Tensor-Network Inference in a Field-Coupled XY Model for Portfolio Allocation

Abstract

We apply tensor-network methods to a field-coupled XY model for long-only portfolio construction. Daily return statistics set asset-specific fields and correlation couplings. Correlation distance, four-point Gromov hyperbolicity, and Ward clustering are used to construct a sparse interaction path. A Fourier-Bessel expansion maps the continuous angular partition function to a finite-current tensor network; bottom-up and top-down contractions then give the one-site marginals and equilibrium cosine scores. A softmax map converts these scores into positive, fully invested portfolio weights. We study five equity markets over continuous ranges of inverse temperature beta and concentration gamma, and compare selected parameter pairs with long-only Markowitz frontiers and standard benchmarks. The same-sample comparisons demonstrate a tractable route from financial time series to network-adjusted allocations; predictive trading performance is outside their scope.