Hidden $Z_{2}\times Z_{2}$ subspace symmetry protection for quantum scars

TL;DR

This paper investigates the symmetry-protected nature of quantum many-body scars in a spin-1 XY chain, revealing a hidden $Z_{2} imes Z_{2}$ symmetry and analyzing their stability under various perturbations.

Contribution

It uncovers a hidden $Z_{2} imes Z_{2}$ symmetry protecting quantum scars and introduces a classification of perturbations affecting their stability.

Findings

Scar subspace has a symmetry-protected trivial character.

A Lieb-Schultz-Mattis twist operator distinguishes scar and ergodic states.

Scars are more sensitive to perturbations than thermal states.

Abstract

We study the paradigmatic spin-1 XY chain under open boundary conditions, which hosts exact quantum many-body scars generated by an emergent Spectrum Generating Algebra (SGA). We show that the scar subspace possesses a symmetry-protected trivial (SPt) character that we attribute to a hidden $Z_{2}\times Z_{2}$ symmetry of another model, namely the commutant Hamiltonian, for which the scars are the ground states. We construct a Lieb-Schultz-Mattis (LSM) type twist operator, which, for scar states, takes the value $-1,$ and, for ergodic states, approaches zero in the thermodynamic limit. A complementary understanding of the stability of the scars under different perturbations is obtained by analyzing the Loschmidt echo and Quantum Fisher Information (QFI) of the scars. Finite-size scaling analysis of the QFI reveals that the scars are much more sensitive to perturbations as compared to the nearby thermal states. Based on the analysis of QFI and different LSM twist operators, we obtain a classification of different SGA-preserving and SGA-breaking perturbations.