COMPLEX WAVE-FUNCTION, CHIRAL SPIN ORDER-PARAMETER AND PHASE PROBLEM

We study the two dimensional Hubbard model by use of the ground state algorithm in the Monte Carlo simulation. We employ complex wave functi ons as trial function in order to have a close look at properties such as chiral spin order (chiSO) and flux phase. For half filling, a part icle-hole invariance leads to sum rules with respect to the Green's fu nctions for a certain choice of a set of wave functions. It is then an alytically shown that the sum rules lead to the absence of the chiSO. Upon doping, we are confronted with the sign problem, which in our cas e appears as a ''phase problem'' due to the phase of the Monte Carlo w eights. The average of the phase-shows an exponential decay as a funct ion of inverse temperature similarly to that of sign by Loh Jr. et al. We compare the numerical results with those of exact numerical calcul ations.