Monitored interacting Dirac fermions

TL;DR

This paper investigates how weak local measurements affect the phase transition and correlations in interacting Dirac fermions modeled by the Thirring model, revealing a BKT-type transition and entanglement properties.

Contribution

It provides an analytical study of measurement-induced phase transitions in interacting Dirac fermions, identifying a BKT transition and analyzing entanglement behavior.

Findings

A measurement-induced phase transition of BKT type occurs at a critical measurement rate.

Localized phase with exponential correlations appears beyond the critical rate.

No entanglement transition is observed in the non-interacting limit at nonzero measurement strength.

Abstract

We analytically study interacting Dirac fermions, described by the Thirring model, under weak local particle number measurements with monitoring rate $\gamma$. This system maps to a bosonic replica field theory, analyzed via the renormalization group. For a nonzero attractive interaction, a phase transition occurs at a critical measurement strength $\gamma_c$. When $\gamma>\gamma_c$, the system enters a localized phase characterized by exponentially decaying density-density correlations beyond a finite correlation length; for $\gamma<\gamma_c$, the correlations decay algebraically. The transition is of BKT-type, reflected by a characteristic scaling of the correlation length. In the non-interacting limit, $\gamma_c\to0$ shifts to zero, reducing the algebraic phase to a single point in parameter space. This identifies weak measurements in the free case as an implicit double fine-tuning to the critical endpoint of the BKT phase transition. Along the non-interacting line, we compute the entanglement entropy from density-density correlation functions and find no entanglement transition at nonzero measurement strength in the thermodynamic limit.