Oscillating charge currents of one-dimensional Hubbard model in an electric field

TL;DR

This paper rigorously analyzes the time evolution of charge currents in a one-dimensional Hubbard model under an electric field, revealing oscillatory and zero-current states influenced by strong correlations.

Contribution

It introduces a complete set of time-evolution states for the Hubbard model, showing charge current oscillates or remains zero, differing from typical damped Bloch oscillations.

Findings

Charge current can only stay zero or oscillate constantly.

A set of constant phase factors uniquely determines long-time behavior.

The results differ from traditional damped Bloch oscillations.

Abstract

The time evolution properties of charge current for the one-dimensional Hubbard model in an electric field have been studied in a rigorous manner. We find that there is a complete and orthonormal set of time-evolution states for which the charge current can only keep zero or oscillate constantly, differing from the possible picture of damped or over-damped Bloch oscillations due to strong correlations. It is also found that, associated with these states, there is a set of constant phase factors, which are uniquely determined and are very useful on discussing the long-time evolution behaviors of the system.