Transport in the one-dimensional spin-S XXZ model

Abstract

The Stochastic Series Expansion (SSE) method with the Directed Loop updates allows for efficient simulation of quantum spin lattice systems at finite temperatures. Here we develop a new approach for sampling response functions in the SSE framework to calculate transport properties in the linear regime. This procedure is based on an imaginary time representation of the SSE configurations. It allows us to bypass the calculation of hypergeometric functions present in existing approaches, and to write a sampling algorithm with linear complexity. As so, we are able to perform accurate calculations for the DC spin conductivity, in the low temperature regime, for spin-S XXZ chains. Calculations for the heat conductivity and the spin-Seebeck coefficient are possible but have large standard deviations. We are able to reproduce results from Bosonization for the spin conductivity in spin-1/2 XXZ chains. We extend these calculations to spin-1 and spin-3/2 XXZ chains, and found different types behaviours of the conductivity between integer and half-integer spin chains. Furthermore, an extrapolation to the large spin limit is also performed, showing good agreement with the spin conductivity in classical spin systems.