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Finite-temperature properties of the anisotropic AFM Kitaev model in the magnetic field

S.L. Jia, Ya‐Min Quan, Hai‐Qing Lin, Liang‐Jian Zou

Published Apr 27, 2021• 0 citations
OpenAlex

Abstract

We investigate the quantum spin liquid (QSL) ground state of anisotropic Kitaev model with antiferromagnetic (AFM) coupling under the $[001]$ magnetic field with the finite-temperature Lanczos method (FTLM). In this anisotropic AFM Kitaev model with $K_{X}=K_{Y}$, $K_{X}+K_{Y}+K_{Z}=-3K$, and $K_{Z}<-K$, with magnetic field increasing, the gapped QSL experiences a transition to a gapless QSL at $h_{c1}=g\mu_{B}H_{z1}/K$, to another gapless QSL with $C_{6}$ rotational symmetry at $h_{c2}$, and to a new $U(1)$ gapless QSL between $h_{c3}$ and $h_{c4}$, respectively. These indicate that magnetic field could first turn the anisotropic gapped or gapless QSL back into the isotropic $C_{6}$ gapless one and then make it to undergo the similar evolution as the isotropic case. Moreover, the critical magnetic fields $h_{c1}$, $h_{c2}$, $h_{c3}$, and $h_{c4}$ come up monotonically with the increasing Kitaev coupling; this suggests that the magnetic field can be applied to the modulation of the anisotropic Kitaev materials.

