Chaos in a classical limit of the Sachdev-Ye-Kitaev model
Abstract
We study chaos in a classical limit of the Sachdev-Ye-Kitaev (SYK) model obtained in a suitably defined large-S limit. The low-temperature Lyapunov exponent is found to depend linearly on temperature, with a slope that is parametrically different than in the quantum case: It is proportional to N/S. The classical dynamics can be understood as the rotation of an N-dimensional body with a random inertia tensor, corresponding to the random couplings of the SYK Hamiltonian. This allows us to find an extensive number of fixed points, corresponding to the body's principal axes of rotation. Finally, the thermodynamics is mapped to the p-spin model with p = 2, which exhibits a spin glass phase at low temperature whose presence does not preclude the existence of chaos.
- Authors:
-
- Univ. of California, Berkeley, CA (United States)
- Univ. of Toronto, ON (Canada)
- Publication Date:
- Research Org.:
- Univ. of California, Oakland, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- Gordon and Betty Moore Foundation; European Research Council (ERC); USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1803759
- Grant/Contract Number:
- SC0019380; AC02-05CH11231; UQUAM
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 15; 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; Materials Science; Physics
Citation Formats
Scaffidi, Thomas, and Altman, Ehud. Chaos in a classical limit of the Sachdev-Ye-Kitaev model. United States: N. p., 2019.
Web. doi:10.1103/physrevb.100.155128.
Scaffidi, Thomas, & Altman, Ehud. Chaos in a classical limit of the Sachdev-Ye-Kitaev model. United States. https://doi.org/10.1103/physrevb.100.155128
Scaffidi, Thomas, and Altman, Ehud. Tue .
"Chaos in a classical limit of the Sachdev-Ye-Kitaev model". United States. https://doi.org/10.1103/physrevb.100.155128. https://www.osti.gov/servlets/purl/1803759.
@article{osti_1803759,
title = {Chaos in a classical limit of the Sachdev-Ye-Kitaev model},
author = {Scaffidi, Thomas and Altman, Ehud},
abstractNote = {We study chaos in a classical limit of the Sachdev-Ye-Kitaev (SYK) model obtained in a suitably defined large-S limit. The low-temperature Lyapunov exponent is found to depend linearly on temperature, with a slope that is parametrically different than in the quantum case: It is proportional to N/S. The classical dynamics can be understood as the rotation of an N-dimensional body with a random inertia tensor, corresponding to the random couplings of the SYK Hamiltonian. This allows us to find an extensive number of fixed points, corresponding to the body's principal axes of rotation. Finally, the thermodynamics is mapped to the p-spin model with p = 2, which exhibits a spin glass phase at low temperature whose presence does not preclude the existence of chaos.},
doi = {10.1103/physrevb.100.155128},
journal = {Physical Review. B},
number = 15,
volume = 100,
place = {United States},
year = {Tue Oct 15 00:00:00 EDT 2019},
month = {Tue Oct 15 00:00:00 EDT 2019}
}
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