Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain

TL;DR

This paper investigates classical analogs of quantum spin transport in an XXZ chain under boundary drive, revealing detailed regimes of ballistic, subdiffusive, and insulating behavior, and demonstrating robustness to disorder through analytical and numerical methods.

Contribution

It introduces a classical model that accurately reproduces quantum spin transport phenomena and analyzes the effects of disorder on these regimes.

Findings

Classical model matches quantum results in spin transport.

Identifies three transport regimes: ballistic, subdiffusive, insulating.

Shows robustness of transport regimes to bond disorder.

Abstract

Motivated by recent experiments on Google's sycamore NISQ platform on the spin transport resulting from a non-unitary periodic boundary drive of an XXZ chain, we study a classical variant thereof by a combination of analytical and numerical means. We find the classical model reproduces the quantum results in remarkable detail, and provides an analytical handle on the nature and shape of the spin transport's three distinct regimes: ballistic (easy-plane), subdiffusive (isotropic) and insulating (easy-axis). Further, we show that this phenomenology is remarkably robust to the inclusion of bond disorder -- albeit that the transient dynamics approaching the steady states differs qualitatively between the clean and disordered cases -- providing an accessible instance of ballistic transport in a disordered setting.