Number of zero-energy eigenstates in the PXP model

TL;DR

This paper establishes tight lower bounds on the number of zero-energy eigenstates in the PXP model, enhancing understanding of quantum many-body scars with rigorous, assumption-free derivations across various boundary and symmetry sectors.

Contribution

It provides the first assumption-free, tight lower bounds on zero-energy states in the PXP model for different boundary conditions and symmetry sectors.

Findings

Lower bounds are tight with numerical results.

Bounds are valid for open and periodic boundary conditions.

Separate bounds are derived for different symmetry sectors.

Abstract

The PXP model is paradigmatic in the field of quantum many-body scars. This model has a number of zero-energy eigenstates that is exponentially large in system size. Lower bounds on the number of zero-energy eigenstates are obtained for both open and periodic (zero and $\pi$-momentum sectors) boundary conditions. These bounds are found to be tight up to system sizes accessible by numerical exact diagonalization, and can be expected to be tight in general. In addition to previous results, separate lower bounds are obtained for the spatial inversion-symmetric and inversion-antisymmetric symmetry sectors. Furthermore, the derivations improve on previous ones as these are free of assumptions.