Efficient thermodynamic-limit evaluation of the SkFCI variational energy

Develop an efficient algorithm for evaluating expectation values and variational energies of the skyrmion fractional Chern insulator wavefunction, including its sum over skyrmion-vacancy configurations, in the thermodynamic limit.

Background

The skyrmion fractional Chern insulator (SkFCI) trial wavefunction is constructed as a sum over configurations of skyrmion vacancies. Evaluating observables for this state therefore requires handling a potentially extensive configuration sum. The paper evaluates the variational energy by treating each configuration as an electron Slater determinant and applying a brute-force method, but the computational cost restricts the calculation to a 3×3 torus. An efficient method applicable in the thermodynamic limit remains unresolved and is necessary for reliable large-system energetic and correlation studies of the SkFCI.

References

Evaluating expectation values of $\Psi{\text{SkFCI}$ is challenging because of the sum over configurations ${\bm{\eta}}$. We are not aware of an efficient algorithm for doing so in the thermodynamic limit.

— Skyrmion Fractional Chern Insulator: An Intrinsically Multiband Route to Fractionalization in Rhombohedral Graphene  (2608.14535 - May-Mann et al., 14 Aug 2026) in Section 5, “Microscopic energetics”