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

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.

15 pages, 8 figures

References in corpus (9)

• Thermalization and its mechanism for generic isolated quantum systems
• Probing many-body dynamics on a 51-atom quantum simulator
• Many body localization and thermalization in quantum statistical mechanics
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Emergent SU(2) dynamics and perfect quantum many-body scars
• Competing density-wave orders in a one-dimensional hard-boson model
• Quantum Many-Body Scar States with Emergent Kinetic Constraints and Finite-Entanglement Revivals
• Systematic construction of scarred many-body dynamics in 1D lattice models
• Energy level dynamics across the many-body localization transition