High-temperature coherent transport in the XXZ chain in the presence of an impurity

TL;DR

This study investigates high-temperature spin transport in an XXZ chain with a single impurity, revealing ballistic transport persists despite integrability breaking and Wigner-Dyson level statistics.

Contribution

It demonstrates that a single impurity does not necessarily induce diffusive transport in an otherwise ballistic XXZ chain, challenging previous assumptions about integrability breaking effects.

Findings

Transport remains ballistic despite Wigner-Dyson level statistics.

Partial domain wall forms in the steady state magnetization.

Results align with linear response theory and show subtle Drude weight behavior.

Abstract

We study high-temperature spin transport through an anisotropic spin-1/2 Heisenberg chain in which integrability is broken by a single impurity close to the center of the chain. For a finite impurity strength, the level spacing statistics of this model is known to be Wigner-Dyson. Our aim is to understand if this integrability breaking is manifested in the high-temperature spin transport. We focus first on the nonequilibrium steady state (NESS), where the chain is connected to spin baths that act as sources and sinks for spin excitations at the boundaries. Using a combination of open quantum system theory and matrix product operators techniques, we extract the transport properties by means of a finite-size scaling of the spin current in the NESS. Our results indicate that, despite the formation of a partial domain wall in the steady state magnetization (and despite the Wigner-Dyson level spacing distribution of the model), transport remains ballistic. We contrast this behavior with the one produced by a staggered magnetic field in the XXZ chain, for which it is known that transport is diffusive. By performing a numerical computation of the real part of the spin conductivity, we show that our findings are consistent with linear response theory. We discuss subtleties associated with the apparent vanishing of the Drude in the presence of an impurity.