Universal Thermodynamics in the Kitaev Fractional Liquid

Abstract

In the Kitaev honeycomb model, the quantum spin fractionalizes into itinerant Majorana and gauge flux spontaneously upon cooling, leading to rich experimental ramifications at finite temperature and an upsurge of research interest. In this work, we employ the exponential tensor renormalization group approach to explore the Kitaev model under various perturbations, including the external fields, Heisenberg, and the off-diagonal couplings that are common in the Kitaev materials. Through large-scale manybody calculations, we find a Kitaev fractional liquid at intermediate temperature that is robust against perturbations. The fractional liquid exhibits universal thermodynamic behaviors, including the fractional thermal entropy, metallic specific heat, and an intermediate-temperature Curie law of magnetic susceptibility. The emergent universal susceptibility behavior, with a modified Curie constant, can be ascribed to the strongly fluctuating ${\mathbb{Z}}_2$ fluxes as well as the extremely short-ranged and bond-directional spin correlations. With this insight, we revisit the susceptibility measurements of Na${}_2$IrO${}_3$ and $\alpha$-RuCl${}_3$, and find evident signatures of finite-temperature fractionalization and ferromagnetic Kitaev couplings. Moreover, the peculiar spin correlation in the fractional liquid corresponds to a stripy structure factor which rotates in the extended Brillouin zone as the spin component changes. Therefore, our findings encourage future experimental exploration of fractional liquid in the Kitaev materials by thermodynamic measurements and spin-resolved structure factor probes.

arXiv comment16 pages, 16 figures

References in corpus (52)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Quantum Spin Liquid States
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Kitaev quantum spin liquid - concept and materialization
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Neutron tomography of magnetic Majorana fermions in a proximate quantum spin liquid
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Models and Materials for Generalized Kitaev Magnetism
• On the Origin of Zigzag Magnetic Order in Iridium Oxide Na2IrO3
• Challenges in Design of Kitaev Materials: Magnetic Interactions from Competing Energy Scales
• Magnetic order in $\alpha$-RuCl${}_3$: a honeycomb lattice quantum magnet with strong spin-orbit coupling
• Physics of the Kitaev model: fractionalization, dynamical correlations, and material connections
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Successive magnetic phase transitions in $\mathbf{\alpha }$-RuCl${}_3$: XY-like frustrated magnet on the honeycomb lattice
• Breakdown of Magnons in a Strongly Spin-Orbital Coupled Magnet
• Hunting Majorana Fermions in Kitaev Magnets
• Kitaev interactions between j=1/2 moments in honeycomb Na2IrO3 are large and ferromagnetic: insights from ab initio quantum chemistry calculations
• Thermal fractionalization of quantum spins in a Kitaev model: $T$-linear specific heat and coherent transport of Majorana fermions
• Gapless Spin Excitations in the Field-Induced Quantum Spin Liquid Phase of alpha-RuCl3
• Spin-wave excitations evidencing the Kitaev interaction in single crystalline $\alpha$-RuCl${}_3$
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• First-Principles Study of the Honeycomb-Lattice Iridates Na2IrO3 in the Presence of Strong Spin-Orbit Interaction and Electron Correlations
• Vaporization of Kitaev spin liquids
• Finite-temperature phase diagram of the Heisenberg-Kitaev model
• Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $\alpha$-RuCl${}_3$ and Na${}_2$IrO${}_3$
• Emergence of a Field-Driven U(1) Spin Liquid in the Kitaev Honeycomb Model
• Probing $\alpha$-RuCl${}_3$ Beyond Magnetic Order: Effects of Temperature and Magnetic Field
• Ferromagnetic Kitaev interaction and the origin of large magnetic anisotropy in $\alpha$-RuCl${}_3$
• Quantum spin liquid signatures in Kitaev-like frustrated magnets
• Critical properties of the Kitaev-Heisenberg model
• Fractional Spin Fluctuation as a Precursor of Quantum Spin Liquids: Majorana Dynamical Mean-Field Study for the Kitaev Model
• Clues and criteria for designing Kitaev spin liquid revealed by thermal and spin excitations of honeycomb iridates Na${}_2$IrO${}_3$
• Quantum Phase Transition in Heisenberg-Kitaev Model
• Exponential Thermal Tensor Network Approach for Quantum Lattice Models
• Kosterlitz-Thouless Melting of Magnetic Order in the Triangular Quantum Ising Material TmMgGaO${}_4$
• One Proximate Kitaev Spin Liquid in the $K$-$J$-$\Gamma$ Model on the Honeycomb Lattice
• Thermodynamic evidence of fractionalized excitations in α-RuCl3
• Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects
• Two-temperature scales in the triangular-lattice Heisenberg antiferromagnet
• Dirac and Chiral Quantum Spin Liquids on the Honeycomb Lattice in a Magnetic Field
• Heat capacity evidence for proximity to the Kitaev QSL in A${}_2$IrO${}_3$ ($A=$ Na, Li)
• Kitaev-like honeycomb magnets: Global phase behavior and emergent effective models
• Series-Expansion Thermal Tensor Network Approach for Quantum Lattice Models
• Thermal Tensor Renormalization Group Simulations of Square-Lattice Quantum Spin Models
• Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: Influence of fluctuating gauge fluxes
• Majorana-Magnon Crossover by a Magnetic Field in the Kitaev Model: Continuous-Time Quantum Monte Carlo Study
• Bilayer Linearized Tensor Renormalization Group Approach for Thermal Tensor Networks

Cited by in corpus (22)

• Stripes, Antiferromagnetism, and the Pseudogap in the Doped Hubbard Model at Finite Temperature
• Identification of Magnetic Interactions and High-field Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Spin Supersolidity in Nearly Ideal Easy-axis Triangular Quantum Antiferromagnet Na${}_2$BaCo(PO${}_4$)${}_2$
• Unusual heat transport of the Kitaev material Na${}_2$Co${}_2$TeO${}_6$: putative quantum spin liquid and low-energy spin excitations
• Modified Curie-Weiss Law for $j_{\mathrm{eff}}$ Magnets
• Unusual excitations and double-peak specific heat in a bond-alternating spin-$1$ $K$-$\Gamma$ chain
• Kitaev Quantum Spin Liquids
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material $\alpha$-RuCl${}_3$
• Further insights into the thermodynamics of the Kitaev honeycomb model
• Quantum Monte Carlo Simulation of Generalized Kitaev Models
• Analytic calculation of the vison gap in the Kitaev spin liquid
• Generic Field-Driven Phenomena in Kitaev Spin Liquids: Canted Magnetism and Proximate Spin Liquid Physics
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• Evidence for magnetic fractional excitations in a Kitaev quantum-spin-liquid candidate $\alpha$-RuCl${}_3$
• Honeycomb oxide heterostructure: a new platform for Kitaev quantum spin liquid
• Neutron spectroscopy evidence for a possible magnetic-field-induced gapless quantum-spin-liquid phase in a Kitaev material $\alpha$-RuCl${}_3$
• High-field quantum spin liquid transitions and angle-field phase diagram of Kitaev magnet $\alpha$-RuCl${}_3$
• Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev honeycomb spin liquid state
• (H,Li)${}_6$Ru${}_2$O${}_6$ : a possible zero-field Ru${}^{3+}$-based Kitaev Quantum Spin Liquid
• Optical detection of bond-dependent and frustrated spin in the two-dimensional cobalt-based honeycomb antiferromagnet Cu3Co2SbO6
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Specific heat and susceptibility of S=1/2 antiferromagnets on square, triangular, and kagome lattices