The Sachdev-Ye-Kitaev (SYK) model has emerged as a new paradigm of non-Fermi-liquid behavior. Here we investigate a possibility of having a superconducting off-diagonal long-range order (ODLRO) and a pseudogap phase within the SYK framework. We found that ODLRO may be established in a spin-1/2 version of the model with the time-reversal invariance and an extra attractive interaction. If the latter is taken as the on-site negative U Hubbard term, it leads to the pseudogap phase at U<Uc dominated by quantum fluctuations of local phases. These fluctuations are described by a quantum version of the Kuramoto model, traditionally employed to illustrate synchronization of classical nonlinear oscillators. In the opposite limit of large U, the SYK + Hubbard model is approaching a certain generalization of the integrable Richardson model. We present exact diagonalization studies, along with analytic solutions of the aforementioned limiting cases. We also discuss possible holographic interpretations of the model, ODLRO, and the pseudogap.
|Original language||English (US)|
|Journal||Physical Review Research|
|State||Published - Jul 2020|
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© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.