A strongly correlated metal built from Sachdev-Ye-Kitaev models

TL;DR

This paper constructs and analyzes a lattice model based on Sachdev-Ye-Kitaev (SYK) dots, revealing a crossover from a heavy Fermi liquid to an incoherent metal with linear resistivity and universal Lorentz ratio behavior, providing a controlled study of strongly correlated metals.

Contribution

It introduces a lattice of complex-fermion SYK dots with quadratic hopping, enabling an exact analytical study of strongly correlated metal behavior and crossovers.

Findings

Identifies a crossover from Fermi liquid to incoherent metal.

Finds linear temperature dependence of resistivity in the incoherent regime.

Shows the Lorentz ratio varies between two universal values with temperature.

Abstract

Strongly correlated metals comprise an enduring puzzle at the heart of condensed matter physics. Commonly a highly renormalized heavy Fermi liquid occurs below a small coherence scale, while at higher temperatures a broad incoherent regime pertains in which quasi-particle description fails. Despite the ubiquity of this phenomenology, strong correlations and quantum fluctuations make it challenging to study. The Sachdev-Ye-Kitaev(SYK) model describes a $0+1$D quantum cluster with random all-to-all \emph{four}-fermion interactions among $N$ Fermion modes which becomes exactly solvable as $N\rightarrow \infty$, exhibiting a zero-dimensional non-Fermi liquid with emergent conformal symmetry and complete absence of quasi-particles. Here we study a lattice of complex-fermion SYK dots with random inter-site \emph{quadratic} hopping. Combining the imaginary time path integral with \emph{real} time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio $L\equiv \frac{\kappa\rho}{T}$ varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.