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Functional Renormalization Group for Correlated Fermion Systems |
Research Unit of the German Research Foundation |
In this project we use functional RG methods to study the dynamics and competition of order parameter fields, as well as their interplay with one another and with the fermionic degrees of freedom, to get a detailed picture of phases with spontaneously broken symmetries in models for correlated fermions in low dimensions.
Applications include superconductivity and magnetism in the two-dimensional Hubbard model. Theoretical issues are the dynamics of Goldstone degrees of freedom, the effects of low dimensionality, Ward identities, the emergence of effective scales, as well as the relation between different RG schemes.
In this project we study several types of quantum phase transitions between a normal metal and an ordered phase with spontaneously broken symmetry: ferromagnet, antiferromagnet, and a 'Pomeranchunk phase' with a symmetry-broken Fermi surface.
The functional RG will be used to analyse the coupled system of electronic excitations and order parameter fluctuations. We will try to derive and solve a set of flow equations which captures all the entangled singularities appearing near the quantum phase transition in two- as well as in three-dimensional systems. We will investigate the efficiency of an effective theory of order parameter fluctuations, where electronic degrees of freedom are integrated out, and the validity of the theory of Hertz and Millis, in which the interactions between order parameter fluctuations are assumed to be regular.
The main objective of this project is the development of an truncation scheme of the functional RG approach that includes dynamical effects and thus inelastic processes due to electron-electron scattering. The scheme should be simple and flexible enough such that it can be applied to study the role of inelastic processes in one-dimensional chains and systems of quantum dots.
We will extend or work on correlation effects in inhommogeneous chains and dots. In particular for systems of quantum dots, we will be able to study transport and spectral properties at intermediate to large temperatures. Further issues we will investigate using our established frequency independent truncation scheme are (1) the importance of the feedback of the inhomogeneity on the flow of the effective interaction in one-dimensional systems with spin and (2) the crossover from the physics of local Coulomb correlations in dots to Tomonaga-Luttinger liquid physics in long chains. In particular, we expect interesting effects in ring geometries (Aharonov-Bohm geometries) of increasing length due to the development of spin-charge seperation.
The aim of this project is the combination of functional RG methods with noequilibrium many-body techniques to describe nonlinear charge and spin transport through strongly correlated mesoscopic systems and quantum wires. In addition, a functional RG method based on operator vertices will be further developed and applied to describe systems with strong Coulomb interaction. In the applications we shall focus on Kondo and dephasing effects in transport through quantum dots with spin and/or orbital degeneracy, and on the interplay of interference and inelastic interactions in transport through Tomonaga-Luttinger liquids with impurities.
The condesation phenomena in gases of ultracold fermionic atoms, in particular the crossover from Bose-Einstein condensation of molecules to BCS superfluidity, witness a series of experimental breakthroughs. We aim at a functional integral description of the corresponding many-body physics, focusing on the most relevant strong-coupling aspects.
We use the functional RG as a quantitative tool to relate the microscopic properties of atoms and molecules to the macroscopic observables at finite density and temperature. The resulting formalism is intended to support a detailed investigation of the whole phase diagram, including a quantitative determination of the critical temperature and corresponding critical exponents. From a more fundamental perspective, this project aims at revealing aspects of enhanced universality induced by a new fixed-point structure in the RG flow of ultracold ferminonic atom systems.