Absence of finite-temperature ballistic charge transport in the 1D half-filled Hubbard model

TL;DR

This paper proves that the one-dimensional half-filled Hubbard model does not exhibit finite-temperature ballistic charge transport for any positive temperature, resolving a long-standing open problem in quantum many-body physics.

Contribution

It demonstrates, using Bethe ansatz and symmetry, that the charge stiffness vanishes at finite temperature in the half-filled Hubbard model, showing absence of ballistic transport.

Findings

Charge stiffness D(T) is zero for T>0 at half-filling.

Ballistic charge transport does not occur at finite temperature in this model.

Provides an exact proof resolving a long-standing question.

Abstract

Finite-temperature T>0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing in the metallic phases ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is an integrable system of wide physical interest. For electronic densities $n\neq1$ it is an ideal conductor, with ballistic charge transport for T larger or equal to 0. In spite that it is solvable by the Bethe ansatz, at $n=1$ its T>0 transport properties are a collective-behavior issue that remains poorly understood. Here we combine that solution with symmetry to show that for on-site repulsion U>0 the charge stiffness D (T) vanishes for T>0 in the thermodynamic limit. This absence of finite-temperature ballistic charge transport is an exact result that clarifies a long-standing open problem.