Establish a universal finite-current truncation error bound

Establish a universal error bound for the adaptive finite-current cutoff used to approximate the infinite Fourier–Bessel current representation of the field-coupled XY partition function and its observables.

Background

The exact Fourier–Bessel representation of the XY partition function contains infinitely many positive and negative integer currents. Numerical tensor-network contraction therefore restricts every edge current to a finite window |n|≤K, with K chosen by an adaptive heuristic depending on β and the largest retained coupling.

The authors validate the chosen cutoff empirically by comparing it with a wider window, but they do not provide a general analytical guarantee. A universal bound would quantify the truncation error across model parameters, couplings, fields, graph sizes, and observables.

References

This conservative numerical rule has no universal error bound, so we assess cutoff accuracy by increasing K and checking the stability of the computed observables.

— Tensor-Network Inference in a Field-Coupled XY Model for Portfolio Allocation  (2609.05045 - Chowdhry et al., 4 Sep 2026) in Section 3.2, subsection “Fourier–Bessel expansion and integer-current representation”