Abstract
We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.
Highlights
The dynamics of entanglement in many-body systems is a topic under intensive study, as entanglement is a fundamental notion of quantum physics, deeply tied to basic issues such as thermalization of closed quantum systems [1,2,3,4], holography [5,6,7], quantum chaos and information scrambling [8, 9]
We note that numerous variants of this model have been studied [33,34,35,36,37] using an open quantum system approach [38,39,40], which focuses on the Lindblad equation, and its large deviation theory extension [26, 35, 37]
The main result of this work is a quantitative description of the entanglement dynamics in a free fermion chain under continuous measurement of all occupation numbers, called the collapsed quasiparticle pair Ansatz
Summary
The dynamics of entanglement in many-body systems is a topic under intensive study, as entanglement is a fundamental notion of quantum physics, deeply tied to basic issues such as thermalization of closed quantum systems [1,2,3,4], holography [5,6,7], quantum chaos and information scrambling [8, 9]. We note that numerous variants of this model have been studied [33,34,35,36,37] using an open quantum system approach [38,39,40], which focuses on the Lindblad equation, and its large deviation theory extension [26, 35, 37] These methods have been used to compute observables of the averaged density of state (“mean state”), for instance, the integrated current statistics in an nonequilibrium stationary state. (The entanglement of the mean state could certainly be derived from these earlier results, but is a less interesting and in any case different quantity.) At the QT level, the model was addressed before us only in the strong measurement limit [41]; beyond this limit, the behavior of non-linear observables of the density of state, including the notable example of entanglement entropy, has not been understood. The evolution of nonlinear functionals of the conditional state is significantly more complex than that of the mean state; for recent related works, see Refs. [62, 63] 2
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