Enhancing entanglement asymmetry in fragmented quantum systems

TL;DR

This paper investigates entanglement asymmetry in many-body quantum states, revealing universal bounds and behaviors in systems with Hilbert-space fragmentation, and introduces a formalism to distinguish classical from quantum fragmentation.

Contribution

It generalizes entanglement asymmetry to fragmented systems, derives bounds, and connects asymmetry dynamics to random matrix product states and ergodic systems.

Findings

Entanglement asymmetry is bounded by a universal fraction of its maximum.

In fragmented systems, asymmetry can scale extensively, unlike in conventional symmetries.

Random matrix product states reproduce asymmetry dynamics, indicating universal behavior.

Abstract

Entanglement asymmetry provides a quantitative measure of symmetry breaking in many-body quantum states. Focusing on inhomogeneous $U(1)$ charges, such as dipole and multipole moments, we show that the typical asymmetry is bounded by a universal fraction of its maximal value. Multipole charges naturally arise in systems with Hilbert-space fragmentation, where the dynamics splits into exponentially many disconnected sectors. Using the commutant algebra formalism, we generalize entanglement asymmetry to account for fragmentation. While the asymmetry grows logarithmically for conventional symmetries, it can scale extensively in fragmented systems and distinguish classical from quantum fragmentation. We derive general upper bounds for the asymmetry and identify states that saturate them. To study the typical behavior of the asymmetry, we consider the ensemble of random matrix product states. By identifying the bond dimension with an effective time parameter, we qualitatively reproduce recent results on asymmetry dynamics in random quantum circuits, suggesting a universal behavior for the asymmetry of $U(1)$ charges in local ergodic systems.