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This is the simplest d-wave BCS state appropriate for the single-band Hubbard model and could be further improved by considering a long-range density-density or holon-doublon Jastrow term, see for instance, M. Capello, F. Becca, M. Fabrizio, S. Sorella, and E. Tosatti, Phys. Rev. Lett. 94, 026406 (2005).
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