Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session N51: Kitaev Spin Liquid: TheoryFocus Recordings Available
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Sponsoring Units: GMAG DCMP Chair: Peter Stavropoulos, University of Minnesota Room: McCormick Place W-474B |
Wednesday, March 16, 2022 11:30AM - 11:42AM |
N51.00001: Measuring quantum entanglement in Kitaev quantum spin liquid Yanjun He, Shi Feng, Nandini Trivedi Quantum spin liquids possess long-ranged entangled topological order without symmetry breaking. Quantum entanglement is a fundamental property of the many body ground state wave function; it is however not directly measurable. In this work, our aim is to connect quantum entanglement with physical observables in the paradigmatic Kitaev spin liquid on a honeycomb lattice. Our central result is to show that through physical observables, we can reconstruct the quantum entanglement entropy. Furthermore, we show that both the entanglement entropy and the correlators capture the non-analytic behavior at quantum phase transitions at and away from the exactly solvable points when tuned by a magnetic field and by anisotropy of the bond interaction. Through this work, we provide a more intuitive understanding of quantum entanglement and highlight its role in detecting quantum phase transitions. |
Wednesday, March 16, 2022 11:42AM - 11:54AM |
N51.00002: Field-revealed gapless spin liquid and hidden chiral order in a hierarchical mean-field theory study of an extended Kitaev honeycomb model William Holdhusen, Daniel Huerga, Gerardo Ortiz The Kitaev honeycomb model is an emblematic example of a topologically ordered quantum spin liquid. Due to its exact solvability, the model provides a benchmark for evaluating the success of numerical methods that can be applied to nonintegrable models with similar behaviors. In this work, we apply hierarchical mean-field theory (HMFT) to the Kitaev model and its nonintegrable extensions. HMFT is a cluster mean-field theory that has been shown to accurately capture the thermodynamic limit phase diagrams of frustrated magnetic systems in an unbiased manner using minimal computational resources. In applying it to the Kitaev model, we provide the first example of the technique’s success in modeling a gapless topologically ordered system, as well as unveil a potential hidden chiral order in the model via controlled symmetry breaking. In addition, we apply HMFT to the model in the presence of a strong magnetic field, found in previous work to have a potential U(1) gapless spin liquid phase. The previous results were obtained via exact-diagonalization on small clusters and density-matrix renormalization group on thin strips. Both geometries present difficulties in extrapolating to a full two-dimensional infinite system, while this information is inherently captured by our HMFT study. |
Wednesday, March 16, 2022 11:54AM - 12:06PM |
N51.00003: On-demand anyon generation in Kitaev honeycomb non-Abelian spin liquids Yue Liu, Kevin Slagle, Kenneth S Burch, Jason F Alicea Spin-orbit-coupled Mott insulators known as 'Kitaev materials' provide possible realizations of spin liquids hosting non-Abelian anyons. Motivated by fault-tolerant quantum-computing applications in this setting, we introduce a dynamical anyon-generation protocol that exploits universal edge physics. The setup features holes in the spin liquid, which define energetically cheap locations for non-Abelian anyons, connected by a narrow bridge that can be tuned between spin liquid and trivial phases. We show that modulating the bridge from trivial to spin liquid over intermediatetime scales—quantified by analytics and extensive simulations—deposits non-Abelian anyons into the holes with O(1) probability. The required bridge manipulations are enabled by coupling the Kitaev material to locally tunable ferromagnets that engender the Zeeman field required to stabilize the non-Abelian spin liquid. Combined with existing readout strategies, our protocol reveals a path to topological qubit experiments in Kitaev materials at zero applied magnetic field. |
Wednesday, March 16, 2022 12:06PM - 12:18PM |
N51.00004: Nonlinear response of Kitaev spin model on square-octagon lattice Yihua Qiang, Victor L Quito, Thais V Trevisan, Peter P Orth Quantum computing promises to significantly accelerate research in materials discovery, characterization, and understanding. Simulations of correlated quantum spin systems and their dynamics are a primary application since such simulations are difficult on classical computers. Here, we focus on the computation of nonlinear correlation functions in frustrated quantum spin systems and perform a purely classical first benchmarking calculation in the Kitaev model on the square-octagon lattice. We show how the information contained in the nonlinear response functions allows distinguishing between different types of fractionalized excitations in the system, which we identify as a suitable target for future calculations of nonlinear response functions using quantum computers. |
Wednesday, March 16, 2022 12:18PM - 12:30PM |
