Hilbert-Space Fragmentation from Strict Confinement

TL;DR

This paper investigates how strict confinement in one-dimensional spin-1/2 models causes Hilbert space to fragment into many disconnected parts, with some parts thermalizing and others being integrable, revealing a hierarchy of time scales.

Contribution

It introduces a novel mechanism for Hilbert-space fragmentation driven by confinement and conserved quantities, distinct from dipole moment conservation, and connects it to gauge theory and experimental realizations.

Findings

Hilbert space fragments into exponentially many disconnected subspaces.

Some components thermalize, others are integrable via Bethe ansatz.

Hierarchy of time scales emerges from confining interactions.

Abstract

We study one-dimensional spin-1/2 models in which strict confinement of Ising domain walls leads to the fragmentation of Hilbert space into exponentially many disconnected subspaces. Whereas most previous works emphasize dipole moment conservation as an essential ingredient for such fragmentation, we instead require two commuting U(1) conserved quantities associated with the total domain-wall number and the total magnetization. The latter arises naturally from the confinement of domain walls. Remarkably, while some connected components of the Hilbert space thermalize, others are integrable by Bethe ansatz. We further demonstrate how this Hilbert-space fragmentation pattern arises perturbatively in the confining limit of $\mathbb{Z}_2$ gauge theory coupled to fermionic matter, leading to a hierarchy of time scales for motion of the fermions. This model can be realized experimentally in two complementary settings.