Translationally invariant non-Fermi liquid metals with critical Fermi-surfaces: Solvable models

TL;DR

This paper introduces solvable models of strongly-correlated, translationally invariant metals that exhibit non-Fermi liquid behavior, critical Fermi-surfaces, and quantum oscillations, providing insights into local quantum criticality and relaxation bounds.

Contribution

The authors construct exactly solvable lattice models with local interactions that display non-Fermi liquid regimes and critical Fermi-surfaces, advancing understanding of strongly correlated metals.

Findings

Models show crossover to local quantum criticality and marginal-Fermi liquid behavior.

In the marginal Fermi liquid regime, resistivity increases linearly with temperature.

Critical Fermi-surfaces produce quantum oscillations without quasiparticles.

Abstract

We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<\infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.