R., Kwang-Hyun Jang, Hasung Sim, Hwanbeom Cho, Junghwan Lee, Nam-Geun Yang, Seongsu Lee i in. "Spin glass behavior in frustrated quantum spin system CuAl2O4with a possible orbital liquid state". Journal of Physics: Condensed Matter 29, nr 13 (15.02.2017): 13LT01. http://dx.doi.org/10.1088/1361-648x/aa5c72.

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Broholm, C., R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman i T. Senthil. "Quantum spin liquids". Science 367, nr 6475 (16.01.2020): eaay0668. http://dx.doi.org/10.1126/science.aay0668.

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Spin liquids are quantum phases of matter with a variety of unusual features arising from their topological character, including “fractionalization”—elementary excitations that behave as fractions of an electron. Although there is not yet universally accepted experimental evidence that establishes that any single material has a spin liquid ground state, in the past few years a number of materials have been shown to exhibit distinctive properties that are expected of a quantum spin liquid. Here, we review theoretical and experimental progress in this area.

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Zhu, W., Shou-shu Gong i D. N. Sheng. "Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice". Proceedings of the National Academy of Sciences 116, nr 12 (4.03.2019): 5437–41. http://dx.doi.org/10.1073/pnas.1807840116.

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A spin-1/2lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around theQ=Mpoint in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.

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Oguri, A., K. Yamanaka, J. Inoue i S. Maekawa. "Quantum spin-liquid state with a hole". Physical Review B 43, nr 1 (1.01.1991): 186–92. http://dx.doi.org/10.1103/physrevb.43.186.

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Calvera, Vladimir, Steven A. Kivelson i Erez Berg. "Pseudo-spin order of Wigner crystals in multi-valley electron gases". Low Temperature Physics 49, nr 6 (1.06.2023): 679–700. http://dx.doi.org/10.1063/10.0019425.

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We study multi-valley electron gases in the low density (rs ≫ 1) limit. Here the ground-state is always a Wigner crystal (WC), with additional pseudo-spin order where the pseudo-spins are related to valley occupancies. Depending on the symmetries of the host semiconductor and the values of the parameters such as the anisotropy of the effective mass tensors, we find a striped or chiral pseudo-spin antiferromagnet, or a time-reversal symmetry breaking orbital loop-current ordered pseudo-spin ferromagnet. Our theory applies to the recently-discovered WC states in AlAs and in mono and bilayer transition metal dichalcogenides. We identify a set of interesting electronic liquid crystalline phases that could arise by continuous quantum melting of such WCs.

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Takatsu, Hiroshi, Hiroaki Kadowaki, Taku J. Sato, Jeffrey W. Lynn, Yoshikazu Tabata, Teruo Yamazaki i Kazuyuki Matsuhira. "Quantum spin fluctuations in the spin-liquid state of Tb2Ti2O7". Journal of Physics: Condensed Matter 24, nr 5 (7.12.2011): 052201. http://dx.doi.org/10.1088/0953-8984/24/5/052201.

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Falson, Joseph, Daniela Tabrea, Ding Zhang, Inti Sodemann, Yusuke Kozuka, Atsushi Tsukazaki, Masashi Kawasaki, Klaus von Klitzing i Jurgen H. Smet. "A cascade of phase transitions in an orbitally mixed half-filled Landau level". Science Advances 4, nr 9 (wrzesień 2018): eaat8742. http://dx.doi.org/10.1126/sciadv.aat8742.

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Half-filled Landau levels host an emergent Fermi liquid that displays instability toward pairing, culminating in a gapped even-denominator fractional quantum Hall ground state. While this pairing may be probed by tuning the polarization of carriers in competing orbital and spin degrees of freedom, sufficiently high quality platforms offering such tunability remain few. We explore the ground states at filling factor ν = 5/2 in ZnO-based two-dimensional electron systems through a forced intersection of opposing spin branches of Landau levels taking quantum numbers N = 1 and 0. We reveal a cascade of phases with distinct magnetotransport features including a gapped phase polarized in the N = 1 level and a compressible phase in N = 0, along with an unexpected Fermi liquid, a second gapped, and a strongly anisotropic nematic-like phase at intermediate polarizations when the levels are near degeneracy. The phase diagram is produced by analyzing the proximity of the intersecting levels and highlights the excellent reproducibility and controllability that ZnO offers for exploring exotic fractionalized electronic phases.

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Hashimoto, Akihiro, Yuta Murakami i Akihisa Koga. "Majorana excitations in the anisotropic Kitaev model with an ordered-flux structure". Journal of Physics: Conference Series 2164, nr 1 (1.03.2022): 012028. http://dx.doi.org/10.1088/1742-6596/2164/1/012028.

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Abstract We investigate the anisotropic S = 1/2 Kitaev model on the honeycomb lattice with the ordered-flux structure. By diagonalizing the Majorana Hamiltonian for the flux configuration, we find two distinct gapped quantum spin liquids. One of them is the gapped state realized in the large anisotropic case, where low energy properties are described by the toric code. On the other hand, when the system has small anisotropy, the other gapped quantum spin liquid is stabilized by the ordered-flux configuration. Since these two gapped quantum spin liquids are separated by the gapless region, these are not adiabatically connected to each other.

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Tsvelik, A. M. "New fermionic description of quantum spin liquid state". Physical Review Letters 69, nr 14 (5.10.1992): 2142–44. http://dx.doi.org/10.1103/physrevlett.69.2142.

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Mirebeau, Isabelle, Sylvain Petit, Julien Robert, Solene Guitteny, Arsen Gukasov, Pierre Bonville, Andrew Sazonov i Claudia Decorse. "Magnetic structures and anisotropic excitations in Tb2Ti2O7spin liquid". Acta Crystallographica Section A Foundations and Advances 70, a1 (5.08.2014): C1543. http://dx.doi.org/10.1107/s2053273314084563.

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Geometrical frustration in the pyrochlore lattice of corner sharing tetrahedra yields exotic short range ordered ground states known as spin liquids or spin ices. Among them, Tb2Ti2O7 spin liquid (also called quantum spin ice) remains the most mysterious, in spite of 15 years of intense investigation. Our recent single crystal experiments using neutron diffraction and inelastic scattering down to 50 mK yield new insight on this question. By applying a high magnetic field along a [111] anisotropy axis [1], the Tb moments reorient gradually without showing the magnetization plateau observed in classical spin ices. Quantitative comparison with mean field calculation supports a dynamical symmetry breaking akin to a dynamic Jahn-Teller distortion, preserving the overall cubic symmetry. In the non-Kramers Tb ion this induce a quantum mixing of the wave-functions of the ground state crystal field doublet enabling the formation of a spin liquid, viewed as a non-magnetic two-singlet ground state in this mean-field picture [2]. The spin lattice coupling also shows up in the spin fluctuations in zero field [3]. Dispersive excitations emerge from pinch-points in the reciprocal space, with anisotropic spectral weight. This is the first evidence of them in a disordered ground state. They reveal the breaking of some conservation law ruling the relative orientations of the fluctuating magnetic moments in a given tetrahedron, as for the monopole excitations in classical spin ices. The algebraic character of the correlations shows that Tb2Ti2O7 ground state is akin to a Coulomb phase. Finally, the first excited crystal field level and an acoustic phonon mode interact, repelling each other. The whole results show that the magnetoelastic coupling is a key feature to understand the surprising spin liquid ground state. They call for an interaction between quadrupolar moments, whose Jahn-Teller distortion is the first (single site) approximation.

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Boya, K., K. Nam, K. Kargeti, A. Jain, R. Kumar, S. K. Panda, S. M. Yusuf i in. "Signatures of spin-liquid state in a 3D frustrated lattice compound KSrFe₂(PO₄)₃ with S = 5/2". APL Materials 10, nr 10 (1.10.2022): 101103. http://dx.doi.org/10.1063/5.0096942.

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A quantum spin-liquid is a spin disordered state of matter in which spins are strongly correlated and highly entangled with low-energy excitations. It has been often found in two-dimensional S = ½, highly frustrated spin networks but rarely observed in three-dimensional (3D) frustrated quantum magnets. Here, KSrFe2(PO4)3, forming a complicated 3D frustrated lattice with a spin moment S = 5/2, is investigated by thermodynamic, neutron diffraction measurements and electronic structure calculations. Despite the relatively sizable Curie–Weiss temperature θCW = −70 K, a conventional magnetic long-range order is confirmed to be absent down to 0.19 K. The magnetic heat capacity data follow the power-law behavior at the lowest temperature region, supporting gapless excitations in a 3D spin-liquid state. Strong geometrical spin frustration responsible for the spin-liquid feature is understood as originating from the almost comparable five competing nearest-neighbor antiferromagnetic exchange interactions, which form the complicated 3D frustrated spin network. All these results suggest that the compound KSrFe2(PO4)3, representing a unique 3D spin frustrated network, could be a rare example of forming a gapless spin-liquid state even with a large spin moment of S = 5/2.

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Bukhanko F. N. i Bukhanko A. F. "Phase transition of quantum spin liquid in La-=SUB=-0.15-=/SUB=-Sm-=SUB=-0.85-=/SUB=-MnO-=SUB=-3+delta-=/SUB=- in weak magnetic field tochiral state with topological order during sample magnetization reversal". Physics of the Solid State 64, nr 7 (2022): 802. http://dx.doi.org/10.21883/pss.2022.07.54584.304.

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In this work, a detailed study of the nature of phase transitions in the Z2 quantum spin liquid in La La0.15Sm0.85MnO3+delta manganites induced at a temperature of 4.2 K by a weak external dc magnetic field in the ZFC and FC regimesof measuring the field dependences of the magnetization in the field range of ± 5 kOe is carried out. It is shown that during the magnetization reversal of the sample in the ZFC-regime near the external magnetic field H=0, a second-order phase transition Z2 quantum spin liquid occurs in the state of a chiral gap quantum spin liquid with a topological order. The transition is accompanied by an unusual hump-like increase in the number of magnetic excitations in the form of Majorana fermions and local gauge Z2 magnetic fluxes in the range of fields ± 500 Oe near zero field. A characteristic feature of the magnetization features is their strong dependence on the direction of growth of the external magnetic field, which is accompanied by the breakingof the mirror symmetry of the sample magnetization upon reversal of the sign of the external magnetic field, which is typical for the Z2 chiral state of a quantum spin liquid. In the FC-measurementregime, characteristic signs of excitation-destruction of 1D-fragments of gapless charge/spin density waves were found near H=0 during sample magnetization reversal due to confinement-deconfinement of spinon pairs in a system of spin chains. Keywords: chiral quantum spin liquid, Majorana fermions, confinement-deconfinement of spinon pairs, 1D-charge/spin density waves.

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Miksch, Björn, Andrej Pustogow, Mojtaba Javaheri Rahim, Andrey A. Bardin, Kazushi Kanoda, John A. Schlueter, Ralph Hübner, Marc Scheffler i Martin Dressel. "Gapped magnetic ground state in quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3". Science 372, nr 6539 (15.04.2021): 276–79. http://dx.doi.org/10.1126/science.abc6363.

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Geometrical frustration, quantum entanglement, and disorder may prevent long-range ordering of localized spins with strong exchange interactions, resulting in an exotic state of matter. κ-(BEDT-TTF)2Cu2(CN)3 is considered the prime candidate for this elusive quantum spin liquid state, but its ground-state properties remain puzzling. We present a multifrequency electron spin resonance (ESR) study down to millikelvin temperatures, revealing a rapid drop of the spin susceptibility at 6 kelvin. This opening of a spin gap, accompanied by structural modifications, is consistent with the formation of a valence bond solid ground state. We identify an impurity contribution to the ESR response that becomes dominant when the intrinsic spins form singlets. Probing the electrons directly manifests the pivotal role of defects for the low-energy properties of quantum spin systems without magnetic order.

