Exact Quantum Many-Body Scars in 2D Quantum Gauge Models

TL;DR

This paper identifies exact quantum many-body scars in a 2D quantum gauge model by leveraging duality with a 2D XY model, revealing ergodicity-breaking states in higher dimensions.

Contribution

It introduces a method to find exact QMBS in 2D gauge models using duality with XY models, expanding the understanding of ergodicity-breaking in higher dimensions.

Findings

Exact QMBS identified in a 2D $ ext{Z}_2$ gauge model.

Duality transformation relates QMBS of XY model to gauge model.

Versatile construction applicable to other higher-dimensional models.

Abstract

Quantum many-body scars (QMBS) serve as important examples of ergodicity-breaking phenomena in quantum many-body systems. Despite recent extensive studies, exact QMBS are rare in dimensions higher than one. In this paper, we study a two-dimensional quantum $\mathbb{Z}_2$ gauge model that is dual to a two-dimensional spin-$1/2$ XY model defined on bipartite graphs. We identify the exact eigenstates of the XY model with a tower structure as exact QMBS. Exploiting the duality transformation, we show that the exact QMBS of the XY model (and XXZ model) after the transformation are the exact QMBS of the dual $\mathbb{Z}_2$ gauge model. This construction is versatile and has potential applications for finding new QMBS in other higher-dimensional models.