Generalized Hartree Fock Theory for Dispersion Relations of Interacting   Fermionic Lattice Systems
  We study the variational solution of generic interacting fermionic lattice systems using fermionic Gaussian states and show that the process of "gaussification", leading to a nonlinear closed equation of motion for the covariance matrix, is locally optimal in time by relating it to the time-dependent variational principle. By linearising our nonlinear equation of motion around the ground-state fixed point we describe a method to study low-lying excited states leading to a variational method to determine the dispersion relations of generic interacting fermionic lattice systems. This procedure is applied to study the attractive and repulsive Hubbard model on a two-dimensional lattice. 
Christina V. Kraus, Tobias J. Osborne
quant-ph cond-mat.str-el