Marginal Fermi Liquid in a lattice of three-body bound-states

TL;DR

This paper introduces a lattice model where electron interactions with three-body bound-states induce marginal Fermi liquid behavior, characterized by unique scattering properties and a crossover to conventional Fermi liquid at low temperatures.

Contribution

The study presents a novel lattice model demonstrating marginal Fermi liquid behavior driven by three-body bound-states and explores its temperature-dependent crossover and instabilities.

Findings

Presence of two relaxation times, one linear and one quadratic in temperature.

Crossover from marginal Fermi liquid to conventional Fermi liquid at low temperatures.

Strong coupling leads to pairing or magnetic instabilities, suppressing marginal behavior.

Abstract

We study a lattice model for Marginal Fermi liquid behavior, involving a gas of electrons coupled to a dense lattice of three-body bound-states. The bound-states change the phase space for electron-electron scattering and induce a marginal self-energy amongst the electron gas. When the three-body bound-states are weakly coupled to the electron gas, there is a substantial window for marginal Fermi liquid behavior. In this regime, the model displays the presence of two relaxation times, one linear, one quadratic in the temperature. At low temperatures the bound-states develop coherence leading to a cross-over to conventional Fermi liquid behavior. At strong-coupling, marginal Fermi liquid behavior is pre-empted by a pairing or magnetic instability, and it is not possible to produce a linear scattering rate comparable with the temperature. We discuss the low temperature instabilities of this model and compare it to the Hubbard model at half-filling.