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Kim Anh, Nguyen Thi. "THE PHYSICS OF SPIN-1/2 XY MODEL WITH FOUR-SITE EXCHANGE INTERACTION ON THE KAGOME LATTICE". Vietnam Journal of Science and Technology 54, nr 1A (16.03.2018): 17. http://dx.doi.org/10.15625/2525-2518/54/1a/11801.

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The quantum spin liquid (QSL) state, proposed more than three decades ago by Fazekas and Anderson remains surprisingly elusive. Although recent experiments provide a strong evidence of their existence in the frustrated spin systems, the microscopic model for this state is still rare. The extensive theoretical framework, developed over decades, continues to extend further motivated by these and other discoveries from large-scale computer simulations of a relatively small number of models. In this work, we discuss the physics of the ground-state phase diagram of a two-dimensional Kagome lattice spin-1/2 XY model with a four-site ring-exchange interaction using quantum Monte Carlo simulation. We found the second order phase transition from superfluid state to a Z2 quantum spin liquid phase driven by the four-site ring exchange interaction. We have characterized the QSL by its vanishing order parameters such as the spin-spin structure factor, the plaquette-plaquette structure factor. Moreover, we have found the large anomalous exponent ηXY* ≈ 1.325 which belongs to a different universality class other than 3D XY universality class. There is no signal of supersolid phase intervening between the superfluid state and QSL state.

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Hiramatsu, Takaaki, Yukihiro Yoshida, Gunzi Saito, Akihiro Otsuka, Hideki Yamochi, Mitsuhiko Maesato, Yasuhiro Shimizu, Hiroshi Ito i Hideo Kishida. "Quantum spin liquid: design of a quantum spin liquid next to a superconducting state based on a dimer-type ET Mott insulator". Journal of Materials Chemistry C 3, nr 6 (2015): 1378–88. http://dx.doi.org/10.1039/c4tc01701c.

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Bruin, J. A. N., R. R. Claus, Y. Matsumoto, N. Kurita, H. Tanaka i H. Takagi. "Robustness of the thermal Hall effect close to half-quantization in α-RuCl3". Nature Physics 18, nr 4 (17.02.2022): 401–5. http://dx.doi.org/10.1038/s41567-021-01501-y.

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AbstractA key feature of quantum spin liquids is the predicted formation of fractionalized excitations. They are expected to produce changes in the physical response, providing a way to observe the quantum spin liquid state1. In the honeycomb magnet α-RuCl3, a quantum spin liquid has been proposed to explain the behaviour observed on applying an in-plane magnetic field H||. Previous work reported that the thermal Hall conductivity took on a half-integer quantized value and suggested this as a signature of a fractionalized Majorana edge mode predicted to exist in Kitaev quantum spin liquids2. However, the temperature and magnetic-field range of the half-quantized signal2–4 and its association with Majorana edge modes are still under debate5,6. Here we present a comprehensive study of the thermal Hall conductivity in α-RuCl3 showing that approximately half-integer quantization exists in an extended region of the phase diagram, particularly across a plateau-like parameter regime for H|| exceeding 10 T and temperature below 6.5 K. At lower fields, the thermal Hall conductivity exhibits correlations with complex anomalies in the longitudinal thermal conductivity and magnetization, and is suppressed by cooling to low temperatures. Our results can be explained by the existence of a topological state in magnetic fields above 10 T.

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Biesner, Tobias, i Ece Uykur. "Pressure-Tuned Interactions in Frustrated Magnets: Pathway to Quantum Spin Liquids?" Crystals 10, nr 1 (18.12.2019): 4. http://dx.doi.org/10.3390/cryst10010004.

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Quantum spin liquids are prime examples of strongly entangled phases of matter with unconventional exotic excitations. Here, strong quantum fluctuations prohibit the freezing of the spin system. On the other hand, frustrated magnets, the proper platforms to search for the quantum spin liquid candidates, still show a magnetic ground state in most of the cases. Pressure is an effective tuning parameter of structural properties and electronic correlations. Nevertheless, the ability to influence the magnetic phases should not be forgotten. We review experimental progress in the field of pressure-tuned magnetic interactions in candidate systems. Elaborating on the possibility of tuned quantum phase transitions, we further show that chemical or external pressure is a suitable parameter in these exotic states of matter.

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Chandra, P., P. Coleman i I. Ritchey. "Questions, Controversies and Frustration in Quantum Antiferromagnetism". International Journal of Modern Physics B 05, nr 01n02 (styczeń 1991): 171–89. http://dx.doi.org/10.1142/s0217979291000122.

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The search for a gapless spin liquid phase has raised many issues in quantum antiferromagnetism. Here we review recent developments in this field, and in particular address questions and controversies surrounding a proposed “spin nematic” state.

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ANGELUCCI, ANTIMO, i GIANCARLO JUG. "NOVEL PATH INTEGRAL APPROACH TO EFFECTIVE FIELD THEORIES FOR D-DIMENSIONAL QUANTUM SPIN SYSTEMS". International Journal of Modern Physics B 03, nr 07 (lipiec 1989): 1069–83. http://dx.doi.org/10.1142/s0217979289000737.

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We present a novel path integral formulation for the effective field theory describing d-dimensional quantum spin models. The new approach avoids the coherent states representation, but at very low temperatures reproduces all known results obtained with the latter technique for describing excitations of the Neél state. The possibility of exploring higher-temperature, unbroken-symmetry state excitations (such as those appropriate for the quantum spin-liquid state) within this method is illustrated.

