Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering

TL;DR

This paper introduces a 1D model capturing key features of 2D Dirac fluids, demonstrating how fast particle-hole scattering leads to linear-in-temperature resistivity, supported by DMRG simulations and relevant to bad metal behavior.

Contribution

It presents a novel 1D lattice model that reproduces bad metal behavior and linear resistivity through particle-hole scattering, bridging 2D Dirac fluids and 1D systems.

Findings

Particle-hole scattering relaxes charge current at zero momentum.

Resistivity is linear in temperature due to fast relaxation.

Numerical DMRG results support the theoretical model.

Abstract

A strongly interacting plasma of linearly dispersing electron and hole excitations in two spatial dimensions (2D), also known as a Dirac fluid, can be captured by relativistic hydrodynamics and shares many universal features with other quantum critical systems. We propose a one-dimensional (1D) model to capture key aspects of the 2D Dirac fluid while including lattice effects and being amenable to non-perturbative computation. When interactions are added to the Dirac-like 1D dispersion without opening a gap, we show that this kind of irrelevant interaction is able to preserve Fermi-liquid-like quasi-particle features while relaxing a zero-momentum charge current via collisions between particle-hole excitations, leading to resistivity that is linear in temperature via a mechanism previously discussed for large-diameter metallic carbon nanotubes. We further provide a microscopic lattice model and obtain numerical results via density-matrix renormalization group (DMRG) simulations, which support the above physical picture. The limits on such fast relaxation at strong coupling are of considerable interest because of the ubiquity of bad metals in experiments.