Remarks on the Sachdev-Ye-Kitaev model

Maldacena, Juan; Stanford, Douglas

doi:10.1103/physrevd.94.106002

Title: Remarks on the Sachdev-Ye-Kitaev model

Journal Article · Fri Nov 04 00:00:00 EDT 2016 · Physical Review D

DOI:https://doi.org/10.1103/physrevd.94.106002· OSTI ID:1536177

Maldacena, Juan ^[1]; Stanford, Douglas ^[1]

Inst. for Advanced Study, Princeton, NJ (United States)

We study a quantum mechanical model proposed by Sachdev, Ye and Kitaev. The model consists of N Majorana fermions with random interactions of a few fermions at a time. It it tractable in the large N limit, where the classical variable is a bilocal fermion bilinear. The model becomes strongly interacting at low energies where it develops an emergent conformal symmetry. We study two and four point functions of the fundamental fermions. This provides the spectrum of physical excitations for the bilocal field. The emergent conformal symmetry is a reparametrization symmetry, which is spontaneously broken to SL(2;R), leading to zero modes. These zero modes are lifted by a small residual explicit breaking, which produces an enhanced contribution to the four point function. This contribution displays a maximal Lyapunov exponent in the chaos region (out of time ordered correlator). We expect these features to be universal properties of large N quantum mechanics systems with emergent reparametrization symmetry. This article is largely based on talks given by Kitaev, which motivated us to work out the details of the ideas described there.

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009988

OSTI ID:: 1536177

Alternate ID(s):: OSTI ID: 1331021

Journal Information:: Physical Review D, Vol. 94, Issue 10; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 1065 works

