Cluster Functional Renormalization Group

TL;DR

This paper introduces a cluster-based functional renormalization group method that treats local clusters exactly and addresses inter-cluster interactions via RG, demonstrated on a spin model to capture low-energy properties.

Contribution

The work generalizes FRG by starting from a cluster product state, enabling exact treatment of local clusters and RG analysis of inter-cluster couplings.

Findings

Reasonable spin susceptibility results near antiferromagnetic order

Accurate magnon dispersion and quasiparticle weights

Applicable to various interacting electron systems

Abstract

Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a non-interacting expansion point of the action, the flow of the RG parameter Lambda allows to trace the evolution of the effective one-particle and two-particle vertices towards low energies by taking into account the vertex corrections between all parquet channels in an unbiased fashion. In this work, we generalize the expansion point at which the diagrammatic resummation procedure is initiated from a free UV limit to a cluster product state. We formulate a cluster FRG scheme where the non-interacting building blocks (i.e., decoupled spin clusters) are treated exactly, and the inter-cluster couplings are addressed via RG. As a benchmark study, we apply our cluster FRG scheme to the spin-1/2 bilayer Heisenberg model (BHM) on a square lattice where the neighboring sites in the two layers form the individual 2-site clusters. Comparing with existing numerical evidence for the BHM, we obtain reasonable findings for the spin susceptibility, magnon dispersion, and magnon quasiparticle weight even in coupling regimes close to antiferromagnetic order. The concept of cluster FRG promises applications to a large class of interacting electron systems.