Probing Hilbert space fragmentation using controlled dephasing

TL;DR

This paper demonstrates that controlled dephasing can effectively mix quantum states within Hilbert space sectors, enabling experimental probing of sector properties in many-body systems like the XXZ chain.

Contribution

It introduces a method using controlled dephasing to reliably explore and differentiate Hilbert space sectors in many-body quantum systems.

Findings

Controlled dephasing mixes states within a Krylov sector.

Spin imbalance distinguishes different sectors.

Analytical and simulation results match at relevant interaction strengths.

Abstract

Dynamical constraints in many-body quantum systems can lead to Hilbert space fragmentation, wherein the system's evolution is restricted to small subspaces of Hilbert space called Krylov sectors. However, unitary dynamics within individual sectors may also be slow or non-ergodic, which limits experiments' ability to measure the properties of the entire sector. We show that additional controlled dephasing reliably mixes the system within a single Krylov sector, and that simple observables can differentiate these sectors. For example, in the strongly interacting XXZ chain with dephasing, the spin imbalance between even and odd sublattices distinguishes sectors. For appropriate choices of initial states, the imbalance begins positive, decays to a negative minimum value at intermediate times, and eventually returns to zero. The minimum reflects the average imbalance of the Krylov sector associated to the initial state. We compute the size of the minimum analytically in the limit of strong interactions, and validate our results with simulations at experimentally relevant interaction strengths.