Interferometric Spectroscopy of Virtual Charge Processes in a Mott Insulator

Virtual charge motion generates magnetic interactions in a Mott insulator, but different virtual processes can produce the same spectral signature. For two neighboring plaquettes, a contribution around their common outer perimeter and a nonlinear product of the elementary-loop responses can both yield a second flux harmonic of order t^6/U^5. We distinguish them by combining four measurements at independently chosen plaquette fluxes with bond-removal comparisons in the half-filled nearest-neighbor Hubbard model on coupled square plaquettes. The phase combination cancels the leading cosine-product background, while particle-hole symmetry excludes the corresponding pair of leading local flux-odd spin interactions. Exact diagonalization of the 2 x 3 cluster gives a nonzero U^-5 spectral contrast when the shared bond is removed but the six-edge outer cycle remains, and no contrast after either outer-edge cut; the same geometric distinction persists within the isolated low-energy band. These finite-cluster results connect phase-resolved magnetic spectra to the spatial extent of virtual charge motion beyond what a harmonic or an interaction power can determine alone.