Interplay between staggered flux and d-wave superconducting states in Hubbard model

With cuprate superconductors in mind, we check whether the d-wave superconducting (dSC) state coexists with or excludes the staggered flux (SF) state, which was revealed to be the strong candidate for the pseudogap state. To this end, we use a variational Monte Carlo method for the square Hubbard model with diagonal transfer t′. In the trial wave function, dSC and SF orders coexist, which allows a continuous description of their interplay; essential factors for Mott physics and band renormalization are also included. It is found that the SF state does not coexist with dSC and is unstable for U/t = 12 regardless of the value of t′/t within the present work.