Multiloop functional renormalization group approach to quantum spin systems

Abstract

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