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IOFFE, L. B., i A. I. LARKIN. "EFFECTIVE ACTION OF A TWO-DIMENSIONAL ANTIFERROMAGNET". International Journal of Modern Physics B 02, nr 02 (kwiecień 1988): 203–19. http://dx.doi.org/10.1142/s0217979288000160.

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In the limit of weak quantum fluctuations an effective long-wave action of the Heisenberg quantum antiferromagnet is obtained which allows one to get a spectrum, spin, and statistics of long-wave fluctuations. In the vicinity of the point of instability of an antiferromagnetic state quantum fluctuations result (at zero temperature as well) in a paramagnetic phase of a spin liquid.

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Tanaka, H., F. Yamada, T. Ono, T. Sakakibara, Y. Uwatoko, A. Oosawa, K. Kakurai i K. Goto. "Magnetic quantum phase transitions from gapped spin liquid state in". Journal of Magnetism and Magnetic Materials 310, nr 2 (marzec 2007): 1343–48. http://dx.doi.org/10.1016/j.jmmm.2006.10.361.

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Tokiwa, Yoshifumi, Christian Stingl, Moo-Sung Kim, Toshiro Takabatake i Philipp Gegenwart. "Characteristic signatures of quantum criticality driven by geometrical frustration". Science Advances 1, nr 3 (kwiecień 2015): e1500001. http://dx.doi.org/10.1126/sciadv.1500001.

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Geometrical frustration describes situations where interactions are incompatible with the lattice geometry and stabilizes exotic phases such as spin liquids. Whether geometrical frustration of magnetic interactions in metals can induce unconventional quantum critical points is an active area of research. We focus on the hexagonal heavy fermion metal CeRhSn, where the Kondo ions are located on distorted kagome planes stacked along the c axis. Low-temperature specific heat, thermal expansion, and magnetic Grüneisen parameter measurements prove a zero-field quantum critical point. The linear thermal expansion, which measures the initial uniaxial pressure derivative of the entropy, displays a striking anisotropy. Critical and noncritical behaviors along and perpendicular to the kagome planes, respectively, prove that quantum criticality is driven be geometrical frustration. We also discovered a spin flop–type metamagnetic crossover. This excludes an itinerant scenario and suggests that quantum criticality is related to local moments in a spin liquid–like state.

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Watanabe, Daiki, Kaori Sugii, Masaaki Shimozawa, Yoshitaka Suzuki, Takeshi Yajima, Hajime Ishikawa, Zenji Hiroi, Takasada Shibauchi, Yuji Matsuda i Minoru Yamashita. "Emergence of nontrivial magnetic excitations in a spin-liquid state of kagomé volborthite". Proceedings of the National Academy of Sciences 113, nr 31 (20.07.2016): 8653–57. http://dx.doi.org/10.1073/pnas.1524076113.

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When quantum fluctuations destroy underlying long-range ordered states, novel quantum states emerge. Spin-liquid (SL) states of frustrated quantum antiferromagnets, in which highly correlated spins fluctuate down to very low temperatures, are prominent examples of such quantum states. SL states often exhibit exotic physical properties, but the precise nature of the elementary excitations behind such phenomena remains entirely elusive. Here, we use thermal Hall measurements that can capture the unexplored property of the elementary excitations in SL states, and report the observation of anomalous excitations that may unveil the unique features of the SL state. Our principal finding is a negative thermal Hall conductivity κxy which the charge-neutral spin excitations in a gapless SL state of the 2D kagomé insulator volborthite Cu3V2O7(OH)2⋅2H2O exhibit, in much the same way in which charged electrons show the conventional electric Hall effect. We find that κxy is absent in the high-temperature paramagnetic state and develops upon entering the SL state in accordance with the growth of the short-range spin correlations, demonstrating that κxy is a key signature of the elementary excitation formed in the SL state. These results suggest the emergence of nontrivial elementary excitations in the gapless SL state which feel the presence of fictitious magnetic flux, whose effective Lorentz force is found to be less than 1/100 of the force experienced by free electrons.

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Szirmai, Péter, Cécile Mézière, Guillaume Bastien, Pawel Wzietek, Patrick Batail, Edoardo Martino, Konstantins Mantulnikovs i in. "Quantum spin-liquid states in an organic magnetic layer and molecular rotor hybrid". Proceedings of the National Academy of Sciences 117, nr 47 (5.11.2020): 29555–60. http://dx.doi.org/10.1073/pnas.2000188117.

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The exotic properties of quantum spin liquids (QSLs) have continually been of interest since Anderson’s 1973 ground-breaking idea. Geometrical frustration, quantum fluctuations, and low dimensionality are the most often evoked material’s characteristics that favor the long-range fluctuating spin state without freezing into an ordered magnet or a spin glass at low temperatures. Among the few known QSL candidates, organic crystals have the advantage of having rich chemistry capable of finely tuning their microscopic parameters. Here, we demonstrate the emergence of a QSL state in [EDT-TTF-CONH2]2+[BABCO−] (EDT-BCO), where the EDT molecules with spin-1/2 on a triangular lattice form layers which are separated by a sublattice of BCO molecular rotors. By several magnetic measurements, we show that the subtle random potential of frozen BCO Brownian rotors suppresses magnetic order down to the lowest temperatures. Our study identifies the relevance of disorder in the stabilization of QSLs.

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Zhong, Ruidan, Tong Gao, Nai Phuan Ong i Robert J. Cava. "Weak-field induced nonmagnetic state in a Co-based honeycomb". Science Advances 6, nr 4 (styczeń 2020): eaay6953. http://dx.doi.org/10.1126/sciadv.aay6953.

