This content will become publicly available on October 9, 2020
Entanglement transitions from holographic random tensor networks
Abstract
Here, we introduce a class of phase transitions separating quantum states with different entanglement features. An example of such an “entanglement phase transition” is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the “holographic” boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.
- Authors:
- Univ. of Massachusetts, Amherst, MA (United States). Dept. of Physics
- Univ. of Texas, Austin, TX (United States). Dept. of Physics
- Harvard Univ., Cambridge, MA (United States). Dept. of Physics; Univ. of California, San Diego, CA (United States). Dept. of Physics
- Univ. of California, Santa Barbara, CA (United States). Dept. of physics
- Publication Date:
- Research Org.:
- Univ. of Massachusetts, Amherst, MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1569745
- Grant/Contract Number:
- SC0019168
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 13; 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; Quantum entanglement; tensor networks
Citation Formats
Vasseur, Romain, Potter, Andrew C., You, Yi-Zhuang, and Ludwig, Andreas W. W. Entanglement transitions from holographic random tensor networks. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.100.134203.
Vasseur, Romain, Potter, Andrew C., You, Yi-Zhuang, & Ludwig, Andreas W. W. Entanglement transitions from holographic random tensor networks. United States. doi:10.1103/PhysRevB.100.134203.
Vasseur, Romain, Potter, Andrew C., You, Yi-Zhuang, and Ludwig, Andreas W. W. Wed .
"Entanglement transitions from holographic random tensor networks". United States. doi:10.1103/PhysRevB.100.134203.
@article{osti_1569745,
title = {Entanglement transitions from holographic random tensor networks},
author = {Vasseur, Romain and Potter, Andrew C. and You, Yi-Zhuang and Ludwig, Andreas W. W.},
abstractNote = {Here, we introduce a class of phase transitions separating quantum states with different entanglement features. An example of such an “entanglement phase transition” is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the “holographic” boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this statistical mechanics model. Our approach allows us to get an analytic handle on the field theory of these entanglement transitions.},
doi = {10.1103/PhysRevB.100.134203},
journal = {Physical Review B},
number = 13,
volume = 100,
place = {United States},
year = {2019},
month = {10}
}
Works referenced in this record:
Black holes as mirrors: quantum information in random subsystems
journal, September 2007
- Hayden, Patrick; Preskill, John
- Journal of High Energy Physics, Vol. 2007, Issue 09
Holographic geometry of the renormalization group and higher spin symmetries
journal, May 2014
- Leigh, Robert G.; Parrikar, Onkar; Weiss, Alexander B.
- Physical Review D, Vol. 89, Issue 10
Towards the fast scrambling conjecture
journal, April 2013
- Lashkari, Nima; Stanford, Douglas; Hastings, Matthew
- Journal of High Energy Physics, Vol. 2013, Issue 4
Interactions and the Anderson transition
journal, March 1980
- Fleishman, L.; Anderson, P. W.
- Physical Review B, Vol. 21, Issue 6
Many-Body Delocalization as a Quantum Avalanche
journal, October 2018
- Thiery, Thimothée; Huveneers, François; Müller, Markus
- Physical Review Letters, Vol. 121, Issue 14
Conformal Field Theories Coupled to 2-d Gravity in the Conformal Gauge
journal, December 1988
- David, F.
- Modern Physics Letters A, Vol. 03, Issue 17
Entanglement Renormalization for Quantum Fields in Real Space
journal, March 2013
- Haegeman, Jutho; Osborne, Tobias J.; Verschelde, Henri
- Physical Review Letters, Vol. 110, Issue 10
Entanglement Renormalization
journal, November 2007
- Vidal, G.
- Physical Review Letters, Vol. 99, Issue 22
Efficient variational diagonalization of fully many-body localized Hamiltonians
journal, July 2016
- Pollmann, Frank; Khemani, Vedika; Cirac, J. Ignacio
- Physical Review B, Vol. 94, Issue 4
Weak and strong typicality in quantum systems
journal, July 2012
- Santos, Lea F.; Polkovnikov, Anatoli; Rigol, Marcos
- Physical Review E, Vol. 86, Issue 1
Density matrix formulation for quantum renormalization groups
journal, November 1992
- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19
Critical properties of randomly triangulated planar random surfaces
journal, July 1985
- Kazakov, V. A.; Kostov, I. K.; Migdal, A. A.
