Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories

Roberts, Daniel A.; Swingle, Brian

doi:10.1103/physrevlett.117.091602

Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories

Journal Article · Tue Aug 23 00:00:00 EDT 2016 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.117.091602· OSTI ID:1505740

Roberts, Daniel A. ^[1]; Swingle, Brian ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics and Dept. of Physics; MIT
Stanford Univ., CA (United States). Inst. for Theoretical Physics and Dept. of Physics

As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one such bound—the Lieb-Robinson bound—and the butterfly effect in strongly coupled quantum systems. The butterfly effect implies the ballistic growth of local operators in time, which can be quantified with the “butterfly” velocity v_B. Similarly, the Lieb-Robinson velocity places a state-independent ballistic upper bound on the size of time evolved operators in nonrelativistic lattice models. Here, we argue that v _B is a state-dependent effective Lieb-Robinson velocity. We study the butterfly velocity in a wide variety of quantum field theories using holography and compare with free-particle computations to understand the role of strong coupling. We find that v B remains constant or decreases with decreasing temperature. We also comment on experimental prospects and on the relationship between the butterfly velocity and signaling.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0012567

OSTI ID:: 1505740

Alternate ID(s):: OSTI ID: 1328616

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 9 Vol. 117; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (59)

The Finite Group Velocity of Quantum Spin Systems Lieb, Elliott H.; Robinson, Derek W. Statistical Mechanics https://doi.org/10.1007/978-3-662-10018-9_25	book	January 1972
The finite group velocity of quantum spin systems Lieb, Elliott H.; Robinson, Derek W. Communications in Mathematical Physics, Vol. 28, Issue 3 https://doi.org/10.1007/BF01645779	journal	September 1972
A continuity property of the entropy density for spin lattice systems Fannes, M. Communications in Mathematical Physics, Vol. 31, Issue 4 https://doi.org/10.1007/BF01646490	journal	December 1973
Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity Iizuka, Norihiro; Kundu, Nilay; Narayan, Prithvi Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)094	journal	January 2012
Holographic Fermi surfaces and entanglement entropy Ogawa, Noriaki; Takayanagi, Tadashi; Ugajin, Tomonori Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)125	journal	January 2012
Chaos in quantum channels Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A. Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)004	journal	February 2016
Black holes and the butterfly effect Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2014, Issue 3 https://doi.org/10.1007/JHEP03(2014)067	journal	March 2014
Localized shocks Roberts, Daniel A.; Stanford, Douglas; Susskind, Leonard Journal of High Energy Physics, Vol. 2015, Issue 3 https://doi.org/10.1007/JHEP03(2015)051	journal	March 2015
The spectrum in the Sachdev-Ye-Kitaev model Polchinski, Joseph; Rosenhaus, Vladimir Journal of High Energy Physics, Vol. 2016, Issue 4 https://doi.org/10.1007/JHEP04(2016)001	journal	April 2016
Time evolution of entanglement entropy from black hole interiors Hartman, Thomas; Maldacena, Juan Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)014	journal	May 2013
Stringy effects in scrambling Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2015, Issue 5 https://doi.org/10.1007/JHEP05(2015)132	journal	May 2015
Four-point function in the IOP matrix model Michel, Ben; Polchinski, Joseph; Rosenhaus, Vladimir Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)048	journal	May 2016
A quantum correction to chaos Fitzpatrick, A. Liam; Kaplan, Jared Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)070	journal	May 2016