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Layered honeycomb magnets are of interest as potential realizations of the Kitaev quantum spin liquid (KQSL), a quantum state with long-range spin entanglement and an exactly solvable Hamiltonian. Conventional magnetically ordered states are present for all currently known candidate materials, however, because non-Kitaev terms in the Hamiltonians obscure the Kitaev physics. Current experimental studies of the KQSL are focused on 4d or 5d transition metal–based honeycombs, in which strong spin-orbit coupling can be expected, yielding Kitaev interaction that dominates in an applied magnetic field. In contrast, for 3d-based layered honeycomb magnets, spin-orbit coupling is weak, and thus, Kitaev physics should be substantially less accessible. Here, we report our studies on BaCo2(AsO4)2, for which we find that the magnetic order associated with the non-Kitaev interactions can be fully suppressed by a relatively low magnetic field, yielding a nonmagnetic material and implying the presence of strong magnetic frustration and weak non-Kitaev interactions.

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Id Bakas, Said, i Mohamed El Hafidi. "Frustration effect and possibility of spin quantum liquid state in a tetrahedral spin ½ molecule". Chinese Journal of Physics 73 (październik 2021): 433–41. http://dx.doi.org/10.1016/j.cjph.2021.07.005.

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Oguri, A., K. Yamanaka, J. Inoue i S. Maekawa. "Hole and its surrounding spins in a quantum spin-liquid state". Physica B: Condensed Matter 165-166 (sierpień 1990): 1027–28. http://dx.doi.org/10.1016/s0921-4526(09)80099-9.

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Fukuyama, Hiroshi, i Masashi Morishita. "A possible quantum spin-liquid state in antiferromagnetic 2D solid 3He". Physica B: Condensed Matter 280, nr 1-4 (maj 2000): 104–5. http://dx.doi.org/10.1016/s0921-4526(99)01502-1.

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Orendáčová, Alžbeta, Róbert Tarasenko, Vladimír Tkáč, Erik Čižmár, Martin Orendáč i Alexander Feher. "Interplay of Spin and Spatial Anisotropy in Low-Dimensional Quantum Magnets with Spin 1/2". Crystals 9, nr 1 (21.12.2018): 6. http://dx.doi.org/10.3390/cryst9010006.

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Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii–Kosterlitz–Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.

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31

Zhong, Ruidan, Shu Guo, Guangyong Xu, Zhijun Xu i Robert J. Cava. "Strong quantum fluctuations in a quantum spin liquid candidate with a Co-based triangular lattice". Proceedings of the National Academy of Sciences 116, nr 29 (2.07.2019): 14505–10. http://dx.doi.org/10.1073/pnas.1906483116.

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Currently under active study in condensed matter physics, both theoretically and experimentally, are quantum spin liquid (QSL) states, in which no long-range magnetic ordering appears at low temperatures due to strong quantum fluctuations of the magnetic moments. The existing QSL candidates all have their intrinsic disadvantages, however, and solid evidence for quantum fluctuations is scarce. Here, we report a previously unreported compound, Na2BaCo(PO4)2, a geometrically frustrated system with effective spin-1/2 local moments for Co2+ ions on an isotropic 2-dimensional (2D) triangular lattice. Magnetic susceptibility and neutron scattering experiments show no magnetic ordering down to 0.05 K. Thermodynamic measurements show that there is a tremendous amount of magnetic entropy present below 1 K in 0-applied magnetic field. The presence of localized low-energy spin fluctuations is revealed by inelastic neutron measurements. At low applied fields, these spin excitations are confined to low energy and contribute to the anomalously large specific heat. In larger applied fields, the system reverts to normal behavior as evident by both neutron and thermodynamic results. Our experimental characterization thus reveals that this material is an excellent candidate for the experimental realization of a QSL state.

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Wei, Yuan, Xiaoyan Ma, Zili Feng, Yongchao Zhang, Lu Zhang, Huaixin Yang, Yang Qi i in. "Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu₃Zn(OH)₆FBr". Chinese Physics Letters 38, nr 9 (1.10.2021): 097501. http://dx.doi.org/10.1088/0256-307x/38/9/097501.

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We systematically study the low-temperature specific heats for the two-dimensional kagome antiferromagnet, Cu3Zn(OH)6FBr. The specific heat exhibits a T 1.7 dependence at low temperatures and a shoulder-like feature above it. We construct a microscopic lattice model of Z 2 quantum spin liquid and perform large-scale quantum Monte Carlo simulations to show that the above behaviors come from the contributions from gapped anyons and magnetic impurities. Surprisingly, we find the entropy associated with the shoulder decreases quickly with grain size d, although the system is paramagnetic to the lowest temperature. While this can be simply explained by a core-shell picture in that the contribution from the interior state disappears near the surface, the 5.9-nm shell width precludes any trivial explanations. Such a large length scale signifies the coherence length of the nonlocality of the quantum entangled excitations in quantum spin liquid candidate, similar to Pippard’s coherence length in superconductors. Our approach therefore offers a new experimental probe of the intangible quantum state of matter with topological order.

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Ryazanov, Mikhail, i David J. Nesbitt. "Non-equilibrium dynamics at the gas–liquid interface: State-resolved studies of NO evaporation from a benzyl alcohol liquid microjet". Journal of Chemical Physics 158, nr 14 (14.04.2023): 144703. http://dx.doi.org/10.1063/5.0143254.

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First measurements of internal quantum-state distributions for nitric oxide (NO) evaporating from liquid benzyl alcohol are presented over a broad range of temperatures, performed by liquid-microjet techniques in an essentially collision-free regime, with rotational/spin–orbit populations in the 2Π1/2,3/2 manifolds measured by laser-induced fluorescence. The observed rotational distributions exhibit highly linear (i.e., thermal) Boltzmann plots but notably reflect rotational temperatures ( Trot) as much as 30 K lower than the liquid temperature ( Tjet). A comparable lack of equilibrium behavior is also noted in the electronic degrees of freedom but with populations corresponding to spin–orbit temperatures ( TSO) consistently higher than Trot by ∼15 K. These results unambiguously demonstrate evaporation into a non-equilibrium distribution, which, by detailed-balance considerations, predict quantum-state-dependent sticking coefficients for incident collisions of NO at the gas–liquid interface. Comparison and parallels with previous experimental studies of NO thermal desorption and molecular-beam scattering in other systems are discussed, which suggests the emergence of a self-consistent picture for the non-equilibrium dynamics.

