格点三玻色子三聚体的强耦合Birman-Schwinger分析的均匀椭圆约化、阶匹配判据与精度基准
A uniform elliptic reduction, an order-matching criterion, and precision benchmarks for the strong-coupling Birman-Schwinger analysis of the lattice three-boson trimer
- Samara State Technical University（萨马拉国立技术大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对格点三玻色子三聚体的强耦合Birman-Schwinger分析，提出均匀椭圆约化方法与阶匹配判据，推导基态渐近式并验证结果，还对比了少体模型的渐近精度阶。
AI中文摘要：
我们在奇异准动量K = π处研究三玻色子格点薛定谔算子的强耦合Birman-Schwinger分析。首先，我们通过对二维格点积分进行均匀椭圆约化，得到了在所有准动量K下均成立的、对应于特殊平动量的纤维Fredholm行列式的精确闭式基准。其次，我们构建并证明了一个通用的阶匹配判据：该判据用于判断，相对精度为1/μ阶的主导阶Fredholm行列式渐近式是否足以确定强耦合能量中的常数阶加法修正项，还是需要次阶修正。在K = π处应用该判据，我们推导出了完整的强耦合基态渐近式，包括1/μ阶项的系数。所得结果已通过精确闭式基准和两种独立的高精度数值方案进行交叉验证。此外，我们确定了对应的谱隙，并证明了精确的Fredholm行列式低估因子等于2。另外，我们独立确认了先前建立的K = 0常数推导正确，无需类似修正。最后，我们对比了近期格点少体模型中受控的渐近精度阶，并与拓扑能带结构的宇称分类建立了结构平行关系。
英文摘要：
We present a rigorous 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 determining whether a leading-order Fredholm determinant asymptotic, with relative error O(1/mu), suffices to fix the constant-order additive energy correction, or if the next-order refinement is required. Applying the criterion to the formal branch z = -2mu + d, we identify an algebraic crossing -2mu + 6 + 8/mu + O(mu^{-2}), but demonstrate that this crossing does not correspond to a true eigenvalue of the full Hamiltonian. The actual ground state obeys the rigorous variational bounds -3mu <= z_1^{pi,s}(mu) <= -3mu + 6, so that z_1^{pi,s}(mu) = -3mu + O(1), the same leading branch as at K = 0; direct finite-volume diagonalisation confirms the refined asymptotic -3mu + 6 + O(mu^{-1}) and spectral gap 2mu - 2 + O(mu^{-1}). We independently confirm that the known K = 0 constant C approximately 3.96458 requires no analogous refinement. Finally, we compare 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.
