In this talk I will argue that novel ordered phases can be expected for interacting quantum systems away from thermal equilibrium. I will start by reporting a set of mean-field results concerning the effects of large bias voltages applied across an half-filled Hubbard chain. As a function of the applied voltage and temperature a rich set of phases can be found that is induced by the interplay between electron-electron interactions and non-equilibrium conditions. Taking a step back, I try to explain why such phases are possible (at least at the mean field level). This will motivate the characterization of the current-carrying steady-state that arises in the middle of a non-interacting metallic wire connected to macroscopic leads. Finally, I will comment on some ongoing work regarding the fate of the Peierls transition in a similar non-equilibrium setup.

* Pedro Ribeiro, CeFEMA & Physics Department, IST, Universidade de Lisboa.