Revival Dynamics from Equilibrium States: Scars from Chords in SYK

TL;DR

This paper introduces a new method to create quantum scar states in bipartite systems, enabling finite-time revivals and universal dynamics, with an application to the SYK model demonstrating analytical and numerical agreement.

Contribution

It develops a Krylov-based framework for scar states in bipartite systems and applies it to the SYK model, revealing revival dynamics and wavepacket behavior.

Findings

Finite-time revivals occur when initialized in a purification of equilibrium states.

The framework supports a tower of equally-spaced energy eigenstates.

Numerical results agree well with analytical predictions for finite systems.

Abstract

We develop a novel framework to build quantum many-body scar states in bipartite systems characterized by perfect correlation between the Hamiltonians governing the two sides. By means of a Krylov construction, we build an interaction term which supports a tower of equally-spaced energy eigenstates. This gives rise to finite-time revivals whenever the system is initialized in a purification of a generic equilibrium state. The dynamics is universally characterized, and is largely independent of the specific details of the Hamiltonians defining the individual partitions. By considering the two-sided chord states of the double-scaled SYK model, we find an approximate realization of this framework. We analytically study the revival dynamics, finding rigid motion for wavepackets localized on the spectrum of a single SYK copy. These findings are tested numerically for systems of finite size, showing excellent agreement with the analytical predictions.