Excitonic correlations in the system of gated metallic wires with the applied Zeeman magnetic field

We have studied the electron-electron interactions in the system composed of two metallic wires, placed in the external magnetic and electric fields. The interactions between the electrons in the wires have been taken into account within the usual Hubbard model. We have considered both half-filling and partial-filling limits for the occupation of the atomic lattice sites. We show the existence of the excitonic pairing in this low-dimensional system and calculate the excitonic order parameter in different electron-electron interaction regime, magnetic field and temperature. We demonstrate that the usual Hubbard-$U$ interaction leads to strong electron localization which enhance the local antiferromagnetic order in the system.