Tower of quantum scars in a partially many-body localized system

TL;DR

This paper constructs a disordered spin-1/2 model exhibiting both partial many-body localization and quantum many-body scars, revealing how disorder stabilizes scar revivals and introduces additional eigenstate towers.

Contribution

It introduces a method to find Hamiltonians with scar towers in partially localized systems and analyzes their properties through numerical studies.

Findings

Level spacing transitions from GOE to Poisson with disorder.

Entanglement entropy shifts from volume-law to area-law.

Localization stabilizes scar revivals and creates additional eigenstate towers.

Abstract

Isolated quantum many-body systems are often well-described by the eigenstate thermalization hypothesis. There are, however, mechanisms that cause different behavior: many-body localization and quantum many-body scars. Here, we show how one can find disordered Hamiltonians hosting a tower of scars by adapting a known method for finding parent Hamiltonians. Using this method, we construct a spin-1/2 model which is both partially localized and contains scars. We demonstrate that the model is partially localized by studying numerically the level spacing statistics and bipartite entanglement entropy. As disorder is introduced, the adjacent gap ratio transitions from the Gaussian orthogonal ensemble to the Poisson distribution and the entropy shifts from volume-law to area-law scaling. We investigate the properties of scars in a partially localized background and compare with a thermal background. At strong disorder, states initialized inside or outside the scar subspace display different dynamical behavior but have similar entanglement entropy and Schmidt gap. We demonstrate that localization stabilizes scar revivals of initial states with support both inside and outside the scar subspace. Finally, we show how strong disorder introduces additional approximate towers of eigenstates.