Study of the superconducting order parameter in the two-dimensional negative-U Hubbard model by grand-canonical twist-averaged boundary conditions

Seher Karakuzu; Kazuhiro Seki; Sandro Sorella

doi:10.1103/PhysRevB.98.075156

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Study of the superconducting order parameter in the two-dimensional negative-U Hubbard model by grand-canonical twist-averaged boundary conditions

Seher Karakuzu, Kazuhiro Seki, Sandro Sorella

DOI 10.1103/PhysRevB.98.075156 · Physical Review B

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Abstract

By using variational Monte Carlo and auxiliary-field quantum Monte Carlo methods, we perform an accurate finite-size scaling of the s-wave superconducting order parameter and the pairing correlations for the negative-U Hubbard model at zero temperature in the square lattice. We show that the twist-averaged boundary conditions (TABCs) are extremely important to control finite-size effects and to achieve smooth and accurate extrapolations to the thermodynamic limit. We also show that TABCs are much more efficient in the grand-canonical ensemble rather than in the standard canonical ensemble with fixed number of electrons. The superconducting order parameter as a function of the doping is presented for several values of |U|/t and is found to be significantly smaller than the mean-field BCS estimate already for moderate couplings. This reduction is understood by a variational ansatz able to describe the low-energy behavior of the superconducting phase by means of a suitably chosen Jastrow factor including long-range density-density correlations.