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Published January 15, 2014 | Submitted + Published
Journal Article Open

Cluster functional renormalization group

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 free expansion point of the action, the flow of the RG parameter Λ allows us to trace the evolution of the effective one- 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 noninteracting building blocks (i.e., decoupled spin clusters) are treated exactly, and the intercluster 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 two-site clusters. Comparing with existing numerical evidence for the BHM, we obtain reasonable findings for the spin susceptibility, the spin-triplet excitation energy, and 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.

Additional Information

© 2014 American Physical Society. Received 24 September 2013; published 15 January 2014. The authors gratefully acknowledge discussions with W. Brenig, W. Metzner, C. Platt, and P. Wölfle. This research was supported by the Deutsche Akademie der Naturforscher Leopoldina through Grants No. LPDS 2011-14 (J.R.) and through No. DFG-SPP 1458 as well as No. ERC-StG-2013-336012 (R.T.).

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Published - PhysRevB.89.024412.pdf

Submitted - 1309.3262v1.pdf

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August 19, 2023
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