Ground-state wave function of a one-dimensional weakly nonideal lattice Fermi gas

The Bogolyubov–Zubarev method of collective variab|es is used to find the ground-state wave function of a weakly nonideal one-dimensional lattice Fermi gas (in particular, the Hubbard model). The particle momentum distribution in the ground state is found in the first order in the coupling constant, and it is shown that the step in the Fermi distribution is smeared. A more realistic quasione-dimensional system is also considered and its excitation spectrum obtained.