- Physics Letters B, Vol. 157, Issue 4
Critical properties of two-dimensional models
journal, January 1981
- Black, J. L.; Emery, V. J.
- Physical Review B, Vol. 23, Issue 1
Dynamics of entanglement and transport in one-dimensional systems with quenched randomness
journal, July 2018
- Nahum, Adam; Ruhman, Jonathan; Huse, David A.
- Physical Review B, Vol. 98, Issue 3
Quantum Gravity in two Dimensions
journal, November 1987
- Polyakov, A. M.
- Modern Physics Letters A, Vol. 02, Issue 11
Scaling Theory of Entanglement at the Many-Body Localization Transition
journal, September 2017
- Dumitrescu, Philipp T.; Vasseur, Romain; Potter, Andrew C.
- Physical Review Letters, Vol. 119, Issue 11
Many-Body Localization in a Disordered Quantum Ising Chain
journal, September 2014
- Kjäll, Jonas A.; Bardarson, Jens H.; Pollmann, Frank
- Physical Review Letters, Vol. 113, Issue 10
Ab initio holography
journal, August 2015
- Lunts, Peter; Bhattacharjee, Subhro; Miller, Jonah
- Journal of High Energy Physics, Vol. 2015, Issue 8
Emergent statistical mechanics of entanglement in random unitary circuits
journal, May 2019
- Zhou, Tianci; Nahum, Adam
- Physical Review B, Vol. 99, Issue 17
Area laws in a many-body localized state and its implications for topological order
journal, September 2013
- Bauer, Bela; Nayak, Chetan
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 09
Many-body localization and symmetry-protected topological order
journal, April 2014
- Chandran, Anushya; Khemani, Vedika; Laumann, C. R.
- Physical Review B, Vol. 89, Issue 14
Unitary-projective entanglement dynamics
journal, June 2019
- Chan, Amos; Nandkishore, Rahul M.; Pretko, Michael
- Physical Review B, Vol. 99, Issue 22
Many-body localization phase transition
journal, November 2010
- Pal, Arijeet; Huse, David A.
- Physical Review B, Vol. 82, Issue 17
Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications
journal, November 2013
- Cardy, John
- Journal of Physics A: Mathematical and Theoretical, Vol. 46, Issue 49
Colloquium : Area laws for the entanglement entropy
journal, February 2010
- Eisert, J.; Cramer, M.; Plenio, M. B.
- Reviews of Modern Physics, Vol. 82, Issue 1
Localization of interacting fermions at high temperature
journal, April 2007
- Oganesyan, Vadim; Huse, David A.
- Physical Review B, Vol. 75, Issue 15
Solution of a Minimal Model for Many-Body Quantum Chaos
journal, November 2018
- Chan, Amos; De Luca, Andrea; Chalker, J. T.
- Physical Review X, Vol. 8, Issue 4
Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws
journal, September 2018
- Khemani, Vedika; Vishwanath, Ashvin; Huse, David A.
- Physical Review X, Vol. 8, Issue 3
Proof of Page’s conjecture on the average entropy of a subsystem
journal, February 1994
- Foong, S. K.; Kanno, S.
- Physical Review Letters, Vol. 72, Issue 8
Analytical and numerical study of a model of dynamically triangulated random surfaces
journal, December 1986
- Boulatov, D. V.; Kazakov, V. A.; Kostov, I. K.
- Nuclear Physics B, Vol. 275, Issue 4
Boundary states as holographic duals of trivial spacetimes
journal, May 2015
- Miyaji, Masamichi; Ryu, Shinsei; Takayanagi, Tadashi
- Journal of High Energy Physics, Vol. 2015, Issue 5
Quantum Entanglement Growth under Random Unitary Dynamics
journal, July 2017
- Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar
- Physical Review X, Vol. 7, Issue 3
Dense Loops, Supersymmetry, and Goldstone Phases in Two Dimensions
journal, March 2003
- Jacobsen, J. L.; Read, N.; Saleur, H.
