Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions*

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 λ_L ∝T, although
they do not saturate the upper bound of chaos, rendering them truly unique.