N51.00005: Dynamic properties of Kitaev Materials from time-dependent Majorana mean-field theory Tessa Cookmeyer, Joel E Moore Recent years have seen a rapid increase in candidate "Kitaev materials"--potentially realizing the same gapless spin-liquid ground state as the exactly solvable Kitaev model on the honeycomb lattice. The solubility stems from rewriting the spins in terms of Majorana fermions leading naturally to a mean-field description that could be valid even in the presence of perturbations (e.g. magnetic field, Heisenberg coupling, etc.). Since real materials have such perturbations, computing their effect on observables may indicate which features survive and which will not. We show how time-dependent Majorana mean-field theory can be used to compute dynamical quantities directly, which agree with exact results at the Kitaev point, thereby potentially providing exact results in a neighborhood of parameter space around the Kitaev point. |
Wednesday, March 16, 2022 12:30PM - 12:42PM |
N51.00006: Kitaev spin-orbital bilayers and their moiré superlattices Onur Erten, Emilian M Nica, Muhammad Akram, Aayush Vijayvargia We study the phase diagram of bilayer, SU(2) invariant Kitaev spin-orbital models on a honeycomb lattice with interlayer Heisenberg exchange couplings, for different stacking orders and their moiré superlattices. In the absence of interlayer exchange, each layer is in a gapless spin-liquid phase with three flavors of Majorana excitations. The interlayer exchange commutes with the intralayer flux operators and preserves the topological order for weak interactions. We show that for AA stacking, the model maps onto a SU(3) Hubbard model with complex fermions where the sign of the Hubbard coupling U is positive or negative for ferromagnetic or antiferromagnetic exchange couplings, respectively. The Hubbard model has a charge density wave instability for finite negative U. We show that this instability is associated with a mirror symmetry breaking and that it corresponds to a gapped abelian spin liquid state in the Kitaev bilayer. For AB stacking, the Kitaev bilayer does not map onto a simple Hubbard model. Here, the exchange coupling induces an effective interlayer hybridization and the Majorana spectrum resembles that of bilayer graphene with quadratic band touching. We also study the bilayer model with twisting and discuss how its instabilities evolve with twist angle. Our study provides insight into the stability of the abelian spin-liquid phases in candidate bilayer spin-orbital Kitaev materials. |
Wednesday, March 16, 2022 12:42PM - 1:18PM |
N51.00007: Quantum phase transitions of extended Kitaev Model Invited Speaker: Shang-Shun Zhang The Kitaev model is a rare example which is an exactly solvable model of a spin liquid state and also has many candidate materials that contain the required bond-dependent Ising-like interaction. Although most of candidate materials become magnetic ordered at the lowest temperature under experimental conditions, anomalous observations supporting the Kitaev spin liquid are reported when an external magnetic field is applied. Therefore, these Kitaev materials are speculated to be in proximity to the spin liquid phase and can be driven to this liquid phase under external field. In this talk, I will discuss the phase transitions between these distinct states induced by various types of interactions or magnetic fields through a variational scheme. This approach becomes exact in the pure Kitaev limit and is highly relevant to materials with dominant Kitaev interactions. Under different types of perturbations, it successfully describes the quantum phase transitions from the (pure) Kitaev spin liquid to various magnetic orderings via the condensation of preformed bound states of fractional particles or several distinct Abelian spin liquids via a topological phase transition. Given the good agreement with the existing numerical studies, this variational approach provides us with valuable insights about the Kitaev materials. |
Wednesday, March 16, 2022 1:18PM - 1:30PM |
N51.00008: The Phase Diagram of Kitaev Models under Arbitrary Magnetic Field Strengths and Orientations Firat Yilmaz, Arno P Kampf, Sungkit Yip The Kitaev model is an exactly solvable bon anisotropic spin model within the real fermion language. In spite of numerous studies along special field directions such as [001] and [111], there are is a limited knowledge on the complete field angle dependence of the thermal Hall current, which can provide valuable information on the existence of fractionalization. To fulfill this purpose, we first extend the present studies on the field angle response of the anti/ferromagnetic Kitaev. Yet, the realistic Kitaev materials, within the edgesharing octahedra paradigm, arise with the additional exchange terms. The studies on the candidate materials indicates the presence of a large spin-orbit Γ term along with perturbative Γ' and the Heisenberg J terms. It is therefore not reliable to depend on the topological properties of the pure Kitaev model as the only source of the thermal Hall conductivity experiments and it demands an understanding of these models with a complete field response. |
