Hilbert Space Fragmentation from Generalized Symmetries

TL;DR

This paper explores how generalized symmetries, including higher-form and non-invertible types, can cause Hilbert space fragmentation, leading to many disconnected sectors without necessarily breaking ergodicity.

Contribution

It demonstrates that generalized symmetries can induce exponential Hilbert space fragmentation, expanding understanding beyond conventional symmetry-induced sectorization.

Findings

Generalized symmetries can cause exponential Hilbert space fragmentation.

Non-invertible symmetries induce additional fragmentation within sectors.

Disorder-free localization can emerge from Krylov-restricted thermalization without ergodicity breaking.

Abstract

Hilbert space fragmentation refers to exponential growth in the number of dynamically disconnected Krylov sectors with system size. It is taken as evidence of ergodicity breaking, since conventional symmetries generate at most a polynomial number of sectors. However, we demonstrate that generalized symmetries can fragment the Hilbert space. Models with higher-form, subsystem, and gauge symmetries can have exponentially many symmetry sectors. We further prove that non-invertible symmetries can induce additional fragmentation within individual symmetry sectors. Fragmentation in several known models arises from generalized symmetries, and the presence of exponentially many Krylov sectors therefore does not by itself imply ergodicity breaking. Finally, we show that disorder free localization arises naturally from Krylov-restricted thermalization when sectors lack translation invariance, requiring neither ergodicity breaking nor gauge symmetry.