Sign Resolved Measurements in Quantum Simulations

Quantum simulations are a powerful tool for exploring strongly correlated body phenomena. However,for many situations of interest, the weight which enters the averaging over the quantum paths can becomenegative, rendering its use as a probability inappropriate. It is well known that if one ignores the sign ofthe configuration the values of physical observables are incorrect. One of the most dramatic divergencesin auxiliary field Quantum Monte Carlo occurs for the d-wave pairing where ignoring the sign leads to asuppression of the superconducting response as the temperature is lowered, whereas a proper inclusion ofthe sign points to the opposite behavior. The question of characterizing which paths are associated withnegative weights has been extensively considered. In this paper we choose a different approach andexamine the behavior of observables in a sign-resolved fashion: Are the density, double occupancy,structure factor distributions different when the sign is negative from when it is positive?