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arXiv:1908.07671 · Nature Communications

Magnetic field induced quantum phases in a tensor network study of Kitaev magnets

Hyun‐Yong Lee, Ryui Kaneko, Li Ern Chern, Tsuyoshi Okubo, Youhei Yamaji, Naoki Kawashima, Yong Baek Kim

Published Apr 2, 2020• 95 citations
arXivHTMLPDF

Abstract

Recent discovery of the half quantized thermal Hall conductivity in [Formula: see text]-RuCl[Formula: see text], a candidate material for the Kitaev spin liquid, suggests the presence of a highly entangled quantum state in external magnetic fields. This field induced phase appears between the low field zig-zag magnetic order and the high field polarized state. Motivated by this experiment, we study possible field induced quantum phases in theoretical models of the Kitaev magnets, using the two dimensional tensor network approach or infinite tensor product states. We find various quantum ground states in addition to the chiral Kitaev spin liquid occupying a small area in the phase diagram. They form a band of emergent quantum phases in an intermediate window of external magnetic fields, somewhat reminiscent of the experiment. We discuss the implications of these results in view of the experiment and previous theoretical studies.

DOI
10.1038/s41467-020-15320-x

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Abstract Elementary excitations in entangled states such as quantum spin liquids may exhibit exotic statistics different from those obeyed by fundamental bosons and fermions. Non-Abelian anyons exist in a Kitaev spin liquid—the ground state of an exactly solvable model. A smoking-gun signature of these excitations, namely a half-integer quantized thermal Hall conductivity, was recently reported in α-RuCl3. While fascinating, a microscopic theory for this phenomenon remains elusive because the pure Kitaev model cannot display this effect in an intermediate magnetic field. Here we present a microscopic theory of the Kitaev spin liquid emerging between the low- and high-field states. Essential to this result is an antiferromagnetic off-diagonal symmetric interaction which allows the Kitaev spin liquid to protrude from the ferromagnetic Kitaev limit under a magnetic field. This generic model displays a strong field anisotropy, and we predict a wide spin liquid regime when the field is perpendicular to the honeycomb plane.

