Entanglement in a fermion chain under continuous monitoring

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 quasiparticle 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.

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

“…relaxation, dissipation, measurements) will also influence the entanglement dramatically. One notable example is, by introducing a continuous monitoring (damping) term in quench dynamics of free Fermion chain, it is found that the volume law entanglement is unstable under arbitrary weak damping if it is applied everywhere [33]. This is similar to the quantum Zeno effect [34], where the total system is measured continuously and localized near a trivial product state.…”

Entanglement transition from variable-strength weak measurements

“…They, therefore, describe a much more versatile framework to model the influence of the environment on an open quantum system. The effect of POVM on entanglement evolution has been addressed for continuous measurements in free fermionic systems 31 , while the existence of an entanglement transition driven by measurement strength for interacting systems has been inferred by the study of mutual information 21 .…”

Yang-Baxter integrable Lindblad equations

“…where Π j,j+1 is a graded permutation operator (9) and λ α are generalized chemical potentials. The case n B = n F = 1 gives the EKS model (a.k.a.…”

“…The absence of a back action of the system onto its environment then facilitates a well defined mathematical description of open many-particle systems. In the quantum case this a priori results in a Markovian quantum stochastic many-particle system [6][7][8][9], which is however difficult to analyze. The customary approach in therefore to focus on the dynamics averaged over the environment, which leads to a description by the Lindblad master equation [10] for the time-dependent reduced density matrix ρ(t)…”