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Spontaneous breaking of U(1) symmetry in coupled complex SYK models

Author(s): Klebanov, Igor R; Milekhin, Alexey; Tarnopolsky, Grigory; Zhao, Wenli

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Abstract: As shown in [1], two copies of the large N Majorana SYK model can produce spontaneous breaking of a Z2 symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the U(1) × U(1) symmetry. We also present a tensor counterpart of this coupled model. When the coefficient α of the quartic term lies in a certain range, the coupled large N theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of α. We show that the operator c† 1ic2i, which is charged under the axial U(1) symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large N Dyson-Schwinger equations and show that, outside the fixed line, this U(1) symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large N .
Publication Date: 27-Nov-2020
Electronic Publication Date: 27-Nov-2020
Citation: Klebanov, Igor R, Milekhin, Alexey, Tarnopolsky, Grigory, Zhao, Wenli. (2020). Spontaneous breaking of U(1) symmetry in coupled complex SYK models. Journal of High Energy Physics, 2020 (11), 10.1007/jhep11(2020)162
DOI: doi:10.1007/jhep11(2020)162
EISSN: 1029-8479
Keywords: Spontaneous Symmetry Breaking, 1/N Expansion, Holography and condensed matter physics (AdS/CMT)
Language: en
Type of Material: Journal Article
Journal/Proceeding Title: Journal of High Energy Physics
Version: Final published version. This is an open access article.



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