Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach

TL;DR

This paper develops a matrix product state approach to analyze quantum dynamics in constrained many-body systems, revealing unstable periodic orbits that explain long-lived revivals and quantum many-body scars observed experimentally.

Contribution

It introduces a low-bond dimension matrix product state manifold and derives equations of motion, providing a new theoretical framework for understanding quantum many-body scars in constrained models.

Findings

Identification of unstable periodic orbits capturing revivals

Connection between many-body scars and classical chaos

Framework applicable to Rydberg atom experiments

Abstract

We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum quenches in Rydberg atom arrays, we introduce a manifold of locally entangled spin states, representable by low-bond dimension matrix product states, and derive equations of motions for them using the time-dependent variational principle. We find that they feature isolated, unstable periodic orbits, which capture the recurrences and represent nonergodic dynamical trajectories. Our results provide a theoretical framework for understanding quantum dynamics in a class of constrained spin models, which allow us to examine the recently suggested explanation of 'quantum many-body scarring' [Nature Physics (2018), doi:10.1038], and establish a connection to the corresponding phenomenon in chaotic single-particle systems.