Universal Thermodynamics in the Kitaev Fractional Liquid

TL;DR

This paper investigates the finite-temperature fractionalized state in the Kitaev honeycomb model, revealing universal thermodynamic behaviors and experimental signatures of quantum spin fractionalization in Kitaev materials.

Contribution

It demonstrates the robustness of the Kitaev fractional liquid under various perturbations using large-scale tensor network calculations and connects theoretical predictions with experimental observations.

Findings

Identification of a robust fractional liquid at intermediate temperatures.

Universal thermodynamic behaviors including fractional entropy and modified Curie law.

Signatures of finite-temperature fractionalization in susceptibility measurements.

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.