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Kohama, Yoshimitsu, Hajime Ishikawa, Akira Matsuo, Koichi Kindo, Nic Shannon i Zenji Hiroi. "Possible observation of quantum spin-nematic phase in a frustrated magnet". Proceedings of the National Academy of Sciences 116, nr 22 (9.05.2019): 10686–90. http://dx.doi.org/10.1073/pnas.1821969116.

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Water freezes into ice in winter and evaporates into vapor in summer. Scientifically, the transformations between solid, liquid, and gas are called phase transitions and can be classified through the changes in symmetry which occur in each case. A fourth phase of matter was discovered late in the 19th century: the liquid crystal nematic, in which rod- or disk-shaped molecules align like the atoms in a solid, while continuing to flow like a liquid. Here we report thermodynamic evidence of a quantum analog of the classical nematic phase, the quantum spin nematic (SN). In an SN, the spins of a quantum magnet select a common axis, like a nematic liquid crystal, while escaping conventional magnetic order. Our state-of-the-art thermal measurements in high pulsed magnetic fields up to 33 T on the copper mineral volborthite with spin 1/2 on a frustrated lattice provide thermodynamic evidence for SN order, half a century after the theoretical proposal [Blume M, Hsieh YY (1969) J Appl Phys 40:1249; Andreev AF, Grishchuk IA (1984) J Exp Theor Phys 97:467–475].

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FRADKIN, EDUARDO, i STEVEN KIVELSON. "SHORT RANGE RESONATING VALENCE BOND THEORIES AND SUPERCONDUCTIVITY". Modern Physics Letters B 04, nr 03 (10.02.1990): 225–32. http://dx.doi.org/10.1142/s0217984990000295.

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We consider the nature of superconductivity near a spin-liquid state with a large spin-excitation-gap. We argue that the quantum-dimer-model with holes is a good approximation in this limit. The insulator is shown to be exactly equivalent to compact quantum electrodynamics, and has a massive spectrum. The doped system is a superconductor with a low density phase characterized by tightly bound pairs and a high density phase with two weakly coupled condensates.

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Pai, Yun-Yi, Claire E. Marvinney, Liangbo Liang, Jie Xing, Allen Scheie, Alexander A. Puretzky, Gábor B. Halász i in. "Mesoscale interplay between phonons and crystal electric field excitations in quantum spin liquid candidate CsYbSe₂". Journal of Materials Chemistry C 10, nr 11 (2022): 4148–56. http://dx.doi.org/10.1039/d1tc05934c.

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In quantum spin liquid candidate CsYbSe2, phonon coupling to a crystal electric field mode results in a vibronic bound state, and complex, mesoscale interplay between phonon modes and CEF modes is observed.

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Bukhanko F. N i Bukhanko A. F. "Quantization of the spectrum of spinon pairs in a magnetic field and formation of bosons in the form of fragments of 1D-waves of charge/spin density in SmMnO-=SUB=-3+delta-=/SUB=-". Physics of the Solid State 64, nr 2 (2022): 176. http://dx.doi.org/10.21883/pss.2022.02.52965.142.

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Quantum oscillations of the temperature dependences of magnetization of SmMnO3+delta in magnetic fields H=100 and 350 Oe, 1 and 3.5 kOe are studied within a temperature interval of 4.2-12 K. The continuum of thermal excitations of spinon pairs in magnetic field H=100 Oe is divided into three overlapping Landau bands with energies En (n=1,2,3) and fractional band filling factors ν. The symmetric intense "supermagnetization" doublet consisting of two overlapping peaks around mean excitation temperature Tspinon=~8 K produces the primary contribution to magnetization. As the field increases to H=1 kOe, the spinon excitation spectrum transforms into a broad sinusoid peak with its apex around Tspinon=~8 K, which is typical of the excitation continuum of spinon pairs with strong dispersion in the regime of their confinement. The thermal excitation spectrum of spinons changes significantly in magnetic field H=3.5 kOe: a new type of quantization of the spinon spectrum in the form of magnetization features shaped like narrow steps (plateaus), which correspond to integer filling with spinons of three Landau bands with a finite gap, emerges in Landau bands with n=1,2, and 3. The evolution of the boson spectrum in the form of thermal excitations of gapless quasi-one-dimensional waves of charge/spin density in the Luttinger liquid at temperatures below 60 K is examined. A continuous quantum phase transition of the quantum spin liquid into the Luttinger liquid state induced by an increase in the magnetic field intensity is found at temperatures around T=0. This transition has features typical of the formation of 1D-waves of charge/spin density induced by the confinement of spinon pairs and is accompanied by strong field hysteresis. Keywords: quantum spin liquid, Luttinger liquid, confinement of spinon pairs, spinon --- gauge field system, landau quantization, 1D-waves of charge/spin density, quantum oscillations.

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CAVADINI, N., CH RüEGG, A. FURRER, H. U. GüDEL, K. KRäMER, H. MUTKA, A. WILDES, K. HABICHT i P. VORDERWISCH. "TRIPLET MODES IN A QUANTUM SPIN LIQUID ACROSS THE CRITICAL FIELD". International Journal of Modern Physics B 16, nr 20n22 (30.08.2002): 3302–5. http://dx.doi.org/10.1142/s0217979202014243.

