Quantics tensor trains for multiloop functional renormalization group in multiorbital impurity models

Abstract

The full frequency dependence of electronic interactions is central to dynamical correlations, but its numerical cost restricts multiorbital calculations. We formulate the multiloop functional renormalization group directly in the quantics tensor train representation, retaining all three independent vertex frequencies over broad ranges without an explicit high-frequency parametrization. Analytical tensor operators perform frequency transformations and internal summations without dense vertex intermediates. Multiloop corrections improve agreement of vertices and responses with independent references and reproduce the low-energy numerical renormalization group self-energy. Lower-temperature calculations resolve a quadratic frequency contribution to the analytically continued scattering rate. A degenerate two-orbital impurity exhibits distinct spin, orbital, and charge responses at fixed Hund coupling. In a compensated altermagnetic environment, an orbital-level splitting induces a local spin response despite zero magnetization of the unperturbed impurity. Increasing Hund coupling suppresses the orbital response while increasing its spin polarization. Renormalized one-particle propagation alone does not reproduce this strong polarization dependence. These results extend compressed multiloop calculations to dynamical correlations in multiorbital environments.