A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method

TL;DR

This study uses the adaptive time-dependent density matrix renormalization group method to analyze real-time spin dynamics and transport in one-dimensional spin-1/2 systems, distinguishing diffusive and ballistic regimes under various conditions.

Contribution

It introduces a real-time evolution approach to study transport in spin chains, applicable far from equilibrium, and compares diffusive and ballistic behaviors across different models.

Findings

Ballistic transport observed in the easy-plane phase.

Diffusive behavior in massive regimes.

Ballistic behavior in the critical phase of the frustrated chain.

Abstract

Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from linear response theory, we study the real-time evolution of the magnetization starting from spatially inhomogeneous initial states. In particular, we are able to analyze systems far away from equilibrium with this set-up. By computing the time-dependence of the variance of the magnetization, we can distinguish diffusive from ballistic regimes, depending on model parameters. For the example of the anisotropic spin-1/2 chain and at half filling, we find the expected ballistic behavior in the easy-plane phase, while in the massive regime the dynamics of the magnetization is diffusive. Our approach allows us to tune the deviation of the initial state from the ground state and the qualitative behavior of the dynamics turns out to be valid even for highly perturbed initial states in the case of easy-plane exchange anisotropies. We further cover two examples of nonintegrable models, the frustrated chain and the two-leg spin ladder, and we encounter diffusive transport in all massive phases. In the former system, our results indicate ballistic behavior in the critical phase. We discuss our findings in view of experiments on quasi-one dimensional quantum magnets and we propose that the study of the time-dependence of the spatial variance of particle densities could be instrumental in the characterization of the expansion of ultracold atoms in optical lattices as well.