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Title: Measurement-Induced Phase Transitions in the Dynamics of Entanglement

Abstract

We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate p for each degree of freedom, we show that the system has two dynamical phases: “entangling” and “disentangling.” The former occurs for p smaller than a critical rate p c and is characterized by volume-law entanglement in the steady state and “ballistic” entanglement growth after a quench. By contrast, for p> p c the system can sustain only area-law entanglement. At p= p c the steady state is scale invariant, and in 1 + 1 D , the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Rényi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Rényi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains and show that the phenomenology of the two phases is similar to that of the toy model but with distinct “quantum” critical exponents, which we calculate numerically in 1 + 1 D . We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems.

Authors:
ORCiD logo; ;
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); Gordon and Betty Moore Foundation (GBMF)
OSTI Identifier:
1543370
Alternate Identifier(s):
OSTI ID: 1610523
Grant/Contract Number:  
SC0001088
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 9 Journal Issue: 3; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Physics; Condensed Matter Physics; Quantum Physics; Statistical Physics

Citation Formats

Skinner, Brian, Ruhman, Jonathan, and Nahum, Adam. Measurement-Induced Phase Transitions in the Dynamics of Entanglement. United States: N. p., 2019. Web. doi:10.1103/PhysRevX.9.031009.
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Skinner, Brian, Ruhman, Jonathan, & Nahum, Adam. Measurement-Induced Phase Transitions in the Dynamics of Entanglement. United States. https://doi.org/10.1103/PhysRevX.9.031009
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Skinner, Brian, Ruhman, Jonathan, and Nahum, Adam. Mon . "Measurement-Induced Phase Transitions in the Dynamics of Entanglement". United States. https://doi.org/10.1103/PhysRevX.9.031009.
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@article{osti_1543370,
title = {Measurement-Induced Phase Transitions in the Dynamics of Entanglement},
author = {Skinner, Brian and Ruhman, Jonathan and Nahum, Adam},
abstractNote = {We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate p for each degree of freedom, we show that the system has two dynamical phases: “entangling” and “disentangling.” The former occurs for p smaller than a critical rate pc and is characterized by volume-law entanglement in the steady state and “ballistic” entanglement growth after a quench. By contrast, for p>pc the system can sustain only area-law entanglement. At p=pc the steady state is scale invariant, and in 1+1D, the entanglement grows logarithmically after a quench. To obtain a simple heuristic picture for the entangling-disentangling transition, we first construct a toy model that describes the zeroth Rényi entropy in discrete time. We solve this model exactly by mapping it to an optimization problem in classical percolation. The generic entangling-disentangling transition can be diagnosed using the von Neumann entropy and higher Rényi entropies, and it shares many qualitative features with the toy problem. We study the generic transition numerically in quantum spin chains and show that the phenomenology of the two phases is similar to that of the toy model but with distinct “quantum” critical exponents, which we calculate numerically in 1+1D. We examine two different cases for the unitary dynamics: Floquet dynamics for a nonintegrable Ising model, and random circuit dynamics. We obtain compatible universal properties in each case, indicating that the entangling-disentangling phase transition is generic for projectively measured many-body systems. We discuss the significance of this transition for numerical calculations of quantum observables in many-body systems.},
doi = {10.1103/PhysRevX.9.031009},
journal = {Physical Review. X},
number = 3,
volume = 9,
place = {United States},
year = {Mon Jul 22 00:00:00 EDT 2019},
month = {Mon Jul 22 00:00:00 EDT 2019}
}
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https://doi.org/10.1103/PhysRevX.9.031009
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Works referenced in this record:

Quantum jumps of light recording the birth and death of a photon in a cavity
journal, March 2007

  • Gleyzes, Sébastien; Kuhr, Stefan; Guerlin, Christine
  • Nature, Vol. 446, Issue 7133
  • DOI: 10.1038/nature05589

Monte Carlo simulation of master equations in quantum optics for vacuum, thermal, and squeezed reservoirs
journal, October 1992