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We investigate the quantum spin liquid (QSL) ground state of anisotropic Kitaev model with antiferromagnetic (AFM) coupling under the [001][001][001] magnetic field with the finite-temperature Lanczos method (FTLM). In this anisotropic AFM Kitaev model with KX=KYK_{X}=K_{Y}KX​=KY​, KX+KY+KZ=−3KK_{X}+K_{Y}+K_{Z}=-3KKX​+KY​+KZ​=−3K, and KZ<−KK_{Z}<-KKZ​<−K, with magnetic field increasing, the gapped QSL experiences a transition to a gapless QSL at hc1=gμBHz1/Kh_{c1}=g\mu_{B}H_{z1}/Khc1​=gμB​Hz1​/K, to another gapless QSL with C6C_{6}C6​ rotational symmetry at hc2h_{c2}hc2​, and to a new U(1)U(1)U(1) gapless QSL between hc3h_{c3}hc3​ and hc4h_{c4}hc4​, respectively. These indicate that magnetic field could first turn the anisotropic gapped or gapless QSL back into the isotropic C6C_{6}C6​ gapless one and then make it to undergo the similar evolution as the isotropic case. Moreover, the critical magnetic fields hc1h_{c1}hc1​, hc2h_{c2}hc2​, hc3h_{c3}hc3​, and hc4h_{c4}hc4​ come up monotonically with the increasing Kitaev coupling; this suggests that the magnetic field can be applied to the modulation of the anisotropic Kitaev materials.
Abstract The evolution of quantum spin liquid states (QSL) of the anisotropic antiferromagnetic (AFM) Kitaev model with the [001] magnetic field by utilizing the finite‐temperature Lanczos method (FTLM) is investigated. In this anisotropic Kitaev model with and (K is the energy unit), due to the competition between anisotropy and magnetic field, the system emerges four exotic quantum phase transitions (QPTs) when and , while only two QPTs when . At these magnetic‐field tuning quantum phase transition points, the low‐energy excitation spectrums appear level crossover, and the specific heat, magnetic susceptibility and Wilson ratio display anomalies; accordingly, the topological Chern number may also change. These results demonstrate that the anisotropic interacting Kitaev model with modulating magnetic field displays more rich phase diagrams, in comparison with the isotropic Kitaev model.
Recent experimental evidence for a field-induced quantum spin liquid (QSL) in ααα-RuCl3_33​ calls for an understanding for the ground state of honeycomb Kitaev model under a magnetic field. In this work we address the nature of an enigmatic gapless paramagnetic phase in the antiferromagnetic Kitave model, under an intermediate magnetic field perpendicular to the plane. Combining theoretical and numerical efforts, we identify this gapless phase as a U(1)U(1)U(1) QSL with spinon Fermi surfaces. We also reveal the nature of continuous quantum phase transitions involving this U(1)U(1)U(1) QSL, and obtain a phase diagram of the Kitaev model as a function of bond anisotropy and perpendicular magnetic field.
The Kitaev model with an applied magnetic field in the [Formula: see text] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at [Formula: see text] and a second transition at a higher field [Formula: see text] to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function [Formula: see text] and the Fermi surface [Formula: see text] of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.
Motivated by the three-dimensional structure of Kitaev materials we explore multilayer Kitaev models. The magnetic properties of a multilayer of an arbitrary number of Kitaev honeycomb layers stacked on top of each other coupled through a Heisenberg interaction, J, is analyzed through Abrikosov fermion mean-field theory. The system sustains quantum spin liquid (QSL) solutions which have different character depending on parity of the number of layers. While in even layered Kitaev models a gapped QSL emerges, odd-layered models host gapless QSLs. The projective symmetry group analysis of these solutions unravel a layer-to-layer inversion symmetry rather than an expected reflection. Although these QSLs retain features of the single layer Kitaev spin liquid (KSL), they should be regarded hybrid QSLs consisting on several KSLs. The good agreement at large-J between the energy of the Gutzwiller projected mean-field QSL and the exact energy indicates that such QSL Ansatz is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of alpha-RuCl3 and H3LiIr2O6 which are examples of magnetically coupled multilayer Kitaev models.
Kitaev-derived Gapless Spin Liquid in the KKK-JJJ-ΓΓΓ-Γ′Γ'Γ′ Quantum Magnet Na2_22​Co2_22​TeO6_66​
The realization of quantum spin liquids (QSLs) in Kitaev magnets represents an intriguing topic in frustrated quantum magnetism. Despite prediction in the pure Kitaev honeycomb model, realization of QSLs in realistic systems and materials remain scarce. The recent discovery of cobalt-based compound Na2_22​Co2_22​TeO6_66​ has raised significant research interest. By establishing a realistic KKK-JJJ-ΓΓΓ-Γ′Γ'Γ′ model for Na2_22​Co2_22​TeO6_66​ -- with a dominant antiferromagnetic (AFM) Kitaev interaction (K>0K>0K>0) that quantitatively explains its thermodynamics measurements -- we reveal an intermediate gapless QSL phase under [111] magnetic fields with tensor-network calculations. We confirm the QSL nature of this phase by demonstrating its adiabatic connection to the intensively studied intermediate QSL of the pure AFM Kitaev model under out-of-plane fields. Our results show excellent agreement with recent high-field experiments, thereby explaining the intermediate-field phase in Na2_22​Co2_22​TeO6_66​. These findings bridge the gap between theoretical proposals for a Kitaev-derived QSL and experimental realization, opening new avenues for exploring exotic quantum states of matter in realistic Kitaev materials.
Motivated by the three-dimensional structure of Kitaev materials we explore multilayer Kitaev models. The magnetic properties of a multilayer with an arbitrary number of Kitaev honeycomb layers stacked on top of each other coupled through a Heisenberg interaction JJJ is analyzed through Abrikosov fermion mean-field theory. We find quantum spin liquid (QSL) solutions which are gapped (ungapped) for even (odd) number of layers. The presence (absence) of the gap in even- (odd-) layered systems is associated with the spontaneous breaking (nonbreaking) of the inversion symmetry of the multilayer by the mean-field QSL solution. The good agreement between the Gutzwiller projected mean-field energy and the exact energy at large JJJ indicates that our QSL solution is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and H3LiIr2O6{\mathrm{H}}_{3}{\mathrm{LiIr}}_{2}{\mathrm{O}}_{6}H3​LiIr2​O6​ which are examples of magnetically coupled multilayer Kitaev models.