Interactions and integrability in weakly monitored Hamiltonian systems

TL;DR

This paper investigates how interactions, integrability, and symmetry influence entanglement phases in weakly monitored quantum spin chains, revealing that interactions promote volume-law entanglement while non-interacting systems remain sub-extensive.

Contribution

It identifies the key role of interactions in determining entanglement scaling in weakly monitored quantum systems, independent of integrability or U(1) symmetry.

Findings

Interactions correlate with volume-law entanglement in monitored systems.

Non-interacting systems exhibit sub-extensive entanglement scaling.

Integrability and U(1) symmetry do not significantly affect entanglement phases.

Abstract

Interspersing unitary dynamics with local measurements results in measurement-induced phases and transitions in many-body quantum systems. When the evolution is driven by a local Hamiltonian, two types of transitions have been observed, characterized by an abrupt change in the system size scaling of entanglement entropy. The critical point separates the strongly monitored area-law phase from a volume law or a sub-extensive, typically logarithmic-like one at low measurement rates. Identifying the key ingredients responsible for the entanglement scaling in the weakly monitored phase is the key purpose of this work. For this purpose, we consider prototypical one-dimensional spin chains with local monitoring featuring the presence/absence of U(1) symmetry, integrability, and interactions. Using exact numerical methods, the system sizes studied reveal that the presence of interaction is always correlated to a volume-law weakly monitored phase. In contrast, non-interacting systems present sub-extensive scaling of entanglement. Other characteristics, namely integrability or U(1) symmetry, do not play a role in the character of the entanglement phase.