A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimer

• URL: http://arxiv.org/abs/2608.11848v2
• Date: Sun, 16 Aug 2026 08:29:26 GMT
• Title: A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimer
• Abstract summary: We present a strong-coupling analysis of the three-boson lattice Schroedinger operator on Z2 at the exceptional quasimomentum K = pi.<n>We rigorously establish the corresponding spectral gap and the Fredholm-determinant underestimation factor 2 + O(mu-2)<n>We draw a structural parallel with the parity-based classification of topological band insulators at time-reversal-invariant momenta.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a refined strong-coupling Birman-Schwinger analysis of the three-boson lattice Schroedinger operator on Z^2 at the exceptional quasimomentum K = pi. First, we provide an exact closed-form benchmark for the fiber Fredholm determinant, valid for every quasimomentum K, obtained via a uniform elliptic reduction. Second, we formulate and prove a general order-matching criterion that rigorously determines whether a leading-order Fredholm determinant asymptotic, with relative error 1/mu, suffices to fix the constant-order additive energy correction, or if the next-order refinement is required. Applying the criterion at K = pi, we derive the complete strong-coupling ground-state asymptotic expansion z_1^{pi,s}(mu) = -2mu + 6 + 8/mu + O(mu^{-2}), cross-validated against the exact benchmark and two independent high-precision numerical schemes. We rigorously establish the corresponding spectral gap and the Fredholm-determinant underestimation factor 2 + O(mu^{-2}). We independently confirm that the known K = 0 constant requires no analogous refinement. Finally, we contrast the asymptotic precision levels achieved across recent lattice few-body models and draw a structural parallel with the parity-based classification of topological band insulators at time-reversal-invariant momenta.

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