Damping of Bloch oscillations in the Hubbard model

TL;DR

This paper investigates how weak interactions in the Hubbard model affect Bloch oscillations under a static electric field, revealing a transition from oscillatory to steady response at a critical interaction strength.

Contribution

It demonstrates the existence of a critical interaction threshold that determines the transition from Bloch oscillations to a steady current in the Hubbard model.

Findings

Below critical interaction, the system exhibits Bloch oscillations.

Above critical interaction, the system shows a steady DC response.

The transition is characterized by universal long-time behavior.

Abstract

Using nonequilibrium dynamical mean-field theory, we study the isolated Hubbard model in a static electric field in the limit of weak interactions. Linear response behavior is established at long times, but only if the interaction exceeds a critical value, below which the system exhibits an AC-type response with Bloch oscillations. The transition from AC to DC response is defined in terms of the universal long-time behavior of the system, which does not depend on the initial condition.