Non-equilibrium dynamics of the driven Hubbard model

TL;DR

This paper studies the non-equilibrium behavior of a 2D Hubbard model under electric fields, showing how coupling to a bath leads to steady states and mapping out the conditions for maximum current.

Contribution

It provides a detailed analysis of how dissipation influences the formation of non-equilibrium steady states in the driven Hubbard model.

Findings

Steady states are achievable for all coupling strengths with a bath.

A phase diagram of dissipation and electric field effects is constructed.

Maximum steady current occurs at specific dissipation levels.

Abstract

We investigate the dynamics of a two-dimensional Hubbard model in a static electric field in order to identify the conditions to reach a non-equilibrium stationary state. For a generic electric field, the convergence to a stationary state requires the coupling to a thermostating bath absorbing the work done by the external force. Following the real-time dynamics of the system, we show that a non-equilibrium stationary state is reached for essentially any value of the coupling to the bath. We map out a phase diagram in terms of dissipation and electric field strengths and identify the dissipation values in which steady current is largest for a given field.