Vestiges of Topological Phase Transitions in Kitaev Quantum Spin Liquids

TL;DR

This paper explores observable signatures of topological quantum phase transitions in Kitaev quantum spin liquids at nonzero temperatures, focusing on thermal Hall conductivity as a key indicator, with implications for experimental detection.

Contribution

It identifies thermal Hall conductivity features as signatures of TQPTs in $Z_2$ quantum spin liquids at finite temperatures and performs mean-field analysis on a modified Kitaev model.

Findings

Exponential upturn of $rac{\, ext{xy}}{T}$ near zero temperature.

Peak of $rac{\, ext{xy}}{T}$ around excitation energy.

Quantum critical fan-shape temperature dependence across TQPTs.

Abstract

We investigate signatures of topological quantum phase transitions (TQPTs) between the $Z_2$ quantum spin liquids (QSLs). In two spatial dimensions, $Z_2$ QSLs and their TQPTs are only well defined at zero temperature ($T=0$), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between $Z_2$ QSLs with Majorana fermions in terms of thermal Hall conductivity $\kappa_{xy}$ at nonzero temperatures. The $\kappa_{xy}/T$ shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near $T=0$ and the peak of $\kappa_{xy}/T$ around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions finding TQPTs between the phases with different Chern numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in $\alpha$-RuCl$_3$.