Interplay between antiferromagnetism and superconductivity in the Hubbard model with frustration

Coexistence of and competition between antiferromagnetism (AF) and d-wave superconductivity (SC) are studied for a Hubbard model on the square lattice with a diagonal transfer t′, using a variational Monte Carlo method. The following improvements are introduced into the trial function: (1) Coexistence of AF and d-wave singlet gaps that allows a continuous description of their interplay, (2) band renormalization effect, and (3) refined doublon-holon correlation factors. Optimizing this function for a strongly correlated value of U/t, we construct a phase diagram in the δ (doping rate)-t′/t space, and find that for t′/t⩾-0.15 a coexisting state is realized, whose range of δ extends as t′/t increases. In contrast, for t′/t=-0.3, AF and SC states are mutually exclusive, and a coexisting state does not appear. In connection with the “two-gap” problem, we confirm even for the present refined function that the gradient of momentum distribution function at the antinodal point mainly dominates the magnitude of the d-wave SC correlation function.