Nonperturbative quartet order for the microscopically derived Hamiltonian

Extend the nonperturbative proof of quartet off-diagonal long-range order and the absence of charge-2e order from the exact easy-plane family to the microscopically derived Hamiltonian, including its generated longer-range and multibody terms.

Background

The paper rigorously proves quartet off-diagonal long-range order without charge-2e off-diagonal long-range order for the exact finite-range easy-plane family. Separately, a strong-coupling expansion derives an effective quartet model from electron hopping, pair hopping, onsite interactions, and nearest-neighbor density interactions, while establishing charge-2e gaps and short-ranged pair correlations within a controlled perturbative regime.

The microscopically derived Hamiltonian generates higher-order longer-range, multibody, and loop operators that are not covered by the nonperturbative ODLRO theorem for the idealized easy-plane family. Establishing quartet ODLRO and the continued absence of charge-2e condensation directly for this full microscopic Hamiltonian would therefore connect the rigorous benchmark to the proposed microscopic realization.