In Brownian SYK models, operator size under the bath-traced Lindblad definition shows a scrambling signature only for intra-system interactions, with the same early-time critical point as the full-contour definition, plus finite-size corrections.
Generalized Lindblad Master Equation for Measurement-Induced Phase Transition
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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.
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Refining the Understanding of Operator Size Dynamics in Open Quantum Systems
In Brownian SYK models, operator size under the bath-traced Lindblad definition shows a scrambling signature only for intra-system interactions, with the same early-time critical point as the full-contour definition, plus finite-size corrections.