Supersymmetric Sachdev-Ye-Kitaev models

Fu, Wenbo; Gaiotto, Davide; Maldacena, Juan; Sachdev, Subir

doi:10.1103/PhysRevD.95.026009

Title: Supersymmetric Sachdev-Ye-Kitaev models

Journal Article · Fri Jan 13 00:00:00 EST 2017 · Physical Review D

DOI:https://doi.org/10.1103/PhysRevD.95.026009· OSTI ID:1423995

Fu, Wenbo ^[1]; Gaiotto, Davide ^[2]; Maldacena, Juan ^[3]; Sachdev, Subir ^[4]

Harvard Univ., Cambridge, MA (United States)
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Inst. for Advanced Study, Princeton, NJ (United States)
Harvard Univ., Cambridge, MA (United States); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)

We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) model. These are quantum mechanical models involving N Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The N = 1 model with a single supercharge has unbroken supersymmetry at large N , but nonperturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large N equation, and also by performing numerical computations for small values of N . We also compute the large N spectrum of “singlet” operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an N = 2 version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large N computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.

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Research Organization:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

Grant/Contract Number:: SC0009988

OSTI ID:: 1423995

Alternate ID(s):: OSTI ID: 1339477

Journal Information:: Physical Review D, Vol. 95, Issue 2; Related Information: A small addendum was made to the original version - see doi 10.1103/PhysRevD.95.069904; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 222 works

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References (43)

