Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence, and Free Hamiltonian Evolution

TL;DR

This paper investigates how dephasing affects monitored fermion systems, revealing that measurement-induced phase transitions persist under weak decoherence, while strong dephasing introduces an effective temperature and classical diffusion signatures.

Contribution

It provides a comprehensive analysis of monitored fermion dynamics under decoherence using exact solutions, quantum simulations, and field theory, highlighting the robustness of phase transitions and new scaling behaviors.

Findings

Measurement-induced phase transition persists under weak dephasing.

Strong dephasing leads to an effective temperature and increased mixedness.

Scale-invariant correlations indicate classical diffusion in the strongly decohered phase.

Abstract

The interplay of unitary evolution and local measurements in many-body systems gives rise to a stochastic state evolution and to measurement-induced phase transitions in the pure state entanglement. In realistic settings, however, this dynamics may be spoiled by decoherence, e.g., dephasing, due to coupling to an environment or measurement imperfections. We investigate the impact of dephasing and the inevitable evolution into a non-Gaussian, mixed state, on the dynamics of monitored fermions. We approach it from three complementary perspectives: (i) the exact solution of the conditional master equation for small systems, (ii) quantum trajectory simulations of Gaussian states for large systems, and (iii) a renormalization group analysis of a bosonic replica field theory. For weak dephasing, constant monitoring preserves a weakly mixed state, which displays a robust measurement-induced phase transition between a critical and a pinned phase, as in the decoherence-free case. At strong dephasing, we observe the emergence of a new scale describing an effective temperature, which is accompanied with an increased mixedness of the fermion density matrix. Remarkably, observables such as density-density correlation functions or the subsystem parity still display scale invariant behavior even in this strongly mixed phase. We interpret this as a signature of gapless, classical diffusion, which is stabilized by the balanced interplay of Hamiltonian dynamics, measurements, and decoherence.