Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions

Abstract

We address the key open problem of a higher dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model. We construct a model on a lattice of SYK dots with non-random intersite hopping. The crucial feature of the resulting band dispersion is the presence of a Lifshitz point where two bands touch with a tunable powerlaw divergent density of states (DOS). For a certain regime of the powerlaw exponent, we obtain a new class of interaction-dominated non-Fermi liquid (NFL) states, which exhibits exciting features such as a zero-temperature scaling symmetry, an emergent (approximate) time reparameterization invariance, a powerlaw entropy-temperature relationship, and a fermion dimension that depends continuously on the DOS exponent. Notably, we further demonstrate that these NFL states are fast scramblers with a Lyapunov exponent ${\lambda }_L\propto T$, although they do not saturate the upper bound of chaos, rendering them truly unique.

6 pages, 3 figures and Supplemental Material(15 pages, 4 figures)

References in corpus (6)

• Quantum Gravity at a Lifshitz Point
• More on Supersymmetric and 2d Analogs of the SYK Model
• Quantum chaos on a critical Fermi surface
• Higher Dimensional Generalizations of the SYK Model
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Dispersive SYK model: band structure and quantum chaos

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