Quantum dynamics of thermalizing systems
journal, January 2018

  • White, Christopher David; Zaletel, Michael; Mong, Roger S. K.
  • Physical Review B, Vol. 97, Issue 3
  • DOI: 10.1103/PhysRevB.97.035127

Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory
journal, June 2018

Computational complexity and black hole horizons: Computational complexity and black hole horizons
journal, January 2016

Series study of random percolation in three dimensions
journal, March 1983

Entanglement entropy and conformal field theory
journal, December 2009

Chaos and complexity by design
journal, April 2017

  • Roberts, Daniel A.; Yoshida, Beni
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)121

Spectral Statistics in Spatially Extended Chaotic Quantum Many-Body Systems
journal, August 2018

Chaos in quantum channels
journal, February 2016

  • Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)004

Fractal structure of Ising and Potts clusters: Exact results
journal, June 1989

Chaos, complexity, and random matrices
journal, November 2017

  • Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)048

Quantum Zeno effect and the many-body entanglement transition
journal, November 2018

Holographic duality from random tensor networks
journal, November 2016

  • Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)009

Semiclassical limit for the many-body localization transition
journal, July 2015

Membrane theory of entanglement dynamics from holography
journal, November 2018

Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System
journal, September 2013

Stability of Elastic Glass Phases in Random Field XY Magnets and Vortex Lattices in Type-II Superconductors
journal, March 1997

Entanglement entropy dynamics of Heisenberg chains
journal, March 2006

  • Chiara, Gabriele De; Montangero, Simone; Calabrese, Pasquale
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2006, Issue 03
  • DOI: 10.1088/1742-5468/2006/03/P03001

Second law of quantum complexity
journal, April 2018

Complexity and shock wave geometries
journal, December 2014

Matrix product states represent ground states faithfully
journal, March 2006

Quantum Computation as Geometry
journal, February 2006

Entanglement production and information scrambling in a noisy spin system
journal, November 2018

Dynamical phases and intermittency of the dissipative quantum Ising model
journal, April 2012

Entanglement scrambling in 2d conformal field theory
journal, September 2015

  • Asplund, Curtis T.; Bernamonti, Alice; Galli, Federico
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)110

Unbounded Growth of Entanglement in Models of Many-Body Localization
journal, July 2012

Time-integrated observables as order parameters for full counting statistics transitions in closed quantum systems
journal, May 2013

Entanglement dynamics in quantum many-body systems
journal, March 2017

Simultaneous analysis of three-dimensional percolation models
journal, November 2013

Quantum trajectories and open many-body quantum systems
journal, March 2014

Quantum to classical phase transition in noisy quantum computers
journal, November 2000

Emergent statistical mechanics of entanglement in random unitary circuits
journal, May 2019

Monte Carlo wave-function method in quantum optics
journal, January 1993

  • Mølmer, Klaus; Castin, Yvan; Dalibard, Jean
  • Journal of the Optical Society of America B, Vol. 10, Issue 3
  • DOI: 10.1364/JOSAB.10.000524

Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos
journal, October 2018

Critical behavior of the two-dimensional first passage time
journal, December 1986

  • Chayes, J. T.; Chayes, L.; Durrett, R.
  • Journal of Statistical Physics, Vol. 45, Issue 5-6
  • DOI: 10.1007/BF01020583

Observing single quantum trajectories of a superconducting quantum bit
journal, October 2013

  • Murch, K. W.; Weber, S. J.; Macklin, C.
  • Nature, Vol. 502, Issue 7470
  • DOI: 10.1038/nature12539

Unitary-projective entanglement dynamics
journal, June 2019

Exact tricritical exponents for polymers at the FTHETA point in two dimensions
journal, August 1987

Many-body localization in the Heisenberg X X Z magnet in a random field
journal, February 2008

Computing the rates of measurement-induced quantum jumps
journal, June 2015

  • Bauer, Michel; Bernard, Denis; Tilloy, Antoine
  • Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue 25
  • DOI: 10.1088/1751-8113/48/25/25FT02

