Generalized Lindblad Master Equation for Measurement-Induced Phase Transition

TL;DR

This paper introduces a generalized Lindblad master equation that models measurement-induced phase transitions by incorporating post-selection effects, providing a continuous and physically consistent description of the dynamics.

Contribution

It presents a novel generalized Lindblad equation explicitly including post-selection, applicable to MIPT, and confirms its validity through numerical simulation of a specific model.

Findings

The generalized Lindblad equation accurately describes MIPT dynamics.

Numerical results match the expected behavior of the second Rényi entropy.

The equation preserves physical properties like Hermiticity and positivity.

Abstract

The measurement-induced phase transition (MIPT) occurs when the system is evolving under unitary evolution together with local measurements followed by post-selection. We propose a generalized version of the Lindblad master equation as a continuous equation, to describe the dynamics of second R\'enyi entropy in the MIPT. This generalized Lindblad equation explicitly takes into account the post-selection in the MIPT, which is realized as the Einstein-Podolsky-Rosen (EPR) state projection in the equation. Also, this generalized Lindblad equation preserves the Hermitian, unit trace, and positive definiteness of the density matrix. We further use the hard-core Bose-Hubbard model as a concrete example to numerically confirm that our generalized Lindblad equation is applicable to describing the MIPT.