Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales

TL;DR

This paper studies high-temperature transport in translationally invariant spin-1/2 chains using a current auto-correlation approach, revealing diffusive behavior and quantifying diffusion constants through numerical methods.

Contribution

It introduces a method linking density variance evolution to current auto-correlation functions for finite times and lengths, enabling quantitative diffusion analysis.

Findings

Diffusive behavior observed in various spin chains.

Quantitative diffusion constants confirmed via numerical diagonalization.

Method applicable to finite time and length scales for transport analysis.

Abstract

We investigate transport in several translationally invariant spin-1/2 chains in the limit of high temperatures. We concretely consider spin transport in the anisotropic Heisenberg chain, the pure Heisenberg chain within an alternating field, and energy transport in an Ising chain which is exposed to a tilted field. Our approach is essentially based on a connection between the evolution of the variance of an inhomogeneous non-equilibrium density and the current auto-correlation function at finite times. Although this relationship is not restricted to the case of diffusive transport, it allows to extract a quantitative value for the diffusion constant in that case. By means of numerically exact diagonalization we indeed observe diffusive behavior in the considered spin chains for a range of model parameters and confirm the diffusion coefficients which were obtained for these systems from non-equilibrium bath scenarios.