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Title: Supersymmetric Sachdev-Ye-Kitaev models

Abstract

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.

Authors:
 [1];  [2];  [3];  [4]
  1. Harvard Univ., Cambridge, MA (United States)
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  3. Inst. for Advanced Study, Princeton, NJ (United States)
  4. Harvard Univ., Cambridge, MA (United States); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
Publication Date:
Research Org.:
Institute for Advanced Study, Princeton, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES)
OSTI Identifier:
1423995
Alternate Identifier(s):
OSTI ID: 1339477
Grant/Contract Number:  
SC0009988
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 2; Related Information: A small addendum was made to the original version - see doi 10.1103/PhysRevD.95.069904; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS

Citation Formats

Fu, Wenbo, Gaiotto, Davide, Maldacena, Juan, and Sachdev, Subir. Supersymmetric Sachdev-Ye-Kitaev models. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.95.026009.
Fu, Wenbo, Gaiotto, Davide, Maldacena, Juan, & Sachdev, Subir. Supersymmetric Sachdev-Ye-Kitaev models. United States. https://doi.org/10.1103/PhysRevD.95.026009
Fu, Wenbo, Gaiotto, Davide, Maldacena, Juan, and Sachdev, Subir. 2017. "Supersymmetric Sachdev-Ye-Kitaev models". United States. https://doi.org/10.1103/PhysRevD.95.026009. https://www.osti.gov/servlets/purl/1423995.
@article{osti_1423995,
title = {Supersymmetric Sachdev-Ye-Kitaev models},
author = {Fu, Wenbo and Gaiotto, Davide and Maldacena, Juan and Sachdev, Subir},
abstractNote = {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.},
doi = {10.1103/PhysRevD.95.026009},
url = {https://www.osti.gov/biblio/1423995}, journal = {Physical Review D},
issn = {2470-0010},
number = 2,
volume = 95,
place = {United States},
year = {Fri Jan 13 00:00:00 EST 2017},
month = {Fri Jan 13 00:00:00 EST 2017}
}

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Cited by: 222 works
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Works referencing / citing this record:

Quantum simulation of the non-fermi-liquid state of Sachdev-Ye-Kitaev model
journal, June 2019


Mimicking black hole event horizons in atomic and solid-state systems
journal, November 2018


Extended supersymmetry in Dirac action with extra dimensions
journal, September 2018


Ground states of Nicolai and ${\mathbb{Z}_2}$ Nicolai models
journal, December 2018


An introduction to the SYK model
journal, July 2019


Free fermions in disguise
journal, July 2019


An SYK-like model without disorder
journal, October 2019


The ${\imath }\epsilon $ prescription in the SYK model
journal, January 2018


Creating and probing the Sachdev–Ye–Kitaev model with ultracold gases: Towards experimental studies of quantum gravity
journal, August 2017


Classical glasses, black holes, and strange quantum liquids
journal, November 2019


Family of Sachdev-Ye-Kitaev models motivated by experimental considerations
journal, June 2018


Conformality of 1 / N corrections in Sachdev-Ye-Kitaev-like models
journal, December 2019


Chaos and complexity in quantum mechanics
journal, January 2020


Tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
text, January 2019


Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
text, January 2017


Three Dimensional View of the SYK/AdS Duality
text, January 2017


Spread of entanglement in a Sachdev-Ye-Kitaev chain
text, January 2017


Ground states of Nicolai and $\mathbb{Z}_2$ Nicolai models
text, January 2018


Classical Glasses, Black Holes, and Strange Quantum Liquids
text, January 2019