# Undamped Bloch Oscillations in the $U\rightarrow \infty$ one-dimensional Hubbard model

## TL;DR

This paper exactly solves the one-dimensional Hubbard model at infinite interaction strength in an electric field, revealing persistent Bloch oscillations linked to Hamiltonian periodicity, and compares it with a non-integrable continuous model showing similar behavior.

## Contribution

It demonstrates the existence of undamped Bloch oscillations in the $U
ightarrow \infty$ Hubbard model and relates this to Hamiltonian periodicity rather than integrability, with comparative analysis.

## Key findings

- Undamped Bloch oscillations are extensively present in the model.
- Charge current exhibits dissipationless behavior similar to Bloch oscillations in a related non-integrable model.
- The persistence of oscillations is linked to Hamiltonian periodicity, not integrability.

## Abstract

The $U\rightarrow +\infty$ one-dimensional Hubbard model in an electric field has be exactly solved, with an emphasis on the charge current. It is found that undamped Bloch oscillations extensively exist in the system. Such conclusion has also been discussed for more general cases and we find that it is closely related to the temporal periodicity of the model Hamiltonian in electric field, rather than to the integrability of the model. As a comparison, we have also studied a model of electrons with $\delta$-function interactions in continuous space, which is closely related to the Hubbard model, but is non-integrable; and we find that the charge current strangely shows a dissipationless behaior which is comparable with the undamped Bloch oscillations.