Wednesday, March 16, 2022 1:30PM - 1:42PM |
N51.00009: Electric-field control of magnetic anisotropies: application to Kitaev spin liquids Shunsuke Furuya, Masahiro Sato Magnetic anisotropies are a direct descendent of the spin-orbit coupling. Recently, magnetic anisotropies have enjoyed renewed theoretical and experimental interests for their essential roles in topological states of magnetic materials such as Kitaev spin liquids. Kitaev spin liquids show interesting phenomena under external fields. For example, DC magnetic fields can generate the Majorana mass gap in the Kitaev spin liquid. The Kitaev material under magnetic fields thus behaves as a Majorana Chern insulator accompanied by quantized thermal edge currents. The Chern number depends on non-Kitaev interactions such as off-diagonal symmetric magnetic anisotropies. This presentation discusses a microscopic quantum theory of DC electric-field controls of magnetic anisotropies in Kitaev materials. Our theoretical framework is generic and applicable to a broad class of magnetic Mott insulators. When applied to Kitaev materials, our microscopic theory predicts that the DC electric field controls the off-diagonal symmetric magnetic anisotropy and an antisymmetric one (the Dzyaloshinskii-Moriya interaction). |
Wednesday, March 16, 2022 1:42PM - 1:54PM |
N51.00010: S=3/2 Chiral Kitaev Spin Liquid induced by out-of-plane single ion anisotropy Willian M Natori The Kitaev honeycomb model (KHM) has a unique place in quantum magnetism due to its importance in the theory of quantum spin liquids, topological computation and material science. Routes to implement higher spin KHMs in solid-state platforms revived the interest in theoretical studies on this model's characterization for S>1/2, which do not possess an exact solution. In a previous work, we constructed a parton mean-field theory (PMFT) to unveil the ground state of the S=3/2 KHM that displayed a remarkable quantitative agreement with the results of DMRG simulations [1]. In this work, we propose a PMFT that includes the effects of an out-of-plane single ion anisotropy perturbation on the S=3/2 KHM [2]. We show how this anisotropy induces a flux-conserving three-spin-orbital interaction that induces an octupolar order corresponding to a form of orbital ferromagnetism. The onset of such an order also characterizes a chiral spin liquid (CSL) phase, which displays a half-integer thermal Hall conductivity peak. Possible implementations of this CSL on van der Waals monolayers are discussed by the end of the talk. |
Wednesday, March 16, 2022 1:54PM - 2:06PM Withdrawn |
N51.00011: Tensor network studies of thermal Hall transport in Kitaev-Heisenberg model. Aman Kumar The honeycomb lattice Mott insulating systems such as α–RuCl3, have emerged as candidates for realizing the Kitaev spinons. Motivated by the experimental observation of quantized (likely half-integer) thermal Hall conductivity α–RuCl3, we study the thermal Hall conductivity of a nonintegrable Kitaev-Heisenberg model numerically, using tensor network techniques. Our tensor network analysis uses the purification method to represent mixed quantum states at finite temperature as pure states on an enlarged Hilbert space carrying both phyical and ancilla sites. We compare our findings with reported quantized thermal Hall conductivity results. We also study the topological entanglement entropy - a measure of topological order - as a function of the model parameters. Our study confirms continued persistence of topological order deep in the spin density wave order phase. |
Wednesday, March 16, 2022 2:06PM - 2:18PM |
N51.00012: Thermal transport in the Kitaev spin liquid under a staggered magnetic field Kazuki Nakazawa, Yasuyuki Kato, Yukitoshi Motome Many studies have been conducted to detect Majorana fermions as fractional spin excitations in the Kitaev spin liquids. For instance, the half-quantized thermal Hall effect was observed as evidence of the Majorana Chern insulator under a magnetic field [1]. Recently, engineering of the Majorana excitation spectrum was investigated [2], which would also help to identify the fractionalizations, but how to probe the modulated spectrum is yet to be fully clarified. In this talk, we study the Kitaev honeycomb model in both uniform and staggered magnetic fields which shows an asymmetric Majorana spectrum in momentum space. We show that the linear thermal current changes with the magnitudes and directions of the magnetic fields, reflecting the modulation of the Majorana spectrum. In addition, we find that the nonlinear (nonreciprocal) thermal current is induced by the asymmetry of the spectrum and also varies with the magnetic fields. We discuss the estimates of the thermal currents in a realistic situation and the possible experimental setup. [1] Y. Kasahara et al., Nature 559, 227 (2018); T. Yokoi et al., Science 373, 568 (2021). [2] D. Takikawa and S. Fujimoto, Phys. Rev. B 99, 224409 (2019); R. Chari, R. Moessner, and J. G. Rau, Phys. Rev. B 103, 134444 (2021). |
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