Quasi-symmetry groups and many-body scar dynamics

TL;DR

This paper introduces the concept of quasi-symmetry groups in quantum systems, showing how they can generate exactly periodic many-body-scar dynamics in non-integrable models through local operators and external fields.

Contribution

It presents two schemes for constructing 1D spin models with on-demand quasi-symmetry groups enabling exact periodic evolution of specific states.

Findings

Quasi-symmetry groups can induce many-body-scar dynamics.

External fields can lift degeneracy and produce periodic evolution.

Constructed models demonstrate controllable scar dynamics.

Abstract

In quantum systems, a subspace spanned by degenerate eigenvectors of the Hamiltonian may have higher symmetries than those of the Hamiltonian itself. When this enhanced-symmetry group can be generated from local operators, we call it a quasi-symmetry group. When the group is a Lie group, an external field coupled to certain generators of the quasi-symmetry group lifts the degeneracy, and results in exactly periodic dynamics within the degenerate subspace, namely the many-body-scar dynamics (given that Hamiltonian is non-integrable). We provide two related schemes for constructing one-dimensional spin models having on-demand quasi-symmetry groups, with exact periodic evolution of a pre-chosen product or matrix-product state under certain external fields.