Renormalization group flow for fermions into antiferromagnetically ordered phases: Method and mean-field models

Abstract

We present a functional renormalization group flow for many-fermion lattice models into phases with broken spin-rotational symmetry. The flow is expressed purely in terms of fermionic vertex functions. The symmetry breaking is seeded by a small initial anomalous self-energy which grows at the transition scale and which prevents a runaway-flow at nonzero scales. Focusing on the case of commensurate antiferromagnetism we discuss how the interaction vertex can be parametrized efficiently. For reduced models with long-range bare interactions we show the results of standard mean-field theory are reproduced by the fRG and how anisotropies in the spin sector change the flows. We then describe a more efficient decomposition of the interaction vertex that should allow for the treatment of more general models.

revised version; 12 pages, 9 figures

References in corpus (22)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Functional renormalization group approach to correlated fermion systems
• Competing order and nature of the pairing state in the iron pnictides
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• On the fulfillment of Ward identities in the functional renormalization group approach
• Magnetic and superconducting instabilities of the Hubbard model at the van Hove filling
• Functional renormalization for spontaneous symmetry breaking in the Hubbard model
• Renormalization group flows into phases with broken symmetry
• A finite-frequency functional RG approach to the single impurity Anderson model
• Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Renormalization group flow for fermionic superfluids at zero temperature
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Fermionic renormalization group flow into phases with broken discrete symmetry: charge-density wave mean-field model
• Four-point vertex in the Hubbard model and partial bosonization
• Critical scales in anisotropic spin systems from functional renormalization
• Parametrization of Nambu vertex in a singlet superconductor
• Generation of d-wave coupling in the two-dimensional Hubbard model from functional renormalization
• Fermionic functional renormalization group for first-order phase transitions: a mean-field model
• Incommensurate antiferromagnetic fluctuations in the two-dimensional Hubbard model

Cited by in corpus (6)

• Chiral d-wave superconductivity in doped graphene
• Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model
• Effective interactions and fluctuation effects in spin-singlet superfluids
• Nonperturbative renormalization-group approach to fermion systems in the two-particle-irreducible effective action formalism
• Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model
• Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture