Controlling entanglement at absorbing state phase transitions in random circuits

TL;DR

This paper investigates how feedback control operations influence entanglement entropy at absorbing state phase transitions in random quantum circuits, revealing different scaling behaviors and the coupling of fluctuations depending on the control range and strength.

Contribution

It introduces a framework using stabilizer circuits with classical flags to analyze entanglement behavior at absorbing state transitions under feedback control.

Findings

Short-range control leads to distinct sub-extensive entanglement phases.

Long-range feedback induces a transition between volume-law and area-law entanglement.

Entanglement fluctuations are coupled to the order parameter for strong feedback operations.

Abstract

Many-body unitary dynamics interspersed with repeated measurements display a rich phenomenology hallmarked by measurement-induced phase transitions. Employing feedback-control operations that steer the dynamics toward an absorbing state, we study the entanglement entropy behavior at the absorbing state phase transition. For short-range control operations, we observe a transition between phases with distinct sub-extensive scalings of entanglement entropy. In contrast, the system undergoes a transition between volume-law and area-law phases for long-range feedback operations. The fluctuations of entanglement entropy and of the order parameter of the absorbing state transition are fully coupled for sufficiently strongly entangling feedback operations. In that case, entanglement entropy inherits the universal dynamics of the absorbing state transition. This is, however, not the case for arbitrary control operations, and the two transitions are generally distinct. We quantitatively support our results by introducing a framework based on stabilizer circuits with classical flag labels. Our results shed new light on the problem of observability of measurement-induced phase transitions.