Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions

TL;DR

This paper introduces a higher-dimensional generalization of the SYK model on a lattice with Lifshitz points, revealing new non-Fermi liquid states with unique scaling, symmetry, and chaotic properties.

Contribution

The authors construct a lattice SYK model with Lifshitz points, demonstrating novel NFL states with tunable properties and non-saturating chaos, extending the SYK framework to higher dimensions.

Findings

Discovery of a new class of NFL states with Lifshitz dispersion

NFL states exhibit emergent scaling symmetry and time reparameterization invariance

NFL states are fast scramblers with sub-maximal chaos

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.