Scaling of diffusion constants in the spin-1/2 XX ladder

TL;DR

This paper investigates how spin diffusion constants scale in a spin-1/2 XX ladder at finite temperature, revealing a crossover from exponential to Gaussian dissipation with increasing rung interaction, supported by numerical and analytical results.

Contribution

It introduces a new understanding of the dependence of spin diffusion on rung-interaction strength in XX ladders, combining numerical simulations with analytical derivations.

Findings

Spin Drude weights vanish exponentially with system size.

Spin diffusion coefficient shows a crossover from exponential to Gaussian behavior.

Results are relevant for cold atomic gas experiments.

Abstract

We study the dynamics of spin currents in the XX spin-1/2 ladder at finite temperature. Within the framework of linear response theory, we numerically calculate autocorrelation functions for quantum systems larger than what is accessible with exact diagonalization using the concept of dynamical quantum typicality. We show that spin Drude weights vanish exponentially fast with increasing system size. As a main result, we unveil qualitatively different dependencies of the spin diffusion coefficient on the rung-interaction strength, resulting from a crossover from exponential to Gaussian dissipation as the rung coupling increases. This behavior is also derived analytically. We further discuss the relation of our results to experiments with cold atomic gases.