Deformed Symmetry Structures and Quantum Many-body Scar Subspaces

TL;DR

This paper introduces deformed symmetric spaces as a unifying framework for quantum many-body scars, demonstrating their entanglement properties, symmetry requirements, and providing new models including a 2D topologically ordered scar system.

Contribution

It proposes a general structure for scar subspaces using deformed symmetric spaces, linking symmetry, entanglement, and dynamics in quantum many-body systems.

Findings

Deformed symmetric spaces have sub-volume-law entanglement scaling.

At least a U(1) sub-Lie-group symmetry is needed for coherent dynamics.

A new 2D scar model with topologically ordered states is introduced.

Abstract

A quantum many-body scar system usually contains a special non-thermal subspace (approximately) decoupled from the rest of the Hilbert space. In this work, we propose a general structure called deformed symmetric spaces for the decoupled subspaces hosting quantum many-body scars, which are irreducible sectors of simple Lie groups transformed by matrix-product operators (or projected entangled pair operators), of which the entanglement entropies are proved to obey sub-volume-law scaling and thus violate the eigenstate thermalization hypothesis. A deformed symmetric space, in general, is required to have at least a U(1) sub-Lie-group symmetry to allow coherent periodic dynamics from certain low-entangled initial states. We enumerate several possible deforming transformations based on the sub-group symmetry requirement and recover many existing models whose scar states are not connected by symmetry. In particular, a two-dimensional scar model is proposed, which hosts a periodic dynamical trajectory on which all states are topologically ordered.