Title: 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.