•Jan 1, 2019•104 citations
Recent discovery of the half quantized thermal Hall conductivity in [Formula: see text]-RuCl[Formula: see text], a candidate material for the Kitaev spin liquid, suggests the presence of a highly entangled quantum state in external magnetic fields. This field induced phase appears between the low field zig-zag magnetic order and the high field polarized state. Motivated by this experiment, we study possible field induced quantum phases in theoretical models of the Kitaev magnets, using the two dimensional tensor network approach or infinite tensor product states. We find various quantum ground states in addition to the chiral Kitaev spin liquid occupying a small area in the phase diagram. They form a band of emergent quantum phases in an intermediate window of external magnetic fields, somewhat reminiscent of the experiment. We discuss the implications of these results in view of the experiment and previous theoretical studies.
There has been great interest in identifying a Kitaev quantum spin liquid state in frustrated magnets with bond-dependent interactions. In particular, the experimental report of a half-quantized thermal Hall conductivity in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in the presence of a magnetic field has generated excitement as it could be strong evidence for a field-induced chiral spin liquid. More recent experiments, however, provide a conflicting interpretation advocating for topological magnons in the field-polarized state as the origin of the nonquantized thermal Hall conductivity observed in their experiments. An inherent difficulty in distinguishing between the two scenarios is that the phase transition between a putative two-dimensional spin liquid and the field-polarized state exists only at zero temperature, while the behavior at finite temperature is mostly crossover phenomena. In this work, we provide insights into the finite-temperature crossover behavior between the spin excitation continuum in a quantum spin liquid and topological magnons in the field-polarized state in three different theoretical models with large Kitaev interactions. These models allow for a field-induced phase transition from a spin liquid (or an intermediate field-induced spin liquid) to the field-polarized state in the quantum model. We obtain the dynamical spin structure factor as a function of magnetic field using molecular dynamics simulations and compute thermal Hall conductivity in the field-polarized regime. We demonstrate the gradual evolution of the dynamical spin structure factor exhibiting crossover behavior near magnetic fields where zero-temperature phase transitions occur in the quantum model. We also examine nonlinear effects on topological magnons and the validity of thermal Hall conductivity computed using linear spin wave theory. We discuss the implications of our results for existing and future experiments.
Abstract The S = 1/2 Kitaev honeycomb model has attracted significant attention as an exactly solvable example with a quantum spin liquid ground state. In an properly oriented external magnetic field, the system exhibits chiral Majorana edge modes with an associated quantized thermal Hall conductance, and a distinct spin-disordered phase emerges at intermediate field strengths, below the polarized phase. However, since material realizations of Kitaev magnetism invariably display competing exchange interactions, the stability of these exotic phases with respect to additional couplings is a key issue. Here, we report a 24-site exact diagonalization study of the Heisenberg-Kitaev model in a magnetic field applied in the [001] and [111] directions. By mapping the full phase diagram of the model and contrasting the results to recent nonlinear spin-wave calculations, we show that both methods agree well, thus establishing that quantum corrections substantially modify the classical phase diagram. Furthermore, we find that, in a [111] field, the intermediate-field spin-disordered phase is remarkably stable to Heisenberg interactions and may potentially end in a novel quantum tricritical point.
Kitaev magnets have emerged as pivotal systems for investigating frustrated magnetism, providing a unique platform to explore quantum phases governed by the interplay between bond-dependent anisotropy and external magnetic fields. However, the quantum phase diagrams, particularly near the dominant antiferromagnetic Kitaev regime, remain puzzling despite extensive studies. In this work, we perform unbiased exact diagonalization calculations of the Kitaev-ΓΓΓ model in a [111] magnetic field on a C6C_{6}C6​-symmetric 24-site cluster. By calculating the Z2\mathbb{Z}_2Z2​ flux density and the topological entanglement entropy, we reveal multiple phase transitions and identify signatures of both scalar and vector chiral orders in the intermediate-field regime between the Kitaev spin liquid and the polarized phase. As the negative ΓΓΓ interaction increases, we discover a proximate quantum spin liquid featured by a three-peak specific heat and a spin-flop phase at a moderate magnetic field. Our findings provide insight into the field-induced intermediate phases in the antiferromagnetic Kitaev model and pave the way for the hunt for emergent phases in real materials.
The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological Z2{\mathbb{Z}}_{2}Z2​ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic field is at present, a subject of intense scrutiny due to recent experimental signatures pointing to a Z2{\mathbb{Z}}_{2}Z2​ topological phase in certain materials, as well as theoretical studies predicting the emergence of a quantum spin liquid phase of debated nature. In this work, we employ hierarchical mean-field theory, a method based on the use of clusters preserving relevant symmetries and short-range quantum correlations, to investigate the quantum phase diagram of the antiferromagnetic Kitaev's model in a [111] magnetic field. By using clusters of 24 sites, we predict that the Kitaev spin liquid transits through two intermediate phases, characterized by emerging stripe and chiral orders, respectively, before entering the trivial partially polarized phase, differing from previous studies. We assess our results by performing exact diagonalization and computing the scaling of different observables, including the many-body Chern number and other topological quantities, thus establishing hierarchical mean-field theory as a method to study models of frustrated quantum magnetism potentially hosting topological quantum spin liquids.
Abstract Elementary excitations in entangled states such as quantum spin liquids may exhibit exotic statistics different from those obeyed by fundamental bosons and fermions. Non-Abelian anyons exist in a Kitaev spin liquid—the ground state of an exactly solvable model. A smoking-gun signature of these excitations, namely a half-integer quantized thermal Hall conductivity, was recently reported in α-RuCl3. While fascinating, a microscopic theory for this phenomenon remains elusive because the pure Kitaev model cannot display this effect in an intermediate magnetic field. Here we present a microscopic theory of the Kitaev spin liquid emerging between the low- and high-field states. Essential to this result is an antiferromagnetic off-diagonal symmetric interaction which allows the Kitaev spin liquid to protrude from the ferromagnetic Kitaev limit under a magnetic field. This generic model displays a strong field anisotropy, and we predict a wide spin liquid regime when the field is perpendicular to the honeycomb plane.
Abstract Elementary excitations in entangled states such as quantum spin liquids may exhibit exotic statistics different from those obeyed by fundamental bosons and fermions. Non-Abelian anyons exist in a Kitaev spin liquid—the ground state of an exactly solvable model. A smoking-gun signature of these excitations, namely a half-integer quantized thermal Hall conductivity, was recently reported in α-RuCl3. While fascinating, a microscopic theory for this phenomenon remains elusive because the pure Kitaev model cannot display this effect in an intermediate magnetic field. Here we present a microscopic theory of the Kitaev spin liquid emerging between the low- and high-field states. Essential to this result is an antiferromagnetic off-diagonal symmetric interaction which allows the Kitaev spin liquid to protrude from the ferromagnetic Kitaev limit under a magnetic field. This generic model displays a strong field anisotropy, and we predict a wide spin liquid regime when the field is perpendicular to the honeycomb plane.