Thermal Transport in a one-dimensional Z$_{2}$ Spin Liquid

TL;DR

This paper investigates the thermal conductivity of a Kitaev spin model on a ladder, revealing that heat transport is entirely dissipative due to spin fractionalization and emergent disorder, with results supported by multiple computational methods.

Contribution

It demonstrates that heat transport in the Kitaev ladder is fully dissipative, contrasting with conventional integrable systems, and employs three different approaches to analyze gauge fluctuations and conductivity.

Findings

Heat transport is completely dissipative in the Kitaev ladder.

Spin fractionalization leads to emergent thermally activated disorder.

Multiple computational methods confirm the dissipative nature of thermal conductivity.

Abstract

We study the dynamical thermal conductivity of the Kitaev spin model on a two-leg ladder. In contrast to conventional integrable one-dimensional spin systems, we show that heat transport is completely dissipative. This is a direct consequence of fractionalization of spins into mobile Majorana matter and a static $Z_{2}$ gauge field, which acts as an emergent thermally activated disorder. Our finding rests on three complementary calculations of the current correlation function, comprising a phenomenological mean-field treatment of thermal gauge fluctuations, a complete summation over all gauge sectors, as well as exact diagonalization of the original spin model. The results will also be contrasted against the conductivity discarding gauge fluctuations.