Thermal transport in one-dimensional spin gap systems

TL;DR

This paper investigates thermal transport in one-dimensional spin systems, analyzing the effects of impurities, magnetic fields, and temperature on the Drude peak and conductivity, revealing universal behaviors and impurity-induced modifications.

Contribution

It provides a comprehensive analysis of thermal conductivity in spin gap systems, including impurity effects and magnetic field influences, highlighting universal features and new insights into low-temperature behavior.

Findings

Drude peak proportional to temperature in gapless systems

Activated behavior of Drude weight in spin gap systems

Impurities suppress the Drude peak and induce activated conductivity

Abstract

We study thermal transport in one dimensional spin systems both in the presence and absence of impurities. In the absence of disorder, all these spin systems display a temperature dependent Drude peak in the thermal conductivity. In gapless systems, the low temperature Drude weight is proportional to temperature and to the central charge which characterizes the conformal field theory that describes the system at low energies. On the other hand, the low temperature Drude weight of spin gap systems shows an activated behavior modulated by a power law. For temperatures higher than the spin gap, one recovers the linear T behavior akin to gapless systems. For temperatures larger than the exchange coupling, the Drude weight decays as 1/T^2. We argue that this behavior is a generic feature of quasi one dimensional spin gap systems with a relativistic-like low energy dispersion. We also consider the effect of a magnetic field on the Drude weight with emphasis on the commensurate-incommensurate transition induced by it. We then study the effect of nonmagnetic impurities on the thermal conductivity of the dimerized XY chain and the spin-1/2 two leg ladder. Impurities destroy the Drude peak and the thermal conductivity exhibits a purely activated behavior at low temperature, with an activation gap renormalized by disorder. The relevance of these results for experiments is briefly discussed.