Extending the scope of holographic mutual information and chaotic behavior Sircar, Nilanjan; Sonnenschein, Jacob; Tangarife, Walter Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)091	journal	May 2016
Aspects of holography for theories with hyperscaling violation Dong, Xi; Harrison, Sarah; Kachru, Shamit Journal of High Energy Physics, Vol. 2012, Issue 6 https://doi.org/10.1007/JHEP06(2012)041	journal	June 2012
Spread of entanglement and causality Casini, Horacio; Liu, Hong; Mezei, Márk Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)077	journal	July 2016
Holographic thermalization with Lifshitz scaling and hyperscaling violation Fonda, Piermarco; Franti, Lasse; Keränen, Ville Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)051	journal	August 2014
An apologia for firewalls Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph Journal of High Energy Physics, Vol. 2013, Issue 9 https://doi.org/10.1007/JHEP09(2013)018	journal	September 2013
Hyperscaling-violation on probe D-branes Ammon, Martin; Kaminski, Matthias; Karch, Andreas Journal of High Energy Physics, Vol. 2012, Issue 11 https://doi.org/10.1007/JHEP11(2012)028	journal	November 2012
Multiple shocks Shenker, Stephen H.; Stanford, Douglas Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)046	journal	December 2014
Spectral Gap and Exponential Decay of Correlations Hastings, Matthew B.; Koma, Tohru Communications in Mathematical Physics, Vol. 265, Issue 3 https://doi.org/10.1007/s00220-006-0030-4	journal	April 2006
Propagation of Correlations in Quantum Lattice Systems Nachtergaele, Bruno; Ogata, Yoshiko; Sims, Robert Journal of Statistical Physics, Vol. 124, Issue 1 https://doi.org/10.1007/s10955-006-9143-6	journal	July 2006
The black hole interpretation of string theory 't Hooft, G. Nuclear Physics B, Vol. 335, Issue 1 https://doi.org/10.1016/0550-3213(90)90174-C	journal	April 1990
On gravitational shock waves in curved spacetimes Sfetsos, Konstadinos Nuclear Physics B, Vol. 436, Issue 3 https://doi.org/10.1016/0550-3213(94)00573-W	journal	February 1995
Light-cone-like spreading of correlations in a quantum many-body system Cheneau, Marc; Barmettler, Peter; Poletti, Dario Nature, Vol. 481, Issue 7382 https://doi.org/10.1038/nature10748	journal	January 2012
Non-local propagation of correlations in quantum systems with long-range interactions Richerme, Philip; Gong, Zhe-Xuan; Lee, Aaron Nature, Vol. 511, Issue 7508 https://doi.org/10.1038/nature13450	journal	July 2014
Quasiparticle engineering and entanglement propagation in a quantum many-body system Jurcevic, P.; Lanyon, B. P.; Hauke, P. Nature, Vol. 511, Issue 7508 https://doi.org/10.1038/nature13461	journal	July 2014
Quantum many-body systems out of equilibrium Eisert, J.; Friesdorf, M.; Gogolin, C. Nature Physics, Vol. 11, Issue 2 https://doi.org/10.1038/nphys3215	journal	February 2015
Comments on microcausality, chaos, and gravitational observables Marolf, Donald Classical and Quantum Gravity, Vol. 32, Issue 24 https://doi.org/10.1088/0264-9381/32/24/245003	journal	November 2015
Eternal black holes in anti-de Sitter Maldacena, Juan Journal of High Energy Physics, Vol. 2003, Issue 04 https://doi.org/10.1088/1126-6708/2003/04/021	journal	April 2003
Black holes as mirrors: quantum information in random subsystems Hayden, Patrick; Preskill, John Journal of High Energy Physics, Vol. 2007, Issue 09 https://doi.org/10.1088/1126-6708/2007/09/120	journal	September 2007
Fast scramblers Sekino, Yasuhiro; Susskind, L. Journal of High Energy Physics, Vol. 2008, Issue 10 https://doi.org/10.1088/1126-6708/2008/10/065	journal	October 2008
Universal crossovers between entanglement entropy and thermal entropy Swingle, Brian; Senthil, T. Physical Review B, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevB.87.045123	journal	January 2013
Area law for gapless states from local entanglement thermodynamics Swingle, Brian; McGreevy, John Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.205120	journal	May 2016
Black hole horizons and complementarity Kiem, Youngjai; Verlinde, Herman; Verlinde, Erik Physical Review D, Vol. 52, Issue 12 https://doi.org/10.1103/PhysRevD.52.7053	journal	December 1995
