Rényi entropy dynamics and Lindblad spectrum for open quantum systems

Zhou, Yi-Neng; Mao, Liang; Zhai, Hui

doi:10.1103/physrevresearch.3.043060

Cited by 20 publications

(5 citation statements)

References 37 publications

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“…The dynamics of the second Rényi entropy can be mapped to the dynamics of a wave function defined on a double space, and therefore the second Rényi entropy dynamics is more straightforward when it is written on a double space [34,35]. We denote the two copies of the system on double space as the left(L) and the right(R) system, and we use ρ D to denote the total density matrix of the double system.…”

Section: The Application Of Generalized Lindblad Equation On the Miptmentioning

confidence: 99%

Generalized Lindblad master equation for measurement-induced phase transition

Zhou

2023

SciPost Phys. Core

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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.

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Section: The Application Of Generalized Lindblad Equation On the Miptmentioning

confidence: 99%

Generalized Lindblad master equation for measurement-induced phase transition

Zhou

2023

SciPost Phys. Core

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“…The dynamics of the second Rényi entropy can be mapped to the dynamics of a wave function defined on a double space, and therefore the second Rényi entropy dynamics is more straightforward when it is written on a double space [28]. We denote the two copies of the system on double space as the left(L) and the right(R) system, and we use ρ D to denote the total density matrix of the double system.…”

Section: Application On the Measurementinduced Phase Transitionmentioning

confidence: 99%

Generalized Lindblad Master Equation for Measurement-induced Phase Transition

Zhou¹

2022

Preprint

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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 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.

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“…[21] to our model. To outline our FSS theory, we mainly focus on the scaling properties of the critical correlations and one of the most common entanglement quantifiers, i.e., the entanglement entropy [22].…”

Section: Introductionmentioning

confidence: 99%

Liovillian gap and out-of-equilibrium dynamics of a sunburst Kitaev ring: from local to uniform dissipation

Franchi¹,

Tarantelli²

2023

Preprint

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We consider an open quantum system composed of a (1 + 1)-dimensional Kitaev ring coupled with the environment via n particle-loss dissipators in a sunburst geometry. We describe the outof-equilibrium dynamics of the whole apparatus in terms of Lindblad master equations and focus on the scaling behavior of the Liouvillian gap ∆ λ with the system size L. We unveil different regimes, which depend on the number of dissipation sources considered in the large-size limit and the dissipation strength w, which can be either fixed or attenuated to zero as w ∼ 1/L. In the second part, we develop a dynamic Finite-Size Scaling framework close to Continuous Quantum Transitions to monitor the time evolution of the critical correlations and the entanglement entropy, emphasizing the role of ∆ λ in this regime.

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Rényi entropy dynamics and Lindblad spectrum for open quantum systems

Cited by 20 publications

References 37 publications

Generalized Lindblad master equation for measurement-induced phase transition

Generalized Lindblad master equation for measurement-induced phase transition

Generalized Lindblad Master Equation for Measurement-induced Phase Transition

Liovillian gap and out-of-equilibrium dynamics of a sunburst Kitaev ring: from local to uniform dissipation

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