Search for superconductivity in the two-dimensional Hubbard model using the Constrained Path Monte Carlo

Abstract

The search for a superconducting state in the two-dimensional one-band Hubbard model (HM) has been intense in the last few years. Monte Carlo methods, haunted by the infamous fermion sign problem, have been unable to study large enough systems and low enough temperatures. The Constrained Path Monte Carlo method (CPMC) evades the sign problem by introducing an approximate constraining state. We introduce a new formulation of the CPMC that allows the implementation of a whole family of generalized mean-field states as constraint, and calculate superconducting pairing correlation functions in the HM for lattices up to 12×12. We compare the results obtained using a BCS and a free-electron constraining wave-function. We find that the d-wave correlations are insensitive to the constraining state used.