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Title: Symmetry Breaking in Coupled SYK or Tensor Models

Abstract

We study a large- N tensor model with O(N)3 symmetry containing two flavors of Majorana fermions, ψ 1 a b c and ψ 2 a b c . We also study its random counterpart consisting of two coupled Sachdev-Ye-Kitaev (SYK) models, each containing N SYK Majorana fermions. In these models, we assume tetrahedral quartic Hamiltonians which depend on a real coupling parameter α . We find a duality relation between two Hamiltonians with different values of α , which allows us to restrict the model to the range of =-1≤α≤1/3 . The scaling dimension of the fermion number operator Q=i ψ 1 a b c ψ 2 a b c is complex and of the form 1/2+if(α) in the range -1≤α<0 , indicating an instability of the conformal phase. Using Schwinger-Dyson equations to solve for the Green functions, we show that in the true low-temperature phase this operator acquires an expectation value, which demonstrates the breaking of an antiunitary particle-hole symmetry and other discrete symmetries. We also calculate spectra of the coupled SYK models for values of N SYK where exact diagonalizations are possible. For negative α , we find a gap separating the two lowest energy states from the rest of the spectrum, leading to an exponential decay of the zero-temperature correlation functions. For N SYK divisible by 4, the two lowest states have a small splitting. They become degenerate in the large- N SYK limit, as expected from the spontaneous breaking of a Z 2 symmetry.

Authors:
; ; ;
Publication Date:
Research Org.:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
OSTI Identifier:
1523692
Alternate Identifier(s):
OSTI ID: 1610986
Grant/Contract Number:  
SC0007870; SC0019030; PHY-1620059
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 9 Journal Issue: 2; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Physics; Condensed Matter Physics; Particles and Fields; String Theory

Citation Formats

Kim, Jaewon, Klebanov, Igor R., Tarnopolsky, Grigory, and Zhao, Wenli. Symmetry Breaking in Coupled SYK or Tensor Models. United States: N. p., 2019. Web. doi:10.1103/PhysRevX.9.021043.
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Kim, Jaewon, Klebanov, Igor R., Tarnopolsky, Grigory, & Zhao, Wenli. Symmetry Breaking in Coupled SYK or Tensor Models. United States. https://doi.org/10.1103/PhysRevX.9.021043
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Kim, Jaewon, Klebanov, Igor R., Tarnopolsky, Grigory, and Zhao, Wenli. Fri . "Symmetry Breaking in Coupled SYK or Tensor Models". United States. https://doi.org/10.1103/PhysRevX.9.021043.
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@article{osti_1523692,
title = {Symmetry Breaking in Coupled SYK or Tensor Models},
author = {Kim, Jaewon and Klebanov, Igor R. and Tarnopolsky, Grigory and Zhao, Wenli},
abstractNote = {We study a large-N tensor model with O(N)3 symmetry containing two flavors of Majorana fermions, ψ1abc and ψ2abc. We also study its random counterpart consisting of two coupled Sachdev-Ye-Kitaev (SYK) models, each containing NSYK Majorana fermions. In these models, we assume tetrahedral quartic Hamiltonians which depend on a real coupling parameter α. We find a duality relation between two Hamiltonians with different values of α, which allows us to restrict the model to the range of =-1≤α≤1/3. The scaling dimension of the fermion number operator Q=iψ1abcψ2abc is complex and of the form 1/2+if(α) in the range -1≤α<0, indicating an instability of the conformal phase. Using Schwinger-Dyson equations to solve for the Green functions, we show that in the true low-temperature phase this operator acquires an expectation value, which demonstrates the breaking of an antiunitary particle-hole symmetry and other discrete symmetries. We also calculate spectra of the coupled SYK models for values of NSYK where exact diagonalizations are possible. For negative α, we find a gap separating the two lowest energy states from the rest of the spectrum, leading to an exponential decay of the zero-temperature correlation functions. For NSYK divisible by 4, the two lowest states have a small splitting. They become degenerate in the large-NSYK limit, as expected from the spontaneous breaking of a Z2 symmetry.},
doi = {10.1103/PhysRevX.9.021043},
journal = {Physical Review. X},
number = 2,
volume = 9,
place = {United States},
year = {Fri May 31 00:00:00 EDT 2019},
month = {Fri May 31 00:00:00 EDT 2019}
}
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https://doi.org/10.1103/PhysRevX.9.021043
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