Multiloop functional renormalization group approach to quantum spin systems

Renormalization group methods are well-established tools for the (numerical) investigation of low-energy properties correlated quantum many-body systems, allowing us to capture their scale-dependent nature. The functional renormalization (FRG) allows continuously evolve a microscopic model action an effective as function decreasing energy scales via exact flow equation, which is then approximated by some truncation scheme facilitate computation. Here, we report on our implementation multiloop FRG, extended recently developed electronic FRG calculations, within pseudofermion (pf-FRG) framework interacting spin systems. We discuss in detail conceptual intricacies equations generated truncation, well essential refinements integration resulting integrodifferential equations. To benchmark approach, analyze antiferromagnetic Heisenberg models pyrochlore, simple cubic, and face-centered cubic lattice, discussing convergence physical observables higher-loop calculations comparing with existing results where available. Combined, these methodological systematically improve pf-FRG approach one numerical choice when exploring frustrated magnetism higher spatial dimensions.