QUANTUM MONTE-CARLO COMPUTATION - THE SIGN PROBLEM AS A BERRY PHASE

[摘要] The partition function of interacting electrons is often represented as that of noninteracting electrons moving in a stochastic time-dependent field, integrated over the field. Quantum Monte Carlo computation of this functional integral suffers from the sign problem: rapid oscillation of the sign of the integrand at low temperature. The integrand is in general complex: the phase tends to a Berry phase for smooth paths at low temperatures, where spins follow fields adiabatically, and to zero in the high-temperature limit, recovering the static approximation.

[关键词] HUBBARD-MODEL;NUMERICAL-SIMULATION