Monitored interacting Dirac fermions

• URL: http://arxiv.org/abs/2502.02645v1
• Date: Tue, 04 Feb 2025 19:00:04 GMT
• Title: Monitored interacting Dirac fermions
• Authors: Thomas Martin Müller, Michael Buchhold, Sebastian Diehl,
• Abstract summary: We analytically study interacting Dirac fermions under weak local particle number measurements. This system maps to a bosonic replica field theory, analyzed via the renormalization group.
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• 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.

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