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

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 presence of the bound states changes the phase space for electron-electron scattering and induces a;;marginal self-energy among 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 and 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 crossover to conventional Fermi-liquid behavior. At strong coupling, marginal Fermi-liquid behavior is preempted 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.