Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions

TL;DR

This paper investigates the measurement-induced phase transition in monitored, interacting fermions, proposing a conjecture that the transition is governed by a noninteracting critical point, with implications for entanglement behavior.

Contribution

It introduces a conjecture linking the MIPT in interacting fermions to a noninteracting DIII class, supported by analytical and numerical considerations.

Findings

Conjecture that MIPT in interacting fermions is governed by a noninteracting DIII class transition.

Identification of a candidate noninteracting critical point for the phase transition.

Proposal of numerical tests to verify the conjecture.

Abstract

At a generic volume- to area-law entanglement transition in a many-body system, quantum chaos is arrested. We argue that this tends to imply the vanishing of a certain "mass" term in the field theory of the measurement-induced phase transition (MIPT) for monitored, interacting fermions. To explore this idea, we consider the MIPT with no conserved quantities that describes 1D monitored, interacting Majorana fermions in class DIII. We conjecture that the MIPT is the noninteracting DIII one in this case; the volume-law phase arises through the dangerously irrelevant mass. We propose numerical tests of our conjecture and analytically identify a candidate noninteracting critical point.