Restricted and unrestricted Hartree-Fock calculations of conductance for a quantum point contact

Very short quantum wires (quantum contacts) exhibit a conductance structure at a value of conductance close to $0.7\times {2e}^2/h.\mathrm{}$ It is believed that the structure arises due to the electron-electron interaction and is also related to electron spin. Previously we approached the problem within the restricted Hartree-Fock approximation. This calculation demonstrated a structure similar to that observed experimentally. In the present work we perform restricted and unrestricted Hartree-Fock calculations to analyze the validity of the approximations. We also consider the dependence of the effect on the electron density in the leads. The unrestricted Hartree-Fock method allows us to analyze trapping of the single electron within the contact. Such trapping would result in the Kondo model for the “0.7 structure.” The present work does not confirm a spin polized state and rules out the Kondo model scenario. On the other hand, the calculation confirms the picture of the few-electron bound state with total spin zero.