Sachdev–Ye–Kitaev model as Liouville quantum mechanics Bagrets, Dmitry; Altland, Alexander; Kamenev, Alex Nuclear Physics B, Vol. 911 https://doi.org/10.1016/j.nuclphysb.2016.08.002	journal	October 2016
Conformal symmetry breaking and thermodynamics of near-extremal black holes Almheiri, Ahmed; Kang, Byungwoo Journal of High Energy Physics, Vol. 2016, Issue 10 https://doi.org/10.1007/JHEP10(2016)052	journal	October 2016
An investigation of AdS2 backreaction and holography Engelsöy, Julius; Mertens, Thomas G.; Verlinde, Herman Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)139	journal	July 2016
Exact Results for Strongly Correlated Fermions in $2 + 1$ Dimensions Fendley, Paul; Schoutens, Kareljan Physical Review Letters, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevLett.95.046403	journal	July 2005
Black hole microstates in AdS4 from supersymmetric localization Benini, Francesco; Hristov, Kiril; Zaffaroni, Alberto Journal of High Energy Physics, Vol. 2016, Issue 5 https://doi.org/10.1007/JHEP05(2016)054	journal	May 2016
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
An Index for 4 Dimensional Super Conformal Theories Kinney, Justin; Maldacena, Juan; Minwalla, Shiraz Communications in Mathematical Physics, Vol. 275, Issue 1 https://doi.org/10.1007/s00220-007-0258-7	journal	June 2007
Charge Frustration and Quantum Criticality for Strongly Correlated Fermions Huijse, Liza; Halverson, James; Fendley, Paul Physical Review Letters, Vol. 101, Issue 14 https://doi.org/10.1103/PhysRevLett.101.146406	journal	October 2008
Bi-local holography in the SYK model: perturbations Jevicki, Antal; Suzuki, Kenta Journal of High Energy Physics, Vol. 2016, Issue 11 https://doi.org/10.1007/JHEP11(2016)046	journal	November 2016
Lattice fermion models with supersymmetry Fendley, Paul; Nienhuis, Bernard; Schoutens, Kareljan Journal of Physics A: Mathematical and General, Vol. 36, Issue 50 https://doi.org/10.1088/0305-4470/36/50/004	journal	December 2003
Remarks on the Sachdev-Ye-Kitaev model Maldacena, Juan; Stanford, Douglas Physical Review D, Vol. 94, Issue 10 https://doi.org/10.1103/PhysRevD.94.106002	journal	November 2016
Chaos in ${AdS}_{2}$ Holography Jensen, Kristan Physical Review Letters, Vol. 117, Issue 11 https://doi.org/10.1103/PhysRevLett.117.111601	journal	September 2016
$1 / 16$ BPS states in $N = 4$ super-Yang-Mills theory Chang, Chi-Ming; Yin, Xi Physical Review D, Vol. 88, Issue 10 https://doi.org/10.1103/PhysRevD.88.106005	journal	November 2013
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
Supersymmetry, lattice fermions, independence complexes and cohomology theory Huijse, Liza; Schoutens, Kareljan Advances in Theoretical and Mathematical Physics, Vol. 14, Issue 2 https://doi.org/10.4310/ATMP.2010.v14.n2.a8	journal	January 2010
Strange metals and the AdS/CFT correspondence Sachdev, Subir Journal of Statistical Mechanics: Theory and Experiment, Vol. 2010, Issue 11 https://doi.org/10.1088/1742-5468/2010/11/P11022	journal	November 2010
Gapless spin-fluid ground state in a random quantum Heisenberg magnet Sachdev, Subir; Ye, Jinwu Physical Review Letters, Vol. 70, Issue 21 https://doi.org/10.1103/PhysRevLett.70.3339	journal	May 1993
Mean Field Theory of a Quantum Heisenberg Spin Glass Georges, Antoine; Parcollet, Olivier; Sachdev, Subir Physical Review Letters, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevLett.85.840	journal	July 2000
Holographic Metals and the Fractionalized Fermi Liquid Sachdev, Subir Physical Review Letters, Vol. 105, Issue 15 https://doi.org/10.1103/PhysRevLett.105.151602	journal	October 2010
Disordered quivers and cold horizons Anninos, Dionysios; Anous, Tarek; Denef, Frederik Journal of High Energy Physics, Vol. 2016, Issue 12 https://doi.org/10.1007/JHEP12(2016)071	journal	December 2016
Quantum fluctuations of a nearly critical Heisenberg spin glass Georges, A.; Parcollet, O.; Sachdev, S. Physical Review B, Vol. 63, Issue 13 https://doi.org/10.1103/PhysRevB.63.134406	journal	March 2001
Models of AdS2 backreaction and holography Almheiri, Ahmed; Polchinski, Joseph Journal of High Energy Physics, Vol. 2015, Issue 11 https://doi.org/10.1007/JHEP11(2015)014	journal	November 2015
Numerical study of fermion and boson models with infinite-range random interactions Fu, Wenbo; Sachdev, Subir Physical Review B, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevB.94.035135	journal	July 2016
Lattice Models with $N = 2$ Supersymmetry Fendley, Paul; Schoutens, Kareljan; de Boer, Jan Physical Review Letters, Vol. 90, Issue 12 https://doi.org/10.1103/PhysRevLett.90.120402	journal	March 2003
Bi-local holography in the SYK model Jevicki, Antal; Suzuki, Kenta; Yoon, Junggi Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)007	journal	July 2016
Microscopic origin of the Bekenstein-Hawking entropy Strominger, Andrew; Vafa, Cumrun Physics Letters B, Vol. 379, Issue 1-4 https://doi.org/10.1016/0370-2693(96)00345-0	journal	June 1996
AdS2 holographic dictionary Cvetič, Mirjam; Papadimitriou, Ioannis Journal of High Energy Physics, Vol. 2016, Issue 12 https://doi.org/10.1007/JHEP12(2016)008	journal	December 2016
Bekenstein-Hawking Entropy and Strange Metals Sachdev, Subir Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041025	journal	November 2015
Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality Huijse, L.; Mehta, D.; Moran, N. New Journal of Physics, Vol. 14, Issue 7 https://doi.org/10.1088/1367-2630/14/7/073002	journal	July 2012
Exact ground states of a staggered supersymmetric model for lattice fermions Huijse, L.; Moran, N.; Vala, J. Physical Review B, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevB.84.115124	journal	September 2011
Non-Fermi-liquid regime of a doped Mott insulator Parcollet, Olivier; Georges, Antoine Physical Review B, Vol. 59, Issue 8 https://doi.org/10.1103/PhysRevB.59.5341	journal	February 1999
N = 2 super-Riemann surfaces Cohn, J. D. Nuclear Physics B, Vol. 284 https://doi.org/10.1016/0550-3213(87)90039-3	journal	January 1987
Supersymmetry, lattice fermions, independence complexes and cohomology theory Huijse, L.; Schoutens, K. arXiv https://doi.org/10.48550/arxiv.0903.0784	text	January 2009
Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality Huijse, L.; Mehta, D.; Moran, N. arXiv https://doi.org/10.48550/arxiv.1112.3314	text	January 2011
Chaos in quantum channels Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A. arXiv https://doi.org/10.48550/arxiv.1511.04021	text	January 2015
Black hole microstates in AdS$_4$ from supersymmetric localization Benini, Francesco; Hristov, Kiril; Zaffaroni, Alberto arXiv https://doi.org/10.48550/arxiv.1511.04085	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
Bi-Local Holography in the SYK Model Jevicki, Antal; Suzuki, Kenta; Yoon, Junggi arXiv https://doi.org/10.48550/arxiv.1603.06246	text	January 2016
An Investigation of AdS$_2$ Backreaction and Holography Engelsöy, Julius; Mertens, Thomas G.; Verlinde, Herman arXiv https://doi.org/10.48550/arxiv.1606.03438	text	January 2016
AdS$_2$ Holographic Dictionary Cvetič, Mirjam; Papadimitriou, Ioannis arXiv https://doi.org/10.48550/arxiv.1608.07018	text	January 2016
Quantum Fluctuations of a Nearly Critical Heisenberg Spin Glass Georges, A.; Parcollet, O.; Sachdev, S. arXiv https://doi.org/10.48550/arxiv.cond-mat/0009388	text	January 2000
Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet Sachdev, Subir; Ye, Jinwu arXiv https://doi.org/10.48550/arxiv.cond-mat/9212030	text	January 1992
An Index for 4 dimensional Super Conformal Theories Kinney, Justin; Maldacena, Juan; Minwalla, Shiraz arXiv https://doi.org/10.48550/arxiv.hep-th/0510251	text	January 2005

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Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model Behrends, Jan; Bardarson, Jh; Béri, B. Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.40082	text	January 2019
Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity Danshita, Ippei; Hanada, Masanori; Tezuka, Masaki arXiv https://doi.org/10.48550/arxiv.1606.02454	text	January 2016
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