Sign problem, complex wave function and the Hubbard model

昌弘 井町, 博志 米山

昌弘 井町, 博志 米山

Fakher F. Assaad, Diethelm W�rtz

Masahiro Imachi A, Hiroshi Yoneyama C

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

R. E. Hetzel, Wolfgang von der Linden, Werner R. Hanke

Superconducting properties of coupled Hubbard planes are studied by quantum Monte Carlo simulations. It is found that the interlayer coupling supports the pairing mechanism but it does not lead to off-diagonal long-range order in the purely electronic system. In addition, we have performed Monte Carlo studies based on a recently proposed variational wave function. Yielding identical results, the variational wave function overcomes the sign problem and allows us to analyze ground-state properties of strongly correlated many-body problems for system sizes and complexities not accessible otherwise.

Florian Ehmann, C.E. Berger, Lukas Rammelmüller +3 more