Conformal boundary conditions in the critical model and dilute loop models
journal, March 2010

Convergence of repeated quantum nondemolition measurements and wave-function collapse
journal, October 2011

Solution of a Minimal Model for Many-Body Quantum Chaos
journal, November 2018

Characterization of Dynamical Phase Transitions in Quantum Jump Trajectories Beyond the Properties of the Stationary State
journal, April 2013

Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws
journal, September 2018

Critical Percolation Probabilities (Bond Problem)
journal, September 1961

The quantum-jump approach to dissipative dynamics in quantum optics
journal, January 1998

Quantum Entanglement Growth under Random Unitary Dynamics
journal, July 2017

Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation
journal, September 2018

  • Rakovszky, Tibor; Pollmann, Frank; von Keyserlingk, C. W.
  • Physical Review X, Vol. 8, Issue 3
  • DOI: 10.1103/PhysRevX.8.031058

The emergence of typical entanglement in two-party random processes
journal, June 2007

  • Dahlsten, O. C. O.; Oliveira, R.; Plenio, M. B.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 40, Issue 28
  • DOI: 10.1088/1751-8113/40/28/S16

Wave-function approach to dissipative processes in quantum optics
journal, February 1992

Critical Percolation Probabilities by Series Methods
journal, January 1964

Generalized Entanglement Entropies of Quantum Designs
journal, March 2018

On entanglement spreading in chaotic systems
journal, May 2017

Operator Spreading in Random Unitary Circuits
journal, April 2018

On entanglement spreading from holography
journal, May 2017

Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws
journal, April 2018

  • von Keyserlingk, C. W.; Rakovszky, Tibor; Pollmann, Frank
  • Physical Review X, Vol. 8, Issue 2
  • DOI: 10.1103/PhysRevX.8.021013

Holographic Complexity Equals Bulk Action?
journal, May 2016

Huse, Henley, and Fisher respond
journal, December 1985

  • Huse, David A.; Henley, Christopher L.; Fisher, Daniel S.
  • Physical Review Letters, Vol. 55, Issue 26
  • DOI: 10.1103/PhysRevLett.55.2924

Localized shocks
journal, March 2015

  • Roberts, Daniel A.; Stanford, Douglas; Susskind, Leonard
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)051

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
journal, June 2015

  • Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)149

Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System
journal, July 2016

Evolution of entanglement entropy in one-dimensional systems
journal, April 2005

Critical curves in conformally invariant statistical systems
journal, February 2007

  • Rushkin, I.; Bettelheim, E.; Gruzberg, I. A.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 40, Issue 9
  • DOI: 10.1088/1751-8113/40/9/020

Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics
journal, January 2017

Quantum thermalization through entanglement in an isolated many-body system
journal, August 2016

Dynamic Scaling of Growing Interfaces
journal, March 1986

Noisy coupled qubits: Operator spreading and the Fredrickson-Andersen model
journal, November 2018

Efficient Classical Simulation of Slightly Entangled Quantum Computations
journal, October 2003

Thermodynamics of Quantum Jump Trajectories
journal, April 2010

Entanglement Tsunami: Universal Scaling in Holographic Thermalization
journal, January 2014

Spread of entanglement in a Sachdev-Ye-Kitaev chain
journal, September 2017

  • Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang
  • Journal of High Energy Physics, Vol. 2017, Issue 9
  • DOI: 10.1007/JHEP09(2017)120

Exact convergence times for generation of random bipartite entanglement
journal, September 2008

Spikes in quantum trajectories
journal, November 2015

Entanglement renormalization and holography
journal, September 2012

Spread of entanglement and causality
journal, July 2016

  • Casini, Horacio; Liu, Hong; Mezei, Márk
  • Journal of High Energy Physics, Vol. 2016, Issue 7
  • DOI: 10.1007/JHEP07(2016)077

Quantum complexity and negative curvature
journal, February 2017

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