Functional calculation of partition function and
electron Green function for a D-dimensional Hubbard model

Yu-Liang Liu

Center for Advanced Study, Tsinghua University, Beijing 100084, The People's Republic of China

With the eigenfunctional method, we give general functional expressions of the partition function and electron Green function of the D-dimensional Hubbard model for zero and finite temperature, in which the sign problem of commutating fermions is avoided. These expressions can be calculated by solving equation of a phase field and taking functional average over a Lagrange multiplier field, and for some special cases, they can be exactly solved. Moreover, we compare our results with the exact solution of the dynamical mean field theory in the infinite dimension limit.