- Physical Review Letters, Vol. 90, Issue 9
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
Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states
journal, May 2006
- Basko, D. M.; Aleiner, I. L.; Altshuler, B. L.
- Annals of Physics, Vol. 321, Issue 5
Holographic interpretations of the renormalization group
journal, January 2013
- Balasubramanian, Vijay; Guica, Monica; Lawrence, Albion
- Journal of High Energy Physics, Vol. 2013, Issue 1
Operator Spreading in Random Unitary Circuits
journal, April 2018
- Nahum, Adam; Vijay, Sagar; Haah, Jeongwan
- Physical Review X, Vol. 8, Issue 2
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
Encoding the structure of many-body localization with matrix product operators
journal, January 2017
- Pekker, David; Clark, Bryan K.
- Physical Review B, Vol. 95, Issue 3
Ryu-Takayanagi formula for symmetric random tensor networks
journal, June 2018
- Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi
- Physical Review D, Vol. 97, Issue 12
Chaos and quantum thermalization
journal, August 1994
- Srednicki, Mark
- Physical Review E, Vol. 50, Issue 2
Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
journal, January 1998
- Witten, Edward
- Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 3
Localization-protected quantum order
journal, July 2013
- Huse, David A.; Nandkishore, Rahul; Oganesyan, Vadim
- Physical Review B, Vol. 88, Issue 1
Class of Highly Entangled Many-Body States that can be Efficiently Simulated
journal, June 2014
- Evenbly, G.; Vidal, G.
- Physical Review Letters, Vol. 112, Issue 24
Ising model on a dynamical planar random lattice: Exact solution
journal, December 1986
- Kazakov, V. A.
- Physics Letters A, Vol. 119, Issue 3
Renormalization and tensor product states in spin chains and lattices
journal, December 2009
- Cirac, J. Ignacio; Verstraete, Frank
- Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 50
Class of Quantum Many-Body States That Can Be Efficiently Simulated
journal, September 2008
- Vidal, G.
- Physical Review Letters, Vol. 101, Issue 11
Logarithmic operators in conformal field theory
journal, December 1993
- Gurarie, V.
- Nuclear Physics B, Vol. 410, Issue 3
Quantum renormalization group and holography
journal, January 2014
- Lee, Sung-Sik
- Journal of High Energy Physics, Vol. 2014, Issue 1
Gauge theory correlators from non-critical string theory
journal, May 1998
- Gubser, S. S.; Klebanov, I. R.; Polyakov, A. M.
- Physics Letters B, Vol. 428, Issue 1-2
Tensor Network States and Geometry
journal, June 2011
- Evenbly, G.; Vidal, G.
- Journal of Statistical Physics, Vol. 145, Issue 4
Many-body localization edge in the random-field Heisenberg chain
journal, February 2015
- Luitz, David J.; Laflorencie, Nicolas; Alet, Fabien
- Physical Review B, Vol. 91, Issue 8
Average entropy of a subsystem
journal, August 1993
- Page, Don N.
- Physical Review Letters, Vol. 71, Issue 9
Dynamical Quantum Phase Transitions in Random Spin Chains
journal, May 2014
- Vosk, Ronen; Altman, Ehud
- Physical Review Letters, Vol. 112, Issue 21
Quantum Zeno effect and the many-body entanglement transition
journal, November 2018
- Li, Yaodong; Chen, Xiao; Fisher, Matthew P. A.
- Physical Review B, Vol. 98, Issue 20
Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States
journal, June 2006
- Verstraete, F.; Wolf, M. M.; Perez-Garcia, D.
- Physical Review Letters, Vol. 96, Issue 22
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
Fast scramblers
journal, October 2008
- Sekino, Yasuhiro; Susskind, L.
- Journal of High Energy Physics, Vol. 2008, Issue 10
Localization and topology protected quantum coherence at the edge of hot matter
journal, July 2015
- Bahri, Yasaman; Vosk, Ronen; Altman, Ehud
- Nature Communications, Vol. 6, Issue 1
Critical Properties of the Many-Body Localization Transition
journal, April 2017
- Khemani, Vedika; Lim, S. P.; Sheng, D. N.