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S = 1/2 TlCuCl3 is a magnetic insulator with a singlet ground state and a finite spin gap to triplet excited states. At finite fields, the degeneracy of the triplet states is lifted according to the Zeeman interaction term. Field-induced magnetic ordering occurs in TlCuCl3 at the critical field Hc ~ 6 T , when the Zeeman interaction overcomes the spin gap at the antiferromagnetic zone center. A detailed characterization of the elementary excitations realized at H > Hc is obtained by means of inelastic neutron scattering on single crystals. The general framework of field-induced quantum criticality in a three-dimensional spin liquid is illustrated on the complete dynamic range for the first time.

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39

Jaubert, L. D. C. "Monopole Holes in a Partially Ordered Spin Liquid". SPIN 05, nr 02 (czerwiec 2015): 1540005. http://dx.doi.org/10.1142/s2010324715400056.

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If spin liquids have been famously defined by what they are not, i.e., ordered, the past years have seen the frontier between order and spin liquid starting to fade, with a growing number of materials whose low-temperature physics cannot be explained without co-existence of (partial) magnetic order and spin fluctuations. Here, we study an example of such co-existence in the presence of magnetic dipolar interactions, related to spin ice, where the order is long range and the fluctuations support a Coulomb gauge field. Topological defects are effectively coupled via energetic and entropic Coulomb interactions, the latter one being stronger than for the spin-ice ground state. Depending on whether these defects break the divergence-free condition of the Coulomb gauge field or the long-range order, they are respectively categorized as monopoles — as in spin ice — or monopole holes, in analogy with electron holes in semiconductors. The long-range order plays the role of a fully-occupied valence band, while the Coulomb spin liquid can be seen as an empty conducting band. These results are discussed in the context of other lattices and models which support a similar co-existence of Coulomb gauge field and long-range order. We conclude this work by explaining how dipolar interactions lift the spin-liquid degeneracy at very low energy scale by maximizing the number of flippable plaquettes, in light of the equivalent quantum dimer model.

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40

Semeghini, G., H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen i in. "Probing topological spin liquids on a programmable quantum simulator". Science 374, nr 6572 (3.12.2021): 1242–47. http://dx.doi.org/10.1126/science.abi8794.

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Synthesizing topological order Topologically ordered matter exhibits long-range quantum entanglement. However, measuring this entanglement in real materials is extremely tricky. Now, two groups take a different approach and turn to synthetic systems to engineer the topological order of the so-called toric code type (see the Perspective by Bartlett). Satzinger et al . used a quantum processor to study the ground state and excitations of the toric code. Semeghini et al . detected signatures of a toric code–type quantum spin liquid in a two-dimensional array of Rydberg atoms held in optical tweezers. —JS

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Du, Luojun, Yuan Huang, Yimeng Wang, Qinqin Wang, Rong Yang, Jian Tang, Mengzhou Liao i in. "2D proximate quantum spin liquid state in atomic-thin α -RuCl 3". 2D Materials 6, nr 1 (16.11.2018): 015014. http://dx.doi.org/10.1088/2053-1583/aaee29.

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Misumi, Yuki, Akira Yamaguchi, Zhongyue Zhang, Taku Matsushita, Nobuo Wada, Masahisa Tsuchiizu i Kunio Awaga. "Quantum Spin Liquid State in a Two-Dimensional Semiconductive Metal–Organic Framework". Journal of the American Chemical Society 142, nr 39 (4.07.2020): 16513–17. http://dx.doi.org/10.1021/jacs.0c05472.

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Takabayashi, Yasuhiro, Melita Menelaou, Hiroyuki Tamura, Nayuta Takemori, Takashi Koretsune, Aleš Štefančič, Gyöngyi Klupp i in. "π-electron S = ½ quantum spin-liquid state in an ionic polyaromatic hydrocarbon". Nature Chemistry 9, nr 7 (24.04.2017): 635–43. http://dx.doi.org/10.1038/nchem.2764.

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Sun, Gao-Yong, i Su-Peng Kou. "Quantum non-magnetic state near metal-insulator transition —A possible candidate of spin liquid state". EPL (Europhysics Letters) 87, nr 6 (1.09.2009): 67002. http://dx.doi.org/10.1209/0295-5075/87/67002.

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Arian Zad, Hamid, Azam Zoshki, Nerses Ananikian i Michal Jaščur. "Tomonaga–Luttinger Spin Liquid and Kosterlitz–Thouless Transition in the Spin-1/2 Branched Chains: The Study of Topological Phase Transition". Materials 15, nr 12 (13.06.2022): 4183. http://dx.doi.org/10.3390/ma15124183.

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In the present work, we provide a comprehensive numerical investigation of the magnetic properties and phase spectra of three types of spin-1/2 branched chains consisting of one, two and three side spins per unit block with intra-chain interaction and a uniform inter-chain interaction in the presence of an external magnetic field. In a specific magnetic field interval, the low-temperature magnetization of these chains shows a step-like behavior with a pronounced plateau depending on the strength and the type of intra-chain interaction being ferromagnetic or antiferromagnetic. We demonstrate that when inter-chain interaction J1 is antiferromagnetic and intra-chain interaction J2 is ferromagnetic, the magnetization of the models manifests a smooth increase without a plateau, which is evidence of the existence of a Luttinger-like spin liquid phase before reaching its saturation value. On the other hand, when J1 is ferromagnetic and J2 is antiferromagnetic, the low-temperature magnetization of the chain with two branches shows an intermediate plateau at one-half of the saturation magnetization that breaks a quantum spin liquid phase into two regions. The magnetization of the chain with three branches exhibits two intermediate plateaus and two regions of a quantum spin liquid. We demonstrate that the chains with more than one side spin illustrate in their ground-state phase diagram a Kosterlitz–Thouless transition from a gapful Lieb–Mattis phase to a gapless spin liquid phase.

