Monitored fermions with conserved <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>U</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> charge

Abstract

We study measurement-induced phases of free fermion systems with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>U</a:mi> <a:mo>(</a:mo> <a:mn>1</a:mn> <a:mo>)</a:mo> </a:mrow> </a:math> 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 timescales. We focus on a multiflavor 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) nonlinear sigma model ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>NL</b:mi> <b:mi>σ</b:mi> <b:mi mathvariant="normal">M</b:mi> </b:mrow> </b:math> ) coupled to fluctuating hydrodynamics. Contrary to the case of noninteracting Majorana fermions, displaying no <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>U</d:mi> <d:mo>(</d:mo> <d:mn>1</d:mn> <d:mo>)</d:mo> </d:mrow> </d:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:mi>NL</e:mi> <e:mi>σ</e:mi> <e:mi mathvariant="normal">M</e:mi> </e:mrow> </e:math> and also discuss higher-dimensional generalizations. Published by the American Physical Society 2024

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