Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains

TL;DR

This paper introduces a modified Matrix Product State method to simulate signal propagation in infinite quantum spin chains, revealing magnetization plateaus and scaling behaviors after local quenches, with implications for understanding quantum dynamics.

Contribution

The paper develops a windowed MPS approach for long-time simulation of signal fronts in infinite systems, enabling high-precision studies of magnetization dynamics and scaling phenomena.

Findings

Observation of magnetization plateaus at signal fronts in both models.

Scaling behavior of normalized magnetization similar to tight binding fermion density.

Internal structure and interaction effects in the XXZ model's signal front.

Abstract

We present a modification of Matrix Product State time evolution to simulate the propagation of signal fronts on infinite one-dimensional systems. We restrict the calculation to a window moving along with a signal, which by the Lieb-Robinson bound is contained within a light cone. Signal fronts can be studied unperturbed and with high precision for much longer times than on finite systems. Entanglement inside the window is naturally small, greatly lowering computational effort. We investigate the time evolution of the transverse field Ising (TFI) model and of the S=1/2 XXZ antiferromagnet in their symmetry broken phases after several different local quantum quenches. In both models, we observe distinct magnetization plateaus at the signal front for very large times, resembling those previously observed for the particle density of tight binding (TB) fermions. We show that the normalized difference to the magnetization of the ground state exhibits similar scaling behaviour as the density of TB fermions. In the XXZ model there is an additional internal structure of the signal front due to pairing, and wider plateaus with tight binding scaling exponents for the normalized excess magnetization. We also observe parameter dependent interaction effects between individual plateaus, resulting in a slight spatial compression of the plateau widths. In the TFI model, we additionally find that for an initial Jordan-Wigner domain wall state, the complete time evolution of the normalized excess longitudinal magnetization agrees exactly with the particle density of TB fermions.