No measurement induced phase transition in the entanglement dynamics of monitored non-interacting one-dimensional fermions in a disordered or quasiperiodic potential

TL;DR

This study demonstrates that one-dimensional non-interacting fermions under monitoring in disordered or quasiperiodic potentials do not exhibit measurement-induced phase transitions, with entanglement entropy always following an area law.

Contribution

The paper provides numerical and analytical evidence that no measurement-induced phase transition occurs in these systems, correcting previous finite-size based claims.

Findings

Entanglement entropy remains in an area-law phase regardless of monitoring strength.

No critical monitoring strength is found; it is consistent with zero.

Analytical mapping confirms the absence of MIPT for all disorder and monitoring strengths.

Abstract

We show that the entanglement entropy (EE) of one-dimensional (1d) non-interacting fermions with $U(1)$ symmetry in the presence of a disordered or quasi-periodic potential in which the occupation number is being monitored by homodyne or projective protocols is always in an area-law phase so no measurement induced phase transition (MIPT) occurs. The reason for the previously claimed MIPT in these systems was a finite size effect related to the fact that the maximum lattice size $L \sim 500$ was of the order of the correlation length. By increasing the system size up to $L \leq 18000$, employing Graphics Processing Unit (GPU), and performing a careful finite size scaling analysis, we find that the critical monitoring strength is consistent with zero so no MIPT occurs. For the disordered case, these numerical results are fully supported by an analytical calculation based on mapping the problem onto a nonlinear sigma model (NLSM) that confirms the absence of the MIPT for any monitoring or disorder strength. The effect of disorder is captured by a change of symmetry, from BDI to AIII, which results in an enhanced correlation length in the weak disorder limit and, by an effective monitoring strength that increase linearly with disorder.