# Charge diffusion in the one-dimensional Hubbard model

## TL;DR

This study investigates charge diffusion in the one-dimensional Hubbard model at high temperatures, revealing robust diffusive behavior across various initial conditions and confirming theoretical predictions with numerical simulations.

## Contribution

It demonstrates that charge diffusion in the 1D Hubbard model is robust and occurs under diverse initial conditions, providing numerical evidence supporting linear-response theory.

## Key findings

- Charge diffusion is observed in the strongly interacting regime.
- Diffusive behavior is independent of initial state details.
- Numerical results agree with linear-response theory.

## Abstract

We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time evolution of these nonequilibrium states, by using numerical forward-propagation approaches to chains as long as 20 sites. For a class of typical states, we find excellent agreement with linear-response theory and unveil the existence of remarkably clean charge diffusion in the regime of strong particle-particle interactions. Moreover, we demonstrate that this diffusive behavior does not depend on certain details of our initial conditions, i.e., it occurs for five different realizations with random and nonrandom internal degrees of freedom, single and double occupation of the central site, and displacement of spin-up and spin-down particles.