Bad metals in one dimension through fast Umklapp scattering

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 being amenable to non-perturbative computation. When interactions add fast Umklapp scattering (FUS) to the Dirac-like 1D dispersion, 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 a Planckian dissipation (resistivity being linear in temperature). We further provide a microscopic lattice model, and numerically confirm the aforementioned features via density-matrix renormalization (DMRG) simulation.