Dimensional Crossover Driven by an Electric Field

TL;DR

This paper investigates how a strong electric field causes a dimensional reduction in the Hubbard model's steady-state behavior, revealing new insights into non-equilibrium quantum systems with dissipation.

Contribution

It introduces a theoretical framework for understanding electric field-induced dimensional crossover in the Hubbard model with dissipation, including derivation of steady-state equations within dynamical mean field theory.

Findings

Dimensional reduction occurs at very strong electric fields.

Spectral functions and energy distributions are affected by the crossover.

Steady current behavior changes in the non-linear regime.

Abstract

We study the steady-state dynamics of the Hubbard model driven out-of-equilibrium by a constant electric field and coupled to a dissipative heat bath. For very strong field, we find a dimensional reduction: the system behaves as an equilibrium Hubbard model in lower dimensions. We derive steady-state equations for the dynamical mean field theory in the presence of dissipation. We discuss how the electric field induced dimensional crossover affects the momentum resolved and integrated spectral functions, the energy distribution function, as well as the steady current in the non-linear regime.