Mean-field entanglement transitions in random tree tensor networks

Lopez-Piqueres, Javier; Ware, Brayden; Vasseur, Romain

doi:10.1103/physrevb.102.064202

Title: Mean-field entanglement transitions in random tree tensor networks

Abstract

Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. Furthermore, we verify our predictions numerically by computing directly the entanglement of random tree tensor network states.

Authors:

Lopez-Piqueres, Javier ^[1]; Ware, Brayden ^[1]; Vasseur, Romain ^[1]

Univ. of Massachusetts, Amherst, MA (United States)

Publication Date:: Thu Aug 06 00:00:00 EDT 2020

Research Org.:: Univ. of Massachusetts, Amherst, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1647652

Grant/Contract Number:: SC0019168

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. B

Additional Journal Information:: Journal Volume: 102; Journal Issue: 6; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Critical phenomena; Entanglement entropy; Quantum entanglement; Cavity methods; Replica methods; Tensor network methods

Citation Formats


                    Lopez-Piqueres, Javier, Ware, Brayden, and Vasseur, Romain. Mean-field entanglement transitions in random tree tensor networks.  United States: N. p., 2020. 
Web.  doi:10.1103/physrevb.102.064202.

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                    Lopez-Piqueres, Javier, Ware, Brayden, & Vasseur, Romain. Mean-field entanglement transitions in random tree tensor networks.  United States.  https://doi.org/10.1103/physrevb.102.064202

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                    Lopez-Piqueres, Javier, Ware, Brayden, and Vasseur, Romain. Thu .  
"Mean-field entanglement transitions in random tree tensor networks".  United States.  https://doi.org/10.1103/physrevb.102.064202.  https://www.osti.gov/servlets/purl/1647652.

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@article{osti_1647652,

  title        = {Mean-field entanglement transitions in random tree tensor networks},

  author       = {Lopez-Piqueres, Javier and Ware, Brayden and Vasseur, Romain},

  abstractNote = {Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a mean-field theory of such transitions by studying the entanglement properties of random tree tensor networks. As a function of bond dimension, we find a phase transition separating area-law from logarithmic scaling of the entanglement entropy. Using a mapping onto a replica statistical mechanics model defined on a Cayley tree and the cavity method, we analyze the scaling properties of such transitions. Our approach provides a tractable, mean-field-like example of an entanglement transition. Furthermore, we verify our predictions numerically by computing directly the entanglement of random tree tensor network states.},

  doi          = {10.1103/physrevb.102.064202},

  journal      = {Physical Review. B},

  number       = 6,

  volume       = 102,

  place        = {United States},

  year         = {Thu Aug 06 00:00:00 EDT 2020},

  month        = {Thu Aug 06 00:00:00 EDT 2020}

}

Copy to clipboard

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Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
text, January 2021

Turkeshi, Xhek; Biella, Alberto; Fazio, Rosario
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DOI: 10.48550/arxiv.2103.09138

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Title: Mean-field entanglement transitions in random tree tensor networks

Abstract

Citation Formats

Colloquium : Many-body localization, thermalization, and entanglement journal, May 2019

Unitary-projective entanglement dynamics journal, June 2019

Colloquium : Area laws for the entanglement entropy journal, February 2010

Critical properties of the measurement-induced transition in random quantum circuits journal, February 2020

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

Exact Critical Point and Critical Exponents of O ( n ) Models in Two Dimensions journal, October 1982

Entanglement transition from variable-strength weak measurements journal, August 2019

Critical phenomena in complex networks journal, October 2008

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

Entanglement transitions from holographic random tensor networks journal, October 2019

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

Measurement-driven entanglement transition in hybrid quantum circuits journal, October 2019

Measurement-induced criticality in random quantum circuits journal, March 2020

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

Theory of the phase transition in random unitary circuits with measurements journal, March 2020

Quantum Entanglement Growth under Random Unitary Dynamics journal, July 2017

Holographic duality from random tensor networks journal, November 2016

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

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations journal, January 2020

Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge journal, November 2019

Classical simulation of quantum many-body systems with a tree tensor network journal, August 2006

A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal, October 2014

Entanglement in many-body systems journal, May 2008

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization journal, June 2016

Operator Spreading in Random Unitary Circuits journal, April 2018

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

Nonuniversal entanglement level statistics in projection-driven quantum circuits journal, June 2020

Information, Physics, and Computation book, January 2009

Many-Body Localization and Thermalization in Quantum Statistical Mechanics journal, March 2015

Many-body localization: An introduction and selected topics journal, September 2018

Exact correlation functions of Bethe lattice spin models in external magnetic fields journal, August 1998

Quantum entanglement in condensed matter systems journal, August 2016

Bethe Lattice and the Bethe Approximation journal, January 1974

Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition journal, July 2020

Entanglement in a fermion chain under continuous monitoring journal, January 2019

Measurement-Induced Phase Transitions in the Dynamics of Entanglement journal, July 2019

Simulating strongly correlated quantum systems with tree tensor networks journal, November 2010

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

Scalable probes of measurement-induced criticality text, January 2019

Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks text, January 2021

Colloquium : Many-body localization, thermalization, and entanglement
journal, May 2019

Unitary-projective entanglement dynamics
journal, June 2019

Colloquium : Area laws for the entanglement entropy
journal, February 2010

Critical properties of the measurement-induced transition in random quantum circuits
journal, February 2020

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

Exact Critical Point and Critical Exponents of $O (n)$ Models in Two Dimensions
journal, October 1982

Entanglement transition from variable-strength weak measurements
journal, August 2019

Critical phenomena in complex networks
journal, October 2008

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

Entanglement transitions from holographic random tensor networks
journal, October 2019

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

Measurement-driven entanglement transition in hybrid quantum circuits
journal, October 2019

Measurement-induced criticality in random quantum circuits
journal, March 2020

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

Theory of the phase transition in random unitary circuits with measurements
journal, March 2020

Quantum Entanglement Growth under Random Unitary Dynamics
journal, July 2017

Holographic duality from random tensor networks
journal, November 2016

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

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations
journal, January 2020

Spectral Statistics and Many-Body Quantum Chaos with Conserved Charge
journal, November 2019

Classical simulation of quantum many-body systems with a tree tensor network
journal, August 2006

A practical introduction to tensor networks: Matrix product states and projected entangled pair states
journal, October 2014

Entanglement in many-body systems
journal, May 2008

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization
journal, June 2016

Operator Spreading in Random Unitary Circuits
journal, April 2018

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

Nonuniversal entanglement level statistics in projection-driven quantum circuits
journal, June 2020

Information, Physics, and Computation
book, January 2009

Many-Body Localization and Thermalization in Quantum Statistical Mechanics
journal, March 2015

Many-body localization: An introduction and selected topics
journal, September 2018

Exact correlation functions of Bethe lattice spin models in external magnetic fields
journal, August 1998

Quantum entanglement in condensed matter systems
journal, August 2016

Bethe Lattice and the Bethe Approximation
journal, January 1974

Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
journal, July 2020

Entanglement in a fermion chain under continuous monitoring
journal, January 2019

Measurement-Induced Phase Transitions in the Dynamics of Entanglement
journal, July 2019

Simulating strongly correlated quantum systems with tree tensor networks
journal, November 2010

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

Scalable probes of measurement-induced criticality
text, January 2019

Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
text, January 2021