Quantum many-body scars with chiral topological order in 2D and critical properties in 1D

TL;DR

This paper constructs specific many-body Hamiltonians with embedded quantum scar states exhibiting criticality in 1D and chiral topological order in 2D, demonstrating their robustness and unique spectral properties.

Contribution

It introduces nonlocal Hamiltonians with embedded scar states that are independent of disorder realization and can be spectrally tuned, revealing new topological and critical phenomena.

Findings

Scar states exhibit Wigner-Dyson level statistics.

Entanglement entropy approaches the Page value.

Topological order confirmed via anyon insertion.

Abstract

We construct few-body, interacting, nonlocal Hamiltonians with a quantum scar state in an otherwise thermalizing many-body spectrum. In one dimension, the embedded state is a critical state, and in two dimensions, the embedded state is a chiral topologically ordered state. The models are defined on slightly disordered lattices, and the scar state appears independent of the precise realization of the disorder. A parameter allows the scar state to be placed at any position in the spectrum. We show that the level spacing distributions are Wigner-Dyson and that the entanglement entropies of the states in the middle of the spectrum are close to the Page value. Finally, we confirm the topological order in the scar state by showing that one can insert anyons into the state.