Generalized Lindblad master equation for measurement-induced phase transition

Zhou, Yi-Neng

doi:10.21468/SciPostPhysCore.6.1.023

SciPost Physics Core

Generalized Lindblad master equation for measurement-induced phase transition

Yi-Neng Zhou

SciPost Phys. Core 6, 023 (2023) · published 30 March 2023

doi: 10.21468/SciPostPhysCore.6.1.023
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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 the second Rényi 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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.1.023
TI  - Generalized Lindblad master equation for measurement-induced phase transition
PY  - 2023/03/30
UR  - https://www.scipost.org/SciPostPhysCore.6.1.023
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 1
SP  - 023
A1  - Zhou, Yi-Neng
AB  - 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 the second Rényi 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.
ER  -

@Article{10.21468/SciPostPhysCore.6.1.023,
	title={{Generalized Lindblad master equation for measurement-induced phase transition}},
	author={Yi-Neng Zhou},
	journal={SciPost Phys. Core},
	volume={6},
	pages={023},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.1.023},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.1.023},
}

Cited by 3

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¹ Yi-Neng Zhou

¹ Tsinghua University [THU]