Probing the many-body localized spin-glass phase through quench dynamics

TL;DR

This paper investigates the dynamical behavior of a disordered spin chain in the many-body localized spin-glass phase, revealing oscillations, entanglement dynamics, and correlation length growth through tensor-network simulations and theoretical modeling.

Contribution

It introduces a theoretical framework to explain oscillatory dynamics and correlation length growth in the MBL spin-glass phase, validated by numerical simulations.

Findings

Oscillatory local expectation values and entanglement entropy in the spin-glass regime.

Theoretical model explains oscillations deep in the MBL phase.

Correlation length dynamics align with RG predictions after long times.

Abstract

Eigenstates of quantum many-body systems are often used to define phases of matter in and out of equilibrium; however, experimentally accessing highly excited eigenstates is a challenging task, calling for alternative strategies to dynamically probe nonequilibrium phases. In this work, we characterize the dynamical properties of a disordered spin chain, focusing on the spin-glass regime. Using tensor-network simulations, we observe oscillatory behavior of local expectation values and bipartite entanglement entropy. We explain these oscillations deep in the many-body localized spin glass regime via a simple theoretical model. From perturbation theory, we predict the timescales up to which our analytical description is valid and confirm it with numerical simulations. Finally, we study the correlation length dynamics, which, after a long-time plateau, resumes growing in line with renormalization group (RG) expectations. Our work suggests that RG predictions can be quantitatively tested against numerical simulations and experiments, potentially enabling microscopic descriptions of dynamical phases in large systems.