Extreme many-body scarring in a quantum spin chain via weak dynamical constraints

TL;DR

This paper introduces a class of spin chain models with tunable dynamical constraints, revealing that weaker constraints can lead to an extreme form of quantum many-body scarring with exponentially many scar states.

Contribution

The authors develop a family of models parameterized by a discrete variable, demonstrating that weakening dynamical constraints enhances quantum scarring beyond previous models like PXP.

Findings

Weaker constraints lead to more numerous scar states.

Exponential growth of scar states with system size for certain parameters.

Extreme many-body scarring surpassing known models like PXP.

Abstract

It has recently been established that quantum many-body scarring can prevent the thermalisation of some isolated quantum systems, starting from certain initial states. One of the first models to show this was the so-called PXP Hamiltonian, which was used to theoretically model an experiment on a chain of strongly interacting Rydberg atoms. A defining feature of the PXP Hamiltonian is a set of dynamical constraints that make certain states inaccessible to the dynamics. In this paper we construct a class of spin chain models that are parameterised by a discrete variable $\ell$ that controls the "strength" of a dynamical constraint. We show that by increasing $\ell$ the constraint becomes weaker, in the sense that fewer states are excluded from the dynamics. The PXP Hamiltonian is special case for $\ell = 2$. By weakening the constraint to $\ell \geq 4$, however, we find a more extreme version of quantum scarring than in the PXP Hamiltonian, with the number of scar states growing exponentially in the system size.