Cross-Geometry Prediction from Open Trion Transport and Closed-Cycle Response in the Strong-Coupling Attractive Three-Component Hubbard Model

A Prospective Strong-Coupling Test Linking Trion Transport to Closed-Cycle Response

抄録

Open transport of tightly bound composites and closed virtual cycles are usually treated as distinct outputs of strong-coupling expansions. Here we investigate whether their common dependence on the same microscopic hopping processes imposes a quantitative relation that remains valid when the underlying cycle geometry is changed.
For an onsite multi-component bound cluster, the leading open transfer across a lattice edge is governed by repeated microscopic hopping processes, while a primitive closed cycle contains one hopping contribution from each edge of the cycle. Because both responses originate from the same microscopic amplitudes, their leading dependence cancels in an appropriately constructed cross-response ratio, leaving a direct relation between the two effective observables.
For the three-component case, the triangular geometry provides a definite strong-coupling benchmark. We then change the geometry to a four-edge square and combine the same structural relation with an independently derived leading four-cycle response. This fixes a quantitative prediction for the square geometry before the full microscopic calculation is performed. Unlike the triangular benchmark, the resulting prediction has both a different magnitude and an opposite sign, making it a genuine prospective test of the proposed relation.
We test this prediction by exact diagonalization of the complete four-site, three-component microscopic sector and by independently extracting the open composite-transfer response and the flux-sensitive closed-cycle response. The numerical result approaches the pre-fixed prediction with high accuracy, and systematic variation of the hopping-to-interaction ratio confirms convergence toward the predicted strong-coupling limit. Additional tests with weakly nonuniform hopping and alternative effective-Hamiltonian readouts recover the same leading behavior.
The result demonstrates, within the tested onsite-trion strong-coupling regime, that open composite transport and closed-cycle response are not independent at leading order. Their common microscopic hopping origin imposes a quantitative cross-observable constraint that survives a change in cycle geometry and enables a successful prospective prediction for the square configuration.
No universality beyond the stated model class is assumed.