Fermionic functional renormalization group for first-order phase transitions: a mean-field model

Abstract

First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here we introduce a counterterm technique within the functional renormalization-group (fRG) formalism which allows access to all stable and metastable configurations. It becomes possible to study symmetry-broken states which occur through first-order transitions as well as hysteresis phenomena. For continuous transitions, the standard results are reproduced. As an example, we study discrete-symmetry breaking in a mean-field model for a commensurate charge-density wave. An additional benefit of the approach is that away from the critical temperature for the breaking of discrete symmetries large interactions can be avoided at all RG scales.

17 pages, 8 figures. v2 corrects typos, adds references and a discussion of the literature

References in corpus (15)

• Exact evolution equation for the effective potential
• Renormalization Group Approach to Interacting Fermions
• d-wave superconductivity and Pomeranchuk instability in the two-dimensional Hubbard model
• On the fulfillment of Ward identities in the functional renormalization group approach
• Mean-field theory for symmetry-breaking Fermi surface deformations on a square lattice
• Renormalization group flows into phases with broken symmetry
• Renormalized perturbation theory for Fermi systems: Fermi surface deformation and superconductivity in the two-dimensional Hubbard model
• Temperature dependence of antiferromagnetic order in the Hubbard model
• Interaction flow method for many-fermion systems
• Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model
• Perturbation Theory around Non-Nested Fermi Surfaces I. Keeping the Fermi Surface Fixed
• Functional renormalization group with vacuum expectation values and spontaneous symmetry breaking
• Fermionic renormalization group flow into phases with broken discrete symmetry: charge-density wave mean-field model
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Magnetic and superconducting correlations in the two-dimensional Hubbard model

Cited by in corpus (15)

• Functional renormalization group approach to correlated fermion systems
• Pairing in the iron arsenides: a functional RG treatment
• Renormalization group flow for fermionic superfluids at zero temperature
• Superconductivity in the attractive Hubbard model: functional renormalization group analysis
• Rashba spin-orbit coupling in the square lattice Hubbard model: A truncated-unity functional renormalization group study
• The kagome Hubbard model from a functional renormalization group perspective
• Functional renormalization group for fermion lattice models in three dimensions: application to the Hubbard model on the cubic lattice
• Magnetic fluctuations and self--energy effects in two--dimensional itinerant systems with van Hove singularity of electronic spectrum
• Low energy singularities in the ground state of fermionic superfluids
• Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture
• Neel order in the Hubbard model within spin-charge rotating reference frame approach: crossover from weak to strong coupling
• Ferromagnetic instability in itinerant fcc lattice electron systems with higher order van Hove singularities: Functional renormalization group study
• Renormalization group flow for fermions into antiferromagnetically ordered phases: Method and mean-field models
• Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches
• Interaction induced local moments in parallel quantum dots within the functional renormalization group approach