Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

Tang, Qicheng; Zhu, Wei

doi:10.1103/physrevresearch.2.013022

Cited by 171 publications

(79 citation statements)

References 69 publications

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“…More precisely, we aim to show that there is a nonzero critical measurement probability p X c > 0, below which the steady-state volume-law persists. This scenario is similar to the case in previously studied chaotic systems [9][10][11][12][13][14][15][16]18,19,[21][22][23][24][25]32,33].…”

Section: Entanglement Dynamics With X-basis Measurementssupporting

confidence: 82%

“…1(a). With measurements in the X basis, the transition from volume to area-law entanglement occurs at a nonzero measurement probability p X c > 0, similar to previously studied chaotic systems [9][10][11][12][13][14][15][16]18,19,[21][22][23][24][25]32,33]. On the other hand, with measurements in the Z basis, the volume law is destroyed for any nonzero p, similar to previously studied integrable systems [12,17,20].…”

Section: Systems Whose Dynamics Are Governed By An Interactingsupporting

confidence: 72%

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Measurement-induced entanglement transitions in many-body localized systems

Lunt

Pal

2020

Phys. Rev. Research

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The resilience of quantum entanglement to a classicality-inducing environment is tied to fundamental aspects of quantum many-body systems. The dynamics of entanglement has recently been studied in the context of measurement-induced entanglement transitions, where the steady-state entanglement collapses from a volume law to an area law at a critical measurement probability p c. Interestingly, there is a distinction in the value of p c depending on how well the underlying unitary dynamics scramble quantum information. For strongly chaotic systems, p c > 0, whereas for weakly chaotic systems, such as integrable models, p c = 0. In this work, we investigate these measurement-induced entanglement transitions in a system where the underlying unitary dynamics are many-body localized (MBL). We demonstrate that the emergent integrability in an MBL system implies a qualitative difference in the nature of the measurement-induced transition depending on the measurement basis, with p c > 0 when the measurement basis is scrambled and p c = 0 when it is not. This feature is not found in Haar-random circuit models, where all local operators are scrambled in time. When the transition occurs at p c > 0, we use finite-size scaling to obtain the critical exponent ν = 1.3(2), close to the value for (2+0)-dimensional percolation. We also find a dynamical critical exponent of z = 0.98(4) and logarithmic scaling of the Rényi entropies at criticality, suggesting an underlying conformal symmetry at the critical point. This work further demonstrates how the nature of the measurement-induced entanglement transition depends on the scrambling nature of the underlying unitary dynamics. This leads to further questions on the control and simulation of entangled quantum states by measurements in open quantum systems.

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Section: Entanglement Dynamics With X-basis Measurementssupporting

confidence: 82%

Section: Systems Whose Dynamics Are Governed By An Interactingsupporting

confidence: 72%

Measurement-induced entanglement transitions in many-body localized systems

Lunt

Pal

2020

Phys. Rev. Research

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“…Recently it is observed that a unitary dynamics subjected to repeated measurement can exhibit non-thermal phases if we follow the quantum trajectory of the many-body wave function. More strikingly, by varying the measurement rate, there is a continuous entanglement phase transition [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In the phase with slow measurement rate, the state remains highly entangled and the entanglement entropy obeys volume law scaling, while in the phase with fast measurement rate, the entanglement entropy obeys area law scaling.…”

Section: Introductionmentioning

confidence: 99%

Non-unitary dynamics of Sachdev-Ye-Kitaev chain

2021

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We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large N limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

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“…The effective spin model may also be extended to dynamics with measurement, or other types of interaction with an environment, for example, to clarify the relationship between different universality classes of measurementinduced criticality [88,89,[93][94][95][96][97][98][99][100][101][102][103].…”

Section: Discussionmentioning

confidence: 99%

Entanglement Membrane in Chaotic Many-Body Systems

2020

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In certain analytically tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables reduces to an effective theory of an "entanglement membrane" in spacetime. These tractable systems involve an average over random local unitaries defining the dynamical evolution. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries. Our approach relies on introducing effective pairing degrees of freedom in spacetime, describing a pairing of forward and backward Feynman trajectories, inspired by the structure emerging in random unitary circuits. This viewpoint provides a framework for applying ideas of coarse graining to dynamical quantities in chaotic systems. We apply the approach to some translationally invariant Floquet spin chains studied in the literature. We show that a consistent line tension may be defined for the entanglement membrane and that there are qualitative differences in this tension between generic models and "dualunitary" circuits. These results allow scaling pictures for out-of-time-order correlators and for entanglement to be taken over from random circuits to nonrandom Floquet models. We also provide an efficient numerical algorithm for determining the entanglement line tension in 1 þ 1D.

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Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

Cited by 171 publications

References 69 publications

Measurement-induced entanglement transitions in many-body localized systems

Measurement-induced entanglement transitions in many-body localized systems

Non-unitary dynamics of Sachdev-Ye-Kitaev chain

Entanglement Membrane in Chaotic Many-Body Systems

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