Tower of two-dimensional scar states in a localized system

TL;DR

This paper investigates two-dimensional disordered quantum systems with many-body scar states, demonstrating their robustness under strong disorder and analyzing the transition from thermalization to localization through spectral and entanglement measures.

Contribution

The study constructs and analyzes new models hosting scar states in 2D disordered systems, revealing their strong localization and transition behaviors, which broadens understanding of scars beyond 1D.

Findings

Scar states remain as exact eigenstates at weak disorder.

Spectra transition from nonthermal to localized with increasing disorder.

Localization protects quantum scar revivals.

Abstract

The eigenstate thermalization hypothesis describes how most isolated many-body quantum systems reach thermal equilibrium. However, the hypothesis is violated by phenomena such as many-body localization and quantum many-body scars. In this work, we study a finite, two-dimensional, disordered model hosting a tower of scar states. This construction is a particular instance of a general framework and we demonstrate its generality by constructing two disordered models hosting a different tower of scar states. At weak disorder, we find numerically that the spectra are nonthermal, and the scar states appear as exact eigenstates with high entropy for certain bipartitions. At strong disorder, the spectra localize and the scar states are identified as inverted scars since the scar states are embedded in a localized background as opposed to a thermal background. We argue that, for the considered type of models, the localization is stronger than what would be naively expected, and we show this explicitly for one of the models. The argument also provides guidelines for obtaining similarly strong localization in other scarred models. We study the transition from the thermal phase to localization by observing the adjacent gap ratio shifting from the Wigner surmise to the Poisson distribution with increasing disorder strength. Moreover, the entanglement entropy transitions from volume-law scaling with system size at weak disorder to area-law scaling at strong disorder. Finally, we demonstrate that localization protects scar revivals for initial states with partial support in the scar subspace.