- Physical Review X, Vol. 7, Issue 2
Event horizons in static electrovac space-times
journal, September 1968
- Israel, Werner
- Communications in Mathematical Physics, Vol. 8, Issue 3
On the holographic renormalization group
journal, August 2000
- Boer, Jan de; Verlinde, Erik; Verlinde, Herman
- Journal of High Energy Physics, Vol. 2000, Issue 08
Efficient Representation of Fully Many-Body Localized Systems Using Tensor Networks
journal, May 2017
- Wahl, Thorsten B.; Pal, Arijeet; Simon, Steven H.
- Physical Review X, Vol. 7, Issue 2
Holographic coherent states from random tensor networks
journal, August 2017
- Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang
- Journal of High Energy Physics, Vol. 2017, Issue 8
Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models
journal, October 1987
- di Francesco, P.; Saleur, H.; Zuber, J. B.
- Journal of Statistical Physics, Vol. 49, Issue 1-2
Criterion for Many-Body Localization-Delocalization Phase Transition
journal, December 2015
- Serbyn, Maksym; Papić, Z.; Abanin, Dmitry A.
- Physical Review X, Vol. 5, Issue 4
Average Entropy of a Quantum Subsystem
journal, July 1996
- Sen, Siddhartha
- Physical Review Letters, Vol. 77, Issue 1
Finding Matrix Product State Representations of Highly Excited Eigenstates of Many-Body Localized Hamiltonians
journal, January 2017
- Yu, Xiongjie; Pekker, David; Clark, Bryan K.
- Physical Review Letters, Vol. 118, Issue 1
Measurement-Induced Phase Transitions in the Dynamics of Entanglement
journal, July 2019
- Skinner, Brian; Ruhman, Jonathan; Nahum, Adam
- Physical Review X, Vol. 9, Issue 3
Conductivity of disordered quantum lattice models at infinite temperature: Many-body localization
journal, June 2010
- Berkelbach, Timothy C.; Reichman, David R.
- Physical Review B, Vol. 81, Issue 22
Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
journal, June 2016
- Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep
- Physical Review B, Vol. 93, Issue 22
Quantum quenches in the many-body localized phase
journal, November 2014
- Serbyn, Maksym; Papić, Z.; Abanin, D. A.
- Physical Review B, Vol. 90, Issue 17
Time evolution of entanglement entropy from black hole interiors
journal, May 2013
- Hartman, Thomas; Maldacena, Juan
- Journal of High Energy Physics, Vol. 2013, Issue 5
The density-matrix renormalization group in the age of matrix product states
journal, January 2011
- Schollwöck, Ulrich
- Annals of Physics, Vol. 326, Issue 1
Entanglement holographic mapping of many-body localized system by spectrum bifurcation renormalization group
journal, March 2016
- You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke
- Physical Review B, Vol. 93, Issue 10
Obtaining Highly Excited Eigenstates of Many-Body Localized Hamiltonians by the Density Matrix Renormalization Group Approach
journal, June 2016
- Khemani, Vedika; Pollmann, Frank; Sondhi, S. L.
- Physical Review Letters, Vol. 116, Issue 24
Bidirectional holographic codes and sub-AdS locality
journal, January 2016
- Yang, Zhao; Hayden, Patrick; Qi, Xiao-Liang
- Journal of High Energy Physics, Vol. 2016, Issue 1
Conformal invariance and surface critical behavior
journal, November 1984
- Cardy, John L.
- Nuclear Physics B, Vol. 240, Issue 4
Surface/state correspondence as a generalized holography
journal, July 2015
- Miyaji, Masamichi; Takayanagi, Tadashi
- Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 7
Information geometry of entanglement renormalization for free quantum fields
journal, September 2015
- Molina-Vilaplana, J.
- Journal of High Energy Physics, Vol. 2015, Issue 9
Random-matrix physics: spectrum and strength fluctuations
journal, July 1981
- Brody, T. A.; Flores, J.; French, J. B.