Thermalization in backgrounds with hyperscaling violating factor Alishahiha, Mohsen; Faraji Astaneh, Amin; Mohammadi Mozaffar, M. Reza Physical Review D, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevD.90.046004	journal	August 2014
Disrupting entanglement of black holes Leichenauer, Stefan Physical Review D, Vol. 90, Issue 4 https://doi.org/10.1103/PhysRevD.90.046009	journal	August 2014
Entanglement Tsunami: Universal Scaling in Holographic Thermalization Liu, Hong; Suh, S. Josephine Physical Review Letters, Vol. 112, Issue 1 https://doi.org/10.1103/PhysRevLett.112.011601	journal	January 2014
Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory Roberts, Daniel A.; Stanford, Douglas Physical Review Letters, Vol. 115, Issue 13 https://doi.org/10.1103/PhysRevLett.115.131603	journal	September 2015
Universal Charge Diffusion and the Butterfly Effect in Holographic Theories Blake, Mike Physical Review Letters, Vol. 117, Issue 9 https://doi.org/10.1103/PhysRevLett.117.091601	journal	August 2016
Black holes as mirrors: quantum information in random subsystems Hayden, Patrick; Preskill, John arXiv https://doi.org/10.48550/arxiv.0708.4025	text	January 2007
Fast Scramblers Sekino, Yasuhiro; Susskind, Leonard arXiv https://doi.org/10.48550/arxiv.0808.2096	text	January 2008
Light-cone-like spreading of correlations in a quantum many-body system Cheneau, Marc; Barmettler, Peter; Poletti, Dario arXiv https://doi.org/10.48550/arxiv.1111.0776	text	January 2011
Holographic Fermi Surfaces and Entanglement Entropy Ogawa, Noriaki; Takayanagi, Tadashi; Ugajin, Tomonori arXiv https://doi.org/10.48550/arxiv.1111.1023	text	January 2011
Aspects of holography for theories with hyperscaling violation Dong, Xi; Harrison, Sarah; Kachru, Shamit arXiv https://doi.org/10.48550/arxiv.1201.1905	text	January 2012
Hyperscaling-Violation on Probe D-Branes Ammon, Martin; Kaminski, Matthias; Karch, Andreas arXiv https://doi.org/10.48550/arxiv.1207.1726	text	January 2012
Entanglement Tsunami: Universal Scaling in Holographic Thermalization Liu, Hong; Suh, S. Josephine arXiv https://doi.org/10.48550/arxiv.1305.7244	text	January 2013
Holographic thermalization with Lifshitz scaling and hyperscaling violation Fonda, Piermarco; Franti, Lasse; Keranen, Ville arXiv https://doi.org/10.48550/arxiv.1401.6088	text	January 2014
Disrupting Entanglement of Black Holes Leichenauer, Stefan arXiv https://doi.org/10.48550/arxiv.1405.7365	text	January 2014
Quantum many-body systems out of equilibrium Eisert, J.; Friesdorf, M.; Gogolin, C. arXiv https://doi.org/10.48550/arxiv.1408.5148	text	January 2014
Stringy effects in scrambling Shenker, Stephen H.; Stanford, Douglas arXiv https://doi.org/10.48550/arxiv.1412.6087	preprint	January 2014
Area Law for Gapless States from Local Entanglement Thermodynamics Swingle, Brian; McGreevy, John arXiv https://doi.org/10.48550/arxiv.1505.07106	text	January 2015
Comments on Microcausality, Chaos, and Gravitational Observables Marolf, Donald arXiv https://doi.org/10.48550/arxiv.1508.00939	text	January 2015
Spread of entanglement and causality Casini, Horacio; Liu, Hong; Mezei, Márk arXiv https://doi.org/10.48550/arxiv.1509.05044	text	January 2015
Chaos in quantum channels Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A. arXiv https://doi.org/10.48550/arxiv.1511.04021	text	January 2015
The Spectrum in the Sachdev-Ye-Kitaev Model Polchinski, Joseph; Rosenhaus, Vladimir arXiv https://doi.org/10.48550/arxiv.1601.06768	text	January 2016
Four-point function in the IOP matrix model Michel, Ben; Polchinski, Joseph; Rosenhaus, Vladimir arXiv https://doi.org/10.48550/arxiv.1602.06422	preprint	January 2016
Extending the scope of holographic mutual information and chaotic behavior Sircar, Nilanjan; Sonnenschein, Jacob; Tangarife, Walter arXiv https://doi.org/10.48550/arxiv.1602.07307	text	January 2016
Spectral Gap and Exponential Decay of Correlations Hastings, Matthew B.; Koma, Tohru arXiv https://doi.org/10.48550/arxiv.math-ph/0507008	text	January 2005

