Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries

TL;DR

This paper investigates a 2D quantum spin model with subsystem symmetries, revealing extensive Hilbert space fragmentation and inert subsectors, and introduces shielding structures that control the dynamics based on interaction range.

Contribution

It demonstrates that subsystem symmetries alone cannot explain the large inert subsectors and presents a method to construct shielding structures to manage dynamical regions.

Findings

Extensive Hilbert space fragmentation with inert subsectors.

Subsystem symmetries do not fully account for inert states.

Shielding structures depend on interaction range, not system size.

Abstract

We consider a 2D quantum spin model with ring-exchange interaction that has subsystem symmetries associated to conserved magnetization along rows and columns of a square lattice, which implies the conservation of the global dipole moment. In a certain regime, the model is non-integrable, but violates the eigenstate thermalization hypothesis through an extensive Hilbert space fragmentation, including an exponential number of inert subsectors with trivial dynamics, arising from kinetic constraints. While subsystem symmetries are quite restrictive for the dynamics, we show that they alone cannot account for such a number of inert states, even with infinite-range interactions. We present a procedure for constructing shielding structures that can separate and disentangle dynamically active regions from each other. Notably, subsystem symmetries allow the thickness of the shields to be dependent only on the interaction range rather than on the size of the active regions, unlike in the case of generic dipole-conserving systems.