Multiloop functional renormalization group approach to quantum spin systems

TL;DR

This paper advances the functional renormalization group method for quantum spin systems by implementing a multiloop truncation approach, improving accuracy and convergence in studying frustrated quantum magnetism across various lattice geometries.

Contribution

The authors adapt a multiloop truncation scheme from electronic FRG to the pseudo-fermion FRG for quantum spins, enhancing the method's precision and reliability.

Findings

Improved convergence of physical observables with higher-loop calculations.

Benchmarking against known models shows increased accuracy.

Methodological refinements facilitate studies of frustrated quantum magnets.

Abstract

Renormalization group methods are well-established tools for the (numerical) investigation of the low-energy properties of correlated quantum many-body systems, allowing to capture their scale-dependent nature. The functional renormalization group (FRG) allows 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 transcription of a recently developed multiloop truncation approach for electronic FRG calculations to the pseudo-fermion functional renormalization group (pf-FRG) 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 integro-differential 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.