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Symmetry Breaking in Coupled SYK or Tensor Models

Author(s): Kim, Jaewon; Klebanov, Igor R; Tarnopolsky, Grigory; Zhao, Wenli

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dc.contributor.authorKim, Jaewon-
dc.contributor.authorKlebanov, Igor R-
dc.contributor.authorTarnopolsky, Grigory-
dc.contributor.authorZhao, Wenli-
dc.date.accessioned2024-08-06T18:57:28Z-
dc.date.available2024-08-06T18:57:28Z-
dc.date.issued2019-05-31en_US
dc.identifier.citationKim, Jaewon, Klebanov, Igor R, Tarnopolsky, Grigory, Zhao, Wenli. (Symmetry Breaking in Coupled SYK or Tensor Models. Physical Review X, 9 (2), 10.1103/physrevx.9.021043en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1xw47w6b-
dc.description.abstractWe 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.languageenen_US
dc.relation.ispartofPhysical Review Xen_US
dc.rightsAuthor's manuscripten_US
dc.titleSymmetry Breaking in Coupled SYK or Tensor Modelsen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1103/physrevx.9.021043-
dc.date.eissued2019-05-31en_US
dc.identifier.eissn2160-3308-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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