# Strange diffusivity of incoherent metal in half-filled two-dimensional Hubbard model

## TL;DR

This study investigates charge transport in the half-filled 2D Hubbard model, revealing a 'strange metal' behavior with anomalous resistivity scaling and a novel pseudogap metallic state near the metal-insulator transition.

## Contribution

The paper introduces a multiscale approach combining diagrammatic Monte Carlo and analytic theory to analyze incoherent transport and reveals a new pseudogap metal state.

## Key findings

- Diffusivity scales as 1/√T across the anomalous temperature range.
- Identifies a pseudogap metal with insulating charge compressibility and metallic transport.
- High-temperature incoherent transport is dominated by dressed polarization bubbles.

## Abstract

We study charge transport across the metal-insulator crossover in the half-filled two-dimensional Hubbard model, with particular emphasis on precision control. The dynamic current-current correlation function is obtained directly in the thermodynamic limit, and the optical conductivity is extracted using numerical analytic continuation. To achieve this, we develop a multiscale approach: the non-perturbative low-frequency behavior is computed using the unbiased diagrammatic Monte Carlo technique, while the high-frequency physics is captured via a self-consistent (semi-)analytic diagrammatic theory. We found that across a broad temperature range where the DC resistivity displays anomalous scaling, $\sim T^\alpha$ with $0<\alpha\lesssim 1$, the Nernst-Einstein relation implies the diffusion constant with the characteristic $\sim 1/\sqrt{T}$ "strange metal" behavior. It was also revealed that the insulating regime is entered through a peculiar non-Fermi liquid state-which we call a Pseudogap Metal-characterized by insulating charge compressibility coexisting with metallic transport. Diagrammatically, the high-temperature incoherent transport is captured by the dressed polarization bubble, whereas near the metal-insulator crossover, the effective interaction vertex between opposite-spin particles is responsible for transferring the Drude weight to a high-frequency continuum.