Spin and thermal conductivity of quantum spin ladders

TL;DR

This paper investigates the spin and thermal conductivities of quantum spin ladders at finite temperatures using advanced numerical methods, revealing diffusive behavior and temperature-dependent properties relevant for quantum magnet experiments.

Contribution

It provides the first detailed real-time analysis of conductivities in spin ladders using density matrix renormalization group techniques, highlighting diffusive transport characteristics.

Findings

All studied models are normal conductors with no ballistic contribution.

High-temperature XX ladders exhibit simple diffusive spin conductivity.

Heisenberg ladders show complex low-frequency behavior.

Abstract

We study the spin and thermal conductivity of spin-1/2 ladders at finite temperature. This is relevant for experiments with quantum magnets. Using a state-of-the-art density matrix renormalization group algorithm, we compute the current autocorrelation functions on the real-time axis and then carry out a Fourier integral to extract the frequency dependence of the corresponding conductivities. The finite-time error is analyzed carefully. We first investigate the limiting case of spin-1/2 XXZ chains, for which our analysis suggests non-zero dc-conductivities in all interacting cases irrespective of the presence or absence of spin Drude weights. For ladders, we observe that all models studied are normal conductors with no ballistic contribution. Nonetheless, only the high-temperature spin conductivity of XX ladders has a simple diffusive, Drude-like form, while Heisenberg ladders exhibit a more complicated low-frequency behavior. We compute the dc spin conductivity down to temperatures of the order of T~0.5J, where J is the exchange coupling along the legs of the ladder. We further extract mean-free paths and discuss our results in relation to thermal conductivity measurements on quantum magnets.