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Schmidt, M. A., D. M. Silevitch, G. Aeppli i T. F. Rosenbaum. "Using thermal boundary conditions to engineer the quantum state of a bulk magnet". Proceedings of the National Academy of Sciences 111, nr 10 (24.02.2014): 3689–94. http://dx.doi.org/10.1073/pnas.1316070111.

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The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic-centimeter–sized crystals of the Ising magnet LiHoxY1-xF4 to a heat bath can be used to tune the system between a glassy state dominated by thermal excitations over energy barriers and a state with the hallmarks of a quantum spin liquid. Application of a magnetic field transverse to the Ising axis introduces both random magnetic fields and quantum fluctuations, which can retard and speed the annealing process, respectively, thereby providing a mechanism for continuous tuning between the destination states. The nonlinear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways.

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Pustogow, Andrej. "Thirty-Year Anniversary of κ-(BEDT-TTF)2Cu2(CN)3: Reconciling the Spin Gap in a Spin-Liquid Candidate". Solids 3, nr 1 (17.02.2022): 93–110. http://dx.doi.org/10.3390/solids3010007.

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In 1991 the layered organic compound κ-(BEDT-TTF)2Cu2(CN)3 with a triangular lattice was synthesized for the first time. Although, originally, the focus was on the superconducting properties under pressure, this frustrated Mott insulator has been the most promising quantum-spin-liquid candidate for almost two decades, widely believed to host gapless spin excitations down to T→0. The recent observation of a spin gap rules out a gapless spin liquid with itinerant spinons and puts severe constraints on the magnetic ground state. This review evaluates magnetic, thermal transport, and structural anomalies around T⋆=6 K. The opening of a spin gap yields a rapid drop of spin susceptibility, NMR Knight shift, spin-lattice relaxation rate, and μ-SR spin fluctuation rate, but is often concealed by impurity spins. The concomitant structural transition at T⋆ manifests in thermal expansion, THz phonons and 63Cu NQR relaxation. Based on the field dependence of T⋆, a critical field of 30–60 T is estimated for the underlying spin-singlet state. Overall, the physical properties are remarkably similar to those of spin-Peierls compounds. Thus, a strong case is made that the ‘6K anomaly’ in κ-(BEDT-TTF)2Cu2(CN)3 is the transition to a valence-bond-solid state and it is suggested that such a scenario is rather the rule than the exception in materials with strong magnetic frustration.

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Savary, Lucile. "Quantum loop states in spin-orbital models on the honeycomb lattice". Nature Communications 12, nr 1 (21.05.2021). http://dx.doi.org/10.1038/s41467-021-23033-y.

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AbstractThe search for truly quantum phases of matter is a center piece of modern research in condensed matter physics. Quantum spin liquids, which host large amounts of entanglement—an entirely quantum feature where one part of a system cannot be measured without modifying the rest—are exemplars of such phases. Here, we devise a realistic model which relies upon the well-known Haldane chain phase, i.e. the phase of spin-1 chains which host fractional excitations at their ends, akin to the hallmark excitations of quantum spin liquids. We tune our model to exactly soluble points, and find that the ground state realizes Haldane chains whose physical supports fluctuate, realizing both quantum spin liquid like and symmetry-protected topological phases. Crucially, this model is expected to describe actual materials, and we provide a detailed set of material-specific constraints which may be readily used for an experimental realization.

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Banerjee, Saikat, i Shi-Zeng Lin. "Emergent orbital magnetization in Kitaev quantum magnets". SciPost Physics 14, nr 5 (24.05.2023). http://dx.doi.org/10.21468/scipostphys.14.5.127.

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Unambiguous identification of the Kitaev quantum spin liquid (QSL) in materials remains a huge challenge despite many encouraging signs from various measurements. To facilitate the experimental detection of the Kiteav QSL, here we propose to use remnant charge response in Mott insulators hosting QSL to identify the key signatures of QSL. We predict an emergent orbital magnetization in a Kitaev system in an external magnetic field. The direction of the orbital magnetization can be flipped by rotating the external magnetic field in the honeycomb plane. The orbital magnetization is demonstrated explicitly through a detailed microscopic analysis of the multiorbital Hubbard-Kanamori Hamiltonian and also supported by a phenomenological picture. We first derive the localized electrical loop current operator in terms of the spin degrees of freedom. Thereafter, utilizing the Majorana representation, we estimate the loop currents in the ground state of the chiral Kitaev QSL state, and obtain the consequent current textures, which are responsible for the emergent orbital magnetization. Finally, we discuss the possible experimental techniques to visualize the orbital magnetization which can be considered as the signatures of the underlying excitations.

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Lin, Gaoting, Jaehong Jeong, Chaebin Kim, Yao Wang, Qing Huang, Takatsugu Masuda, Shinichiro Asai i in. "Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na2Co2TeO6". Nature Communications 12, nr 1 (21.09.2021). http://dx.doi.org/10.1038/s41467-021-25567-7.

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AbstractSpin-orbit coupled honeycomb magnets with the Kitaev interaction have received a lot of attention due to their potential of hosting exotic quantum states including quantum spin liquids. Thus far, the most studied Kitaev systems are 4d/5d-based honeycomb magnets. Recent theoretical studies predicted that 3d-based honeycomb magnets, including Na2Co2TeO6 (NCTO), could also be a potential Kitaev system. Here, we have used a combination of heat capacity, magnetization, electron spin resonance measurements alongside inelastic neutron scattering (INS) to study NCTO’s quantum magnetism, and we have found a field-induced spin disordered state in an applied magnetic field range of 7.5 T < B (⊥ b-axis) < 10.5 T. The INS spectra were also simulated to tentatively extract the exchange interactions. As a 3d-magnet with a field-induced disordered state on an effective spin-1/2 honeycomb lattice, NCTO expands the Kitaev model to 3d compounds, promoting further interests on the spin-orbital effect in quantum magnets.

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