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.

16 pages, 16 figures

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Cited by in corpus (15)

• 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${}_4$)${}_2$
• Kitaev Quantum Spin Liquids
• Investigation of the magnetoelastic coupling anisotropy in the Kitaev material $\alpha$-RuCl${}_3$
• Analytic calculation of the vison gap in the Kitaev spin liquid
• 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