Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model

2014/06/30 by Andreas Eberlein
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Density matrix renormalization group #Fermion #Functional renormalization group #Hubbard model #Mathematical physics #Pairing #Physics #Physics of Superconductivity and Magnetism #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Renormalization #Renormalization group #Superconductivity #Superfluidity #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.90.115125

published as Phys. Rev. B 90, 115125 (2014) · 14 pages, 14 figures

openalex publication_date 2014/09/12 · arxiv created 2014/09/15 · arxiv updated 2014/09/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We derive an efficient method for treating renormalization contributions at two-loop level within the functional renormalization group in the one-particle irreducible formalism for fermions. It is based on a decomposition of the two-particle vertex in charge, magnetic and pairing channels. The method treats single-particle and collective excitations in all channels on equal footing, allows for the description of symmetry breaking and captures collective mode fluctuation physics in the infrared. As a first application, we study the superfluid ground state of the two-dimensional attractive Hubbard model. We obtain superfluid gaps that are reduced by fluctuations in comparison to the one-loop approximation and demonstrate that the method captures the renormalization of the amplitude mode by long-range phase fluctuations.

Citations

• Exact diagonalization study of the antiferromagnetic spin-12Heisenberg model on the square lattice in a magnetic field
• How generic scale invariance influences quantum and classical phase transitions
• Many-body physics with ultracold gases
• Functional renormalization group for Luttinger liquids with impurities
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• Fulfillment of Ward identities in the functional renormalization group approach
• First-Order Pairing Transition and Single-Particle Spectral Function in the Attractive Hubbard Model
• Temperature dependence of antiferromagnetic order in the Hubbard model