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arXiv:1809.08247

Field induced quantum spin liquid with spinon Fermi surfaces in the Kitaev model

Hong‐Chen Jiang, Chang-Yan Wang, Biao Huang, Yuan-Ming Lu

Published Sep 21, 2018• 21 citations
arXivHTMLPDF

Abstract

Recent experimental evidence for a field-induced quantum spin liquid (QSL) in $α$-RuCl$_3$ 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 $U(1)$ QSL with spinon Fermi surfaces. We also reveal the nature of continuous quantum phase transitions involving this $U(1)$ QSL, and obtain a phase diagram of the Kitaev model as a function of bond anisotropy and perpendicular magnetic field.

DOI
10.48550/arxiv.1809.08247

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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.
The pursuit of quantum spin liquid (QSL) in the Kitaev honeycomb magnets has drawn intensive attention recently. In particular, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ has been widely recognized as a promising candidate for the Kitaev QSL. Although the compound exhibits an antiferromagnetic order under zero field, it is believed to be endowed with fractionalized excitations and can be driven to the QSL phase by magnetic fields. Here, based on a realistic $K\text{\ensuremath{-}}J\text{\ensuremath{-}}\mathrm{\ensuremath{\Gamma}}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ model for $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$, we exploit the exponential tensor renormalization group approach to explore the phase diagram of the compound under magnetic fields. We calculate the thermodynamic quantities, including the specific heat, Gr\"uneisen parameter, magnetic torque, magnetotropic susceptibility, and so on, under a magnetic field with a tilting angle $\ensuremath{\theta}$ to the c∗{c}^{*}c∗-axis perpendicular to the honeycomb plane. We find an extended QSL in the angle-field phase diagram determined with thermodynamic responses. The gapless nature of such field-induced QSL is identified from the specific heat and entropy data computed down to very low temperatures. The present study provides guidance for future high-field experiments for the QSL in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and other candidate Kitaev magnets.
Abstract Pursuing the exotic quantum spin liquid (QSL) state in the Kitaev material α-RuCl3 has intrigued great research interest recently. A fascinating question is on the possible existence of a field-induced QSL phase in this compound. Here we perform high-field magnetization measurements of α-RuCl3 up to 102 T employing the non-destructive and destructive pulsed magnets. Under the out-of-plane field along the c* axis (i.e., perpendicular to the honeycomb plane), two quantum phase transitions are uncovered at respectively 35 T and about 83 T, between which lies an intermediate phase as the predicted QSL. This is in sharp contrast to the case with in-plane fields, where a single transition is found at around 7 T and the intermediate QSL phase is absent instead. By measuring the magnetization data with fields tilted from the c* axis up to 90° (i.e., in-plane direction), we obtain the field-angle phase diagram that contains the zigzag, paramagnetic, and QSL phases. Based on the K-J-Γ- Γ′{{{\Gamma }}}^{{\prime} }Γ′ Γ ′ model for α-RuCl3 with a large Kitaev term we perform density matrix renormalization group simulations and reproduce the quantum phase diagram in excellent agreement with experiments.
Recently considerable excitement has arisen due to the experimental observation of a field-induced spin liquid phase in the compound $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. However, the nature of this putative spin liquid phase and the relevant microscopic model Hamiltonian remain still unclear. In this work, we address these questions by performing large-scale numerical simulations of a generalized Kitaev-Heisenberg model proposed to describe the physics of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. While an intermediate phase does not appear for in-plane magnetic fields, our results strongly suggest that a stable intermediate spin liquid phase, sandwiched between a magnetically ordered phase at low fields and a high-field polarized phase, can be induced by out-of-plane magnetic fields. Moreover, we show that this field-induced spin liquid phase can be smoothly connected to a spin liquid possessing a spinon Fermi surface as proposed recently for the Kitaev model. The relevance of our results to $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ is also discussed.
In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of [Formula: see text] quantum spin liquids. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional interactions and, in the presence of magnetic fields, exhibit no indications of long-range order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless U(1) gauge field. We discuss its stability in the presence of perturbations that naturally arise in spin-orbit entangled candidate materials.
Quantum spin liquids are exotic states of matter that may be realized in frustrated quantum magnets and feature fractionalized excitations and emergent gauge fields. Here we consider a gapless U(1) spin liquid with spinon Fermi pockets in two spatial dimensions. Such a state appears to be the most promising candidate to describe the exotic field-induced behavior observed in numerical simulations of the antiferromagnetic Kitaev honeycomb model. A similar such state may also be responsible for the recently reported quantum oscillations of the thermal conductivity in the field-induced quantum paramagnetic phase of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. We consider the regime close to a Lifshitz transition, at which the spinon Fermi pockets shrink to small circles around high-symmetry points in the Brillouin zone. By employing renormalization group and mean-field arguments, we demonstrate that interactions lead to a gap opening in the spinon spectrum at low temperatures, which can be understood as a nesting instability of the spinon Fermi surface. This leads to proliferation of monopole operators of the emergent U(1) gauge field and confinement of spinons. While signatures of fractionalization may be observable at finite temperatures, the gapless U(1) spin liquid state with nested spinon Fermi pockets is ultimately unstable at low temperatures towards a conventional long-range-ordered ground state, such as a valence bond solid. Implications for Kitaev materials in external magnetic fields are discussed.