Tunable Hilbert space fragmentation and extended critical regime

TL;DR

This paper explores how specific perturbations can gradually eliminate localized integrals of motion in Hilbert space fragmentation systems, leading to an extended critical regime with slow relaxation and multiple phase transitions.

Contribution

It demonstrates that carefully chosen perturbations can systematically remove SLIOMs in the $t$-$J_z$ chain, revealing a tunable transition from nonergodic to ergodic behavior.

Findings

Gradual elimination of SLIOMs with perturbations.

Extended critical regime with multiple fidelity susceptibility peaks.

Ultra-slow relaxation of local observables during transition.

Abstract

Systems exhibiting the Hilbert-space fragmentation are nonergodic, and their Hamiltonians decompose into exponentially many blocks in the computational basis. In many cases, these blocks can be labeled by eigenvalues of statistically localized integrals of motion (SLIOM), which play a similar role in fragmented systems as local integrals of motion in integrable systems. While a nonzero perturbation eliminates all nontrivial conserved quantities from integrable models, we demonstrate for the $t$-$J_z$ chain that an appropriately chosen perturbation may gradually eliminate SLIOMs (one by one) by progressively merging the fragmented subspaces. This gradual recovery of ergodicity manifests as an extended critical regime characterized by multiple peaks of the fidelity susceptibility. Each peak signals a change in the number of SLIOMs and blocks, as well as an ultra-slow relaxation of local observables.