Gaussian state approximation of quantum many-body scars

TL;DR

This paper investigates whether quantum many-body scars in the PXP model can be effectively approximated by Gaussian states, revealing insights into their non-ergodic nature and potential quadratic parent Hamiltonians.

Contribution

The study demonstrates that quantum many-body scars can be well approximated by Gaussian states, unlike thermal eigenstates, suggesting a quadratic structure underlying scars.

Findings

Quantum many-body scars are well approximated by Gaussian states.

Thermal eigenstates are not well approximated by Gaussian states.

Scars are linked to quadratic parent Hamiltonians.

Abstract

Quantum many-body scars are atypical, highly nonthermal eigenstates embedded in a sea of thermal eigenstates that have been observed in, for example, kinetically constrained quantum many-body models. These special eigenstates are characterized by a bipartite entanglement entropy that scales as most logarithmically with the subsystem size. We use numerical optimization techniques to investigate if quantum many-body scars of the experimentally relevant PXP model can be well approximated by Gaussian states. Gaussian states are described by a number of parameters that scales quadratically with system size, thereby having a much lower complexity than generic quantum many-body states, for which this number scales exponentially. We find that while quantum many-body scars can typically be well approximated by (symmetrized) Gaussian states, this is not the case for ergodic (thermal) eigenstates. This observation suggests that the non-ergodic part of the PXP Hamiltonian is related to certain quadratic parent Hamiltonians, thereby hinting on the origin of the quantum many-body scars.