Develop a proper scaling theory for finite-order extrapolations

Develop and prove a proper scaling theory that determines the dependence of the thermodynamic-limit energy and magnetization on the finite perturbation or coupled-cluster order for the cluster-based calculations applied to the J1-J2 Heisenberg model.

Background

The authors extrapolate finite-order coupled-cluster and perturbation-theory results to estimate exact thermodynamic-limit energies and magnetizations. They state that the commonly used fitting forms are empirical and that the perturbation-theory extrapolations are especially sensitive to the polynomial order, producing unphysical results in some parameter regions. A rigorous scaling theory would justify the extrapolation forms and establish how the calculated observables converge with method order.

References

Unfortunately, no scaling theory has been proven so we must rely on empirically derived extrapolation schemes.

— Examining Convergence of Cluster Perturbation Theory and Cluster Coupled Cluster for J1-J2 Heisenberg Spin Lattices  (2609.08768 - Keyes et al., 8 Sep 2026) in Section 2, subsection “Data Extrapolations”