Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG

TL;DR

This paper uses adaptive time-dependent DMRG to study real-time magnetization transport in spin-1/2 chains, revealing different transport regimes depending on interaction strength and analyzing the method's error characteristics.

Contribution

It applies adaptive t-DMRG to analyze transport in XXZ chains and provides a detailed error analysis comparing it with exact solutions in the XX model.

Findings

Ballistic transport at low Jz

Suppressed transport at high Jz

Superdiffusive behavior at Jz=1

Abstract

We investigate the influence of different interaction strengths and dimerizations on the magnetization transport in antiferromagnetic spin-1/2 XXZ-chains. We focus on the real-time evolution of the inhomogeneous initial state with all spins pointing up along the z axis in the left half and down in the right half of the chain, using the adaptive time-dependent density-matrix renormalization group (adaptive t-DMRG). We find on time-scales accessible to us ballistic magnetization transport for small Sz-Sz-interaction and arbitrary dimerization, but almost no transport for stronger Sz-Sz-interaction, with a sharp crossover at Jz=1. At Jz=1 results indicate superdiffusive transport. Additionally, we perform a detailed analysis of the error made by the adaptive time-dependent DMRG using the fact that the evolution in the XX-model is known exactly. We find that the error at small times is dominated by the error made by the Trotter decomposition, whereas for longer times the DMRG truncation error becomes the most important, with a very sharp crossover at some "runaway" time.