Half-filled Hubbard model at low temperature

TLDR: In this article, the ground state energy and momentum distribution of the electrons are expanded from the atomic limit for the half-filled Hubbard model by using the spin correlation functions of the spin 1/2 Heisenberg model.

Abstract: The ground-state energy E and momentum distribution nk of the electrons are expanded from the atomic limit for the half-filled Hubbard model. The coefficients of expansion are represented by the spin correlation functions of the spin 1/2 Heisenberg model. Using the spin-wave theory, approximate values of coefficients are calculated for the square lattice and the simple cubic lattice. In one dimension, the theory shows a good agreement with the exact solution. An effective spin Hamiltonian for the half-filled Hubbard model with arbitrary hopping integrals is obtained up to the fifth order. It is shown that the fourth term contains four spin interactions.