Renormalization group analysis of order parameter fluctuations in fermionic superfluids

Abstract

In this work fluctuation effects in two interacting fermion systems exhibiting fermionic s-wave superfluidity are analyzed with a modern renormalization group method. A description in terms of a fermion-boson theory allows an investigation of order parameter fluctuations already on the one-loop level. In the first project a quantum phase transition between a semimetal and a s-wave superfluid in a Dirac cone model is studied. The interplay between fermions and quantum critical fluctuations close to and at the quantum critical point at zero and finite temperatures are studied within a coupled fermion-boson theory. At the quantum critical point non-Fermi liquid and non-Gaussian behaviour emerge. Close to criticality several quantities as the susceptibility show a power law behaviour with critical exponents. We find an infinite correlation length in the entire semimetallic ground state also away from the quantum critical point. In the second project, the ground state of an s-wave fermionic superfluid is investigated. Here, the mutual interplay between fermions and order parameter fluctuations is studied, especially the impact of massless Goldstone fluctuations, which occur due to spontaneous breaking of the continuous U(1)-symmetry. Fermionic gap and bosonic order parameter are distinguished. Furthermore, the bosonic order parameter is decomposed in transverse and longitudinal fluctuations. The mixing between transverse and longitudinal fluctuations is included in our description. Within a simple truncation of the fermion-boson RG flow, we describe the fermion-boson theory for the first time in a consistent manner. Several singularities appear due the Goldstone fluctuations, which partially cancel due to symmetry. Our RG flow captures the correct infrared asymptotics of the system, where the collective excitations act as an interacting Bose gas. Lowest order Ward identities and the massless Goldstone mode are fulfilled in our truncation.

In dieser Promotionsschrift werden moderne Renormierungsgruppenstrategien angewandt, um Fluktuationseffekte des Ordnungsparameters in wechselwirkenden fermionischen Systemen zu studieren. Es werden zwei Systeme untersucht, die in einem gewissen Parameterbereich Suprafluidiät zeigen. Im ersten Projekt wird ein Quantenphasenübergang zwischen Halbmetall und Supraflüssigkeit untersucht, in dem masselose kritische Fluktuationen das Geschehen am quantenkritischen Punkt bestimmen. Im zweiten Projekt wird der Grundzustand einer fermionischen Supraflüssigkeit untersucht, in dem masselose Goldstone-Fluktuationen einen dramatischen Einfluss auf das Verhalten des Systems haben. Um das vielfältige Wechselspiel zwischen Fermionen und Ordnungsparameterfluktuationen zu untersuchen, werden durch eine Hubbard-Stratonovich-Transformation bosonische Felder zur adäquaten Beschreibung der Ordnungsparameterfluktuationen eingeführt. Die gekoppelte fermionisch-bosonische Theorie wird mit Hilfe der funktionalen Renormierungsgruppenmethode untersucht.