Temperature dependence of charge transport in the half-filled 1D Hubbard model

TL;DR

This paper derives the low-temperature behavior of the charge diffusion constant in the 1D half-filled Hubbard model, revealing it remains finite and decreases with temperature, clarifying the transition from normal to anomalous transport.

Contribution

It provides an exact derivation of the charge diffusion constant at low temperatures, resolving the divergence issue suggested by hydrodynamic theory.

Findings

The diffusion constant is finite and decreases with increasing temperature at low T.

Diverges only at infinite temperature, not at finite T.

The results clarify the transition from diffusive to superdiffusive charge transport.

Abstract

The use of hydrodynamic transport theory seems to indicate that the charge diffusion constant D of the one-dimensional (1D) half-filled Hubbard model, whose Drude weight vanishes, diverges for temperature T>0, which would imply anomalous superdiffusive charge transport. Here the leading term of that constant is derived for low finite temperatures much smaller than the the Mott-Hubbard gap. It only diverges in the temperature infinite limit, being finite and decreasing upon increasing T within the low-temperature regime. Our exact results both provide valuable physical information ona complex quantum problem and bring about the interesting unsolved issue of how charge transport evolves from normal diffusive for low temperatures to anomalous superdiffusive in the infinite temperature limit.