A Pairing-Source Lee–Yang Theorem for Attractive Hubbard Systems

Piyush Sao

Published Sep 15, 2026• 0 citations

Abstract

We prove a Lee–Yang theorem for onsite pairing sources in finite attractive Hubbard systems. For spin-conserving hopping with an arbitrary Hermitian up-spin matrix and its complex conjugate for down spin, real onsite chemical potentials, and nonnegative onsite attractions, the partition function is nonzero whenever the real parts of all local pairing fields have the same strict sign. In particular, its zeros in a uniform pairing field lie on the imaginary axis at every positive inverse temperature. This time-reversal-invariant class includes real spin-independent hopping and opposite orbital fluxes for the two spins. The proof has two steps. After a particle–hole transformation, the free Fock-space trace becomes a determinant. An indefinite-form argument shows that this determinant is nonzero throughout the source domain. We then represent the onsite attraction as a local operation on a quadratic source polynomial and prove that this operation preserves the same zero-free domain. The highest coefficient remains nonzero, so we can iterate the operation and take a locally uniform Trotter product limit to obtain the interacting theorem. For a nonzero uniform real pairing field, the same transfer argument gives a zero-free spin-fugacity annulus, positivity of the parity-twisted trace, and a lower bound on the induced parity gap. The uniform-source zero theorem also yields bounds on pair response and on the first zero. Finally, for uniformly local sequences at fixed temperature, we relate the first zero to uniform equal-time pair order.

DOI: 10.5281/zenodo.22776587

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