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. fRG for 1st-order phase transitions

Functional renormalization group approach to correlated fermion systems

“…II.B. The counterterm method has been implemented for the exactly soluble test case of a chargedensity wave mean-field model by Gersch et al (2006). Popular approximations also beyond mean-field theory can be retrieved from the functional RG by keeping a suitable subset of contributions.…”

Interaction-induced local moments in parallel quantum dots within the functional renormalization group approach

“…To describe the SFL state we decrease the magnetic field continuously during the flow, similarly to a counterterm extension of the fRG [33,34]. To this end, we introduce additional term σχ Λ /2 in the propagator of the quantum dots…”

“…This scheme is similar to a counterterm technique, used earlier to treat the first order quantum phase transitions in lattice fermionic systems [33,34] within fRG approach. This technique was not however applied to description of quantum dot structures.…”

Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture

“…In a number of papers, simplified meanfield models with infinitely long-ranged interactions have been studied. [6][7][8][9] For these models, MFT holds exactly due to the specific form of their interaction terms, and this exact solution can be recovered within a fRG framework. More generic interactions were treated by R. Gersch et al in Ref.…”