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

TL;DR

This paper demonstrates that the charge stiffness in the half-filled 1D Hubbard model vanishes at finite temperature and zero hole concentration, indicating the absence of ballistic charge transport and dominance of diffusive behavior.

Contribution

It provides an analytical upper bound on charge stiffness showing it vanishes under specific conditions, clarifying the transport nature in the 1D Hubbard model.

Findings

Charge stiffness vanishes at T>0 and zero hole concentration.

Charge stiffness vanishes at high temperature near half-filling.

Charge transport is diffusive, not ballistic, at finite temperatures.

Abstract

Whether in the thermodynamic limit of lattice length infinite, hole concentration tending to zero, nonzero temperature, and U/t > 0 the charge stiffness of the 1D Hubbard model with first neighbor transfer integral t and on-site repulsion U is finite or vanishes and thus whether there is or there is no ballistic charge transport, respectively, remains an unsolved and controversial issue, as different approaches yield contradictory results. In this paper we provide an upper bound on the charge stiffness and show that (similarly as at zero temperature), for T >0 and U/t>0 it vanishes in the limit of zero hole concentration within the canonical ensemble in the thermodynamic limit. Moreover, we show that at high temperature the charge stiffness vanishes as well within the grand-canonical ensemble in the infinite lattice length limit and chemical potential approaching half the Mott-Hubbard gap. The lack of charge ballistic transport indicates that charge transport at finite temperatures is dominated by a diffusive contribution. Our scheme uses a suitable exact representation of the electrons in terms of rotated electrons for which the numbers of singly occupied and doubly occupied lattice sites are good quantum numbers for U/t>0. In contrast to often less controllable numerical studies, the use of such a representation reveals the carriers that couple to the charge probes and provides useful physical information on the microscopic processes behind the exotic charge transport properties of the 1D electronic correlated system under study.