Free fermions under adaptive quantum dynamics

TL;DR

This paper investigates free fermion systems under adaptive quantum dynamics with measurements and corrective operations, revealing distinct entanglement and steering phase transitions with different universality classes.

Contribution

It introduces a classical flag mechanism in adaptive dynamics, identifying a new steering transition in the PC universality class and distinguishing it from the entanglement transition.

Findings

Measurement-induced entanglement transition from critical to area-law scaling.

Steering transition characterized by charge-density-wave order.

Both transitions confirmed through numerical simulations.

Abstract

We study free fermion systems under adaptive quantum dynamics consisting of unitary gates and projective measurements followed by corrective unitary operations. We further introduce a classical flag for each site, allowing for an active or inactive status which determines whether or not the unitary gates are allowed to apply. In this dynamics, the individual quantum trajectories exhibit a measurement-induced entanglement transition from critical to area-law scaling above a critical measurement rate, similar to previously studied models of free fermions under continuous monitoring. Furthermore, we find that the corrective unitary operations can steer the system into a state characterized by charge-density-wave order. Consequently, an additional phase transition occurs, which can be observed at both the level of the quantum trajectory and the quantum channel. We establish that the entanglement transition and the steering transition are fundamentally distinct. The latter transition belongs to the parity-conserving (PC) universality class, arising from the interplay between the inherent fermionic parity and classical labelling. We demonstrate both the entanglement and the steering transitions via efficient numerical simulations of free fermion systems, which confirm the PC universality class of the latter.