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Letters in Mathematical Physics

Block Renormalization Group Approach for Correlation Functions of Interacting Fermions

Emmanuel Pereira, Aldo Procacci

Published Nov 1, 1997• 0 citations
Publisher
DOI
10.1023/a:1007391002152

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We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two ``toy applications'' from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy ``block'' excitations, which feature several single-particle Fermi edges.
By simply applying the Local Potential Approximation (LPA) on the Polchinski's Exact Renormalization Group (ERG) flow equation for single Bosonic and spinless Fermionic fields, and initially considering only the coarse-graining (blocking) aspect of Wilson's Renormalization Group program. Within the LPA limit the Polchinski's ERG flow equation simplifies into a heat differential equation for both Bosonic and Fermionic fields. Solving the differential equations leads to logarithmic interactions (logarithmic vertex function) in both Bosonic and Fermionic fields at their fixed points.