- Reviews of Modern Physics, Vol. 53, Issue 3
Spectral tensor networks for many-body localization
journal, July 2015
- Chandran, A.; Carrasquilla, J.; Kim, I. H.
- Physical Review B, Vol. 92, Issue 2
FRACTAL STRUCTURE OF 2d—QUANTUM GRAVITY
journal, July 1988
- Knizhnik, V. G.; Polyakov, A. M.; Zamolodchikov, A. B.
- Modern Physics Letters A, Vol. 03, Issue 08
Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006
- Ryu, Shinsei; Takayanagi, Tadashi
- Physical Review Letters, Vol. 96, Issue 18
On the random-cluster model
journal, February 1972
- Fortuin, C. M.; Kasteleyn, P. W.
- Physica, Vol. 57, Issue 4
Axisymmetric Black Hole Has Only Two Degrees of Freedom
journal, February 1971
- Carter, B.
- Physical Review Letters, Vol. 26, Issue 6
Analytically Solvable Renormalization Group for the Many-Body Localization Transition
journal, January 2019
- Goremykina, Anna; Vasseur, Romain; Serbyn, Maksym
- Physical Review Letters, Vol. 122, Issue 4
Consistency conditions for an AdS multiscale entanglement renormalization ansatz correspondence
journal, June 2015
- Bao, Ning; Cao, ChunJun; Carroll, Sean M.
- Physical Review D, Vol. 91, Issue 12
Universal Properties of Many-Body Delocalization Transitions
journal, September 2015
- Potter, Andrew C.; Vasseur, Romain; Parameswaran, S. A.
- Physical Review X, Vol. 5, Issue 3
Theory of the Many-Body Localization Transition in One-Dimensional Systems
journal, September 2015
- Vosk, Ronen; Huse, David A.; Altman, Ehud
- Physical Review X, Vol. 5, Issue 3
Universal Slow Growth of Entanglement in Interacting Strongly Disordered Systems
journal, June 2013
- Serbyn, Maksym; Papić, Z.; Abanin, Dmitry A.
- Physical Review Letters, Vol. 110, Issue 26
Conformal algebras of two-dimensional disordered systems
journal, June 2002
- Gurarie, Victor; Ludwig, Andreas W. W.
- Journal of Physics A: Mathematical and General, Vol. 35, Issue 27
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
Quantum revivals and many-body localization
journal, April 2015
- Vasseur, R.; Parameswaran, S. A.; Moore, J. E.
- Physical Review B, Vol. 91, Issue 14
Machine learning spatial geometry from entanglement features
journal, January 2018
- You, Yi-Zhuang; Yang, Zhao; Qi, Xiao-Liang
- Physical Review B, Vol. 97, Issue 4
Interacting Electrons in Disordered Wires: Anderson Localization and Low- Transport
journal, November 2005
- Gornyi, I. V.; Mirlin, A. D.; Polyakov, D. G.
- Physical Review Letters, Vol. 95, Issue 20
Holographic geometry of entanglement renormalization in quantum field theories
journal, October 2012
- Nozaki, Masahiro; Ryu, Shinsei; Takayanagi, Tadashi
- Journal of High Energy Physics, Vol. 2012, Issue 10
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008
- Verstraete, F.; Murg, V.; Cirac, J. I.
- Advances in Physics, Vol. 57, Issue 2
Event Horizons in Static Vacuum Space-Times
journal, December 1967
- Israel, Werner
- Physical Review, Vol. 164, Issue 5
Quantum statistical mechanics in a closed system
journal, February 1991
- Deutsch, J. M.
- Physical Review A, Vol. 43, Issue 4
Loop models with crossings
journal, May 2013
- Nahum, Adam; Serna, P.; Somoza, A. M.
- Physical Review B, Vol. 87, Issue 18
Entanglement renormalization and holography
journal, September 2012
- Swingle, Brian
- Physical Review D, Vol. 86, Issue 6
Holographic geometry of cMERA for quantum quenches and finite temperature
journal, March 2014
- Mollabashi, Ali; Naozaki, Masahiro; Ryu, Shinsei
- Journal of High Energy Physics, Vol. 2014, Issue 3