Entanglement transitions in active quantum matter

Quantum many-body systems coupled to out-of-equilibrium reservoirs can behave as active matter and may exhibit flocking transitions [1]. However, the resulting steady states are highly mixed, and it is unclear what the quantum signatures of such states are. In this work, we show that signatures of active matter can also arise in pure states undergoing monitored quantum dynamics. Specifically, we consider a spinful Luttinger liquid subject to non-hermitian measurement processes that shuffle spin-up particles to the left and spin-down particles to the right. We show that at weak measurement strength and in the presence of attractive spin-spin interactions, such processes lead to power-law correlations between spin-current and charge-density as well as charge-current and spin-density which we identify as a hallmark of active quantum matter and an incipient flocking phase. Such correlations imply logarithmic entanglement in the pure trajectory. Upon increasing the measurement strength, the trajectories undergo a BKT transition to area-law entanglement. Finally, we discuss how the inclusion of a dissipative aligning process alters these findings.

[1] R Khasseh, S Wald, R Moessner, CA Weber, M Heyl, arXiv:2308.01603