Exact many-body scars and their stability in constrained quantum chains

TL;DR

This paper investigates the stability of exact quantum many-body scars in constrained quantum chains, revealing their anomalous stability at first order and introducing new analytically constructed scars with similar robustness.

Contribution

It provides an analytical description of new exact quantum scars in models with larger blockade radius and analyzes their stability under perturbations.

Findings

Some scars are stable at first order perturbation

Stability breaks down at higher orders

New exact scars are analytically constructed and exhibit robustness

Abstract

Quantum scars are non-thermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so called PXP model. While most of these special eigenstates elude an analytical description and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states (MPS) with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analysing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to breakdown when all orders are taken into account. We further investigate models with larger blockade radius and find a novel set of exact quantum scars, that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.