Symmetry Breaking in Coupled SYK or Tensor Models
Author(s): Kim, Jaewon; Klebanov, Igor R; Tarnopolsky, Grigory; Zhao, Wenli
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Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kim, Jaewon | - |
dc.contributor.author | Klebanov, Igor R | - |
dc.contributor.author | Tarnopolsky, Grigory | - |
dc.contributor.author | Zhao, Wenli | - |
dc.date.accessioned | 2024-08-06T18:57:28Z | - |
dc.date.available | 2024-08-06T18:57:28Z | - |
dc.date.issued | 2019-05-31 | en_US |
dc.identifier.citation | Kim, Jaewon, Klebanov, Igor R, Tarnopolsky, Grigory, Zhao, Wenli. (Symmetry Breaking in Coupled SYK or Tensor Models. Physical Review X, 9 (2), 10.1103/physrevx.9.021043 | en_US |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/pr1xw47w6b | - |
dc.description.abstract | We study a large N tensor model with O(N )3 symmetry containing two flavors of Majorana fermions, ψabc1 and ψabc2 . We also study its random counterpart consisting of two coupled Sachdev-Ye-Kitaev models, each one 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 = iψabc1 ψabc2 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. This demonstrates the breaking of an anti-unitary 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; this leads to 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. | en_US |
dc.language | en | en_US |
dc.relation.ispartof | Physical Review X | en_US |
dc.rights | Author's manuscript | en_US |
dc.title | Symmetry Breaking in Coupled SYK or Tensor Models | en_US |
dc.type | Journal Article | en_US |
dc.identifier.doi | doi:10.1103/physrevx.9.021043 | - |
dc.date.eissued | 2019-05-31 | en_US |
dc.identifier.eissn | 2160-3308 | - |
pu.type.symplectic | http://www.symplectic.co.uk/publications/atom-terms/1.0/journal-article | en_US |
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