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Measurement of many-body chaos using a quantum clock Zhu, Guanyu; Hafezi, Mohammad; Grover, Tarun arXiv https://doi.org/10.48550/arxiv.1607.00079	text	January 2016
Quantum Complexity and Negative Curvature Brown, Adam R.; Susskind, Leonard; Zhao, Ying arXiv https://doi.org/10.48550/arxiv.1608.02612	text	January 2016
Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation He, Rong-Qiang; Lu, Zhong-Yi arXiv https://doi.org/10.48550/arxiv.1608.03586	text	January 2016
The ABC of Higher-Spin AdS/CFT Giombi, Simone; Klebanov, Igor R.; Tan, Zhong Ming arXiv https://doi.org/10.48550/arxiv.1608.07611	preprint	January 2016
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
Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model García-García, Antonio M.; Verbaarschot, Jacobus J. M. arXiv https://doi.org/10.48550/arxiv.1610.03816	text	January 2016
Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N García-García, Antonio M.; Verbaarschot, Jacobus J. M. arXiv https://doi.org/10.48550/arxiv.1701.06593	text	January 2017
Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories Caputa, Pawel; Kundu, Nilay; Miyaji, Masamichi arXiv https://doi.org/10.48550/arxiv.1703.00456	text	January 2017
Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization Jian, Shao-Kai; Yao, Hong arXiv https://doi.org/10.48550/arxiv.1703.02051	text	January 2017
Approximating the Sachdev-Ye-Kitaev model with Majorana wires Chew, Aaron; Essin, Andrew; Alicea, Jason arXiv https://doi.org/10.48550/arxiv.1703.06890	text	January 2017
De Finetti theorems and entanglement in large-N theories and gravity Magan, Javier M. arXiv https://doi.org/10.48550/arxiv.1705.03048	text	January 2017
Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model Chen, Xin; Fan, Ruihua; Chen, Yiming arXiv https://doi.org/10.48550/arxiv.1705.03406	text	January 2017
Weight Shifting Operators and Conformal Blocks Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1706.07813	text	January 2017
Eigenstate entanglement in the Sachdev-Ye-Kitaev model Huang, Yichen; Gu, Yingfei arXiv https://doi.org/10.48550/arxiv.1709.09160	text	January 2017
Chaos in a classical limit of the Sachdev-Ye-Kitaev model Scaffidi, Thomas; Altman, Ehud arXiv https://doi.org/10.48550/arxiv.1711.04768	text	January 2017
Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model Luo, Zhihuang; You, Yi-Zhuang; Li, Jun arXiv https://doi.org/10.48550/arxiv.1712.06458	text	January 2017
Hierarchy of Information Scrambling, Thermalization, and Hydrodynamic Flow in Graphene Klug, Markus J.; Scheurer, Mathias S.; Schmalian, Jörg arXiv https://doi.org/10.48550/arxiv.1712.08813	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
Universal level statistics of the out-of-time-ordered operator Rozenbaum, Efim B.; Ganeshan, Sriram; Galitski, Victor arXiv https://doi.org/10.48550/arxiv.1801.10591	text	January 2018
Disordered fermions, extra dimensions and a solvable Yang-Mills theory Borici, Artan arXiv https://doi.org/10.48550/arxiv.1802.02542	text	January 2018
Falling Toward Charged Black Holes Brown, Adam R.; Gharibyan, Hrant; Streicher, Alexandre arXiv https://doi.org/10.48550/arxiv.1804.04156	text	January 2018
Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos Seshadri, Akshay; Madhok, Vaibhav; Lakshminarayan, Arul arXiv https://doi.org/10.48550/arxiv.1806.00113	text	January 2018
Localization in fractonic random circuits Pai, Shriya; Pretko, Michael; Nandkishore, Rahul M. arXiv https://doi.org/10.48550/arxiv.1807.09776	text	January 2018
Mimicking black hole event horizons in atomic and solid-state systems Franz, M.; Rozali, M. arXiv https://doi.org/10.48550/arxiv.1808.00541	preprint	January 2018
Operator Spreading in Quantum Maps Moudgalya, Sanjay; Devakul, Trithep; von Keyserlingk, C. W. arXiv https://doi.org/10.48550/arxiv.1808.04889	text	January 2018
Quantum resonant systems, integrable and chaotic Evnin, Oleg; Piensuk, Worapat arXiv https://doi.org/10.48550/arxiv.1808.09173	text	January 2018
Eigenvalue instantons in the spectral form factor of random matrix model Okuyama, Kazumi arXiv https://doi.org/10.48550/arxiv.1812.09469	text	January 2018
Symmetry Breaking in Coupled SYK or Tensor Models Kim, Jaewon; Klebanov, Igor R.; Tarnopolsky, Grigory arXiv https://doi.org/10.48550/arxiv.1902.02287	text	January 2019
Integrable and chaotic dynamics of spins coupled to an optical cavity Bentsen, Gregory; Potirniche, Ionut-Dragos; Bulchandani, Vir B. arXiv https://doi.org/10.48550/arxiv.1904.10966	text	January 2019
Majorana Fermion Quantum Mechanics for Higher Rank Tensors Klebanov, Igor R.; Pallegar, Preethi N.; Popov, Fedor K. arXiv https://doi.org/10.48550/arxiv.1905.06264	text	January 2019
A generalized phase space approach for solving quantum spin dynamics Zhu, Bihui; Rey, Ana Maria; Schachenmayer, Johannes arXiv https://doi.org/10.48550/arxiv.1905.08782	text	January 2019
Classical Glasses, Black Holes, and Strange Quantum Liquids Facoetti, Davide; Biroli, Giulio; Kurchan, Jorge arXiv https://doi.org/10.48550/arxiv.1906.09228	text	January 2019
Near horizon dynamics of three dimensional black holes Grumiller, Daniel; Merbis, Wout arXiv https://doi.org/10.48550/arxiv.1906.10694	text	January 2019
Dynamical thermalization of interacting fermionic atoms in a Sinai-oscillator trap Frahm, Klaus M.; Ermann, Leonardo; Shepelyansky, Dima L. arXiv https://doi.org/10.48550/arxiv.1907.06711	text	January 2019

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