Thermal conductivity of anisotropic and frustrated spin-1/2 chains

TL;DR

This paper investigates the thermal conductivity of anisotropic and frustrated spin-1/2 chains using analytical and numerical methods, revealing temperature-dependent behaviors and the absence of divergence in certain regimes.

Contribution

It combines mean-field theory, bosonization, and exact diagonalization to analyze thermal transport in complex spin chains, providing new insights into their finite-temperature properties.

Findings

Mean-field theory aligns well with known results in the gapless regime.

Bosonization accurately describes low-temperature behavior.

No evidence of diverging thermal conductivity in the antiferromagnetic gapped regime.

Abstract

We analyze the thermal conductivity of anisotropic and frustrated spin-1/2 chains using analytical and numerical techniques. This includes mean-field theory based on the Jordan-Wigner transformation, bosonization, and exact diagonalization of systems with N<=18 sites. We present results for the temperature dependence of the zero-frequency weight of the conductivity for several values of the anisotropy \Delta. In the gapless regime, we show that the mean-field theory compares well to known results and that the low-temperature limit is correctly described by bosonization. In the antiferromagnetic and ferromagnetic gapped regime, we analyze the temperature dependence of the thermal conductivity numerically. The convergence of the finite-size data is remarkably good in the ferromagnetic case. Finally, we apply our numerical method and mean-field theory to the frustrated chain where we find a good agreement of these two approaches on finite systems. Our numerical data do not yield evidence for a diverging thermal conductivity in the thermodynamic limit in case of the antiferromagnetic gapped regime of the frustrated chain.