Plaquette boson-fermion model of cuprates

The strongly interacting Hubbard model on the square lattice is reduced to the low energy plaquette boson fermion model (PBFM). The four bosons (an antiferromagnon triplet and a d-wave hole pair), and the fermions are defined by the lowest plaquette eigenstates. We apply the contractor renormalization method of Morningstar and Weinstein to compute the boson effective interactions. The range-3 truncation error is found to be very small, signaling short hole-pair and magnon coherence lengths. The pair-hopping and magnon interactions are comparable, which explains the rapid destruction of antiferromagnetic order with emergence of superconductivity, and validates a key assumption of the projected SO(5) theory. A vacuum crossing at larger doping marks a transition into the overdoped regime. With hole fermions occupying small Fermi pockets and Andreev coupled to hole pair bosons, the PBFM yields several testable predictions for photoemission, tunneling asymmetry, and entropy measurements.