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Out-of-time-order correlations in many-body localized and thermal phases Chen, Xiao; Zhou, Tianci; Huse, David A. arXiv https://doi.org/10.48550/arxiv.1610.00220	text	January 2016
Chaos and complexity by design Roberts, Daniel A.; Yoshida, Beni arXiv https://doi.org/10.48550/arxiv.1610.04903	text	January 2016
Non-ergodicity in the Anisotropic Dicke model Buijsman, Wouter; Gritsev, Vladimir; Sprik, Rudolf arXiv https://doi.org/10.48550/arxiv.1610.06751	text	January 2016
Higher derivative corrections to incoherent metallic transport in holography Baggioli, Matteo; Goutéraux, Blaise; Kiritsis, Elias arXiv https://doi.org/10.48550/arxiv.1612.05500	text	January 2016
Thermal diffusivity and chaos in metals without quasiparticles Blake, Mike; Davison, Richard A.; Sachdev, Subir arXiv https://doi.org/10.48550/arxiv.1705.07896	text	January 2017
Operator Spreading in Random Unitary Circuits Nahum, Adam; Vijay, Sagar; Haah, Jeongwan arXiv https://doi.org/10.48550/arxiv.1705.08975	text	January 2017
Spread of entanglement in a Sachdev-Ye-Kitaev chain Gu, Yingfei; Lucas, Andrew; Qi, Xiao-Liang arXiv https://doi.org/10.48550/arxiv.1708.00871	text	January 2017
Detecting equilibrium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators Heyl, Markus; Pollmann, Frank; Dóra, Balázs arXiv https://doi.org/10.48550/arxiv.1801.01684	text	January 2018
Study of Open Systems with Molecules in Isotropic Liquids Kondo, Yasushi; Matsuzaki, Masayuki arXiv https://doi.org/10.48550/arxiv.1804.02838	text	January 2018
Butterfly Velocity in Quadratic Gravity Huang, Wung-Hong arXiv https://doi.org/10.48550/arxiv.1804.05527	text	January 2018
Emergent statistical mechanics of entanglement in random unitary circuits Zhou, Tianci; Nahum, Adam arXiv https://doi.org/10.48550/arxiv.1804.09737	text	January 2018
Entropic uncertainty relations for quantum information scrambling Halpern, Nicole Yunger; Bartolotta, Anthony; Pollack, Jason arXiv https://doi.org/10.48550/arxiv.1806.04147	text	January 2018
Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling Alonso, José Raúl González; Halpern, Nicole Yunger; Dressel, Justin arXiv https://doi.org/10.48550/arxiv.1806.09637	text	January 2018
Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators Liao, Yunxiang; Galitski, Victor arXiv https://doi.org/10.48550/arxiv.1807.09799	text	January 2018
Out-of-time-ordered correlator in the quantum bakers map and truncated unitary matrices Lakshminarayan, Arul arXiv https://doi.org/10.48550/arxiv.1810.12029	text	January 2018
Rate of cluster decomposition via Fermat-Steiner point Avdoshkin, Alexander; Astrakhantsev, Lev; Dymarsky, Anatoly arXiv https://doi.org/10.48550/arxiv.1811.03633	text	January 2018
Quantum Scrambling and State Dependence of the Butterfly Velocity Han, Xizhi; Hartnoll, Sean A. arXiv https://doi.org/10.48550/arxiv.1812.07598	text	January 2018
Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach Tuziemski, Jan arXiv https://doi.org/10.48550/arxiv.1903.05025	text	January 2019
Dynamical Scaling Laws of Out-of-Time-Ordered Correlators Wei, Bo-Bo; Sun, Gaoyong; Hwang, Myung-Joong arXiv https://doi.org/10.48550/arxiv.1906.00533	text	January 2019

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