A tractable model of monitored fermions with conserved $\mathrm{U}(1)$ charge

• URL: http://arxiv.org/abs/2407.08045v2
• Date: Thu, 1 Aug 2024 09:45:29 GMT
• Title: A tractable model of monitored fermions with conserved $\mathrm{U}(1)$ charge
• Authors: Michele Fava, Lorenzo Piroli, Denis Bernard, Adam Nahum,
• Abstract summary: We study measurement-induced phases of free fermion systems with U(1) symmetry. We derive a field theory description for the purity and bipartite entanglement at large space and time scales.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study measurement-induced phases of free fermion systems with U(1) symmetry. Following a recent approach developed for Majorana chains, we derive a field theory description for the purity and bipartite entanglement at large space and time scales. We focus on a multi-flavor one-dimensional chain with random complex hoppings and continuous monitoring of the local fermion density. By means of the replica trick, and using the number of flavors as a large parameter controlling our approximations, we derive an effective field theory made up of a SU(N) non-linear sigma model (NL$\sigma$M) coupled to fluctuating hydrodynamics. Contrary to the case of non-interacting Majorana fermions, displaying no U(1) symmetry, we find that the bipartite entanglement entropy satisfies an area law for all monitoring rates, but with a nontrivial scaling of entanglement when the correlation length is large. We provide numerical evidence supporting our claims. We briefly show how imposing a reality condition on the hoppings can change the NL$\sigma$M and also discuss higher dimensional generalizations.

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