ASPECTS OF THE SIGN PROBLEM

The interpretation of the sign problem is discussed with reference to auxiliary field quantum Monte Carlo calculations on the Hubbard and Heisenberg models. In many cases one must use a vector auxiliary field, in which case the sign problem can be interpreted geometrically in terms of a Berry phase. The classical effective Hamiltonian for the auxiliary field, obtained by integrating out finite-frequencies, is complex as a result of the negative-weight Paths. The static approximation is the leading term in a 1/N expansion of this Hamiltonian.