Quantum many-body scars in bipartite Rydberg arrays originate from hidden projector embedding

TL;DR

This paper investigates the origin of quantum many-body scar states in bipartite Rydberg arrays, revealing they stem from a hidden projector-embedding structure in the Hamiltonian, and constructs models with exact scars.

Contribution

It uncovers the projector-embedding origin of scars in Rydberg arrays and introduces a non-Hermitian extension with exact scar states, providing a unified framework.

Findings

Scar states form a nearly equidistant energy tower

Exact scars are analytically constructed as large pseudospin states

Quasi-periodic Néel state dynamics are explained via pseudospin precession

Abstract

We study the nature of the ergodicity-breaking "quantum many-body scar" states that appear in the PXP model describing constrained Rabi oscillations. For a {wide class of bipartite lattices} of Rydberg atoms, we reveal that the nearly energy-equidistant tower of these states arises from the Hamiltonian's close proximity to a generalized projector-embedding form, a structure common to many models hosting quantum many-body scars. We construct a non-Hermitian, but strictly local extension of the PXP model hosting exact quantum scars, and show how various Hermitian scar-stabilizing extensions from the literature can be naturally understood within this framework. The exact scar states are obtained analytically as large spin states of explicitly constructed pseudospins. The quasi-periodic motion ensuing from the N\'eel state is finally shown to be the projection onto the Rydberg-constrained subspace of the precession of the large pseudospin.