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Title:
Quantum critical points in low-rank SYK models
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Abstract:
Motivated by a recent atom-cavity experiment proposal [1], we study a family of solvable variants of the q= 4 Sachdev-Ye-Kitaev (SYK) model whose coupling matrix $J_{ij,kl}$ has tunable rank and eigenvalue distribution. (This is an extension of earlier works [2,3,4].) While SYK is recovered when the rank is super-extensive (much larger than the number of Majorana fermions), and the model becomes non-interacting in the sub-extensive rank regime, the extensive-rank regime has rich low-T behaviors, depending on the eigenvalue distribution. We obtain a classification of possible critical points, unifying and extending earlier results. They include two critical lines with tunable scaling dimension, a Fermi liquid with broken time-reversal symmetry, and a non-Fermi liquid with large specific heat $C_V \sim T^{\nu} \gg T$.
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