Related papers: Luttinger revisted-the renormalization group appro…
We aim here to show that reductionism and emergence play a complementary role in understanding natural processes and in the dynamics of science explanation. In particular, we will show that the renormalization group - one of the most…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Fermi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the 1D Fermi-liquid…
It is explained how field-theoretic methods and the dynamic renormalisation group (RG) can be applied to study the universal scaling properties of systems that either undergo a continuous phase transition or display generic scale…
We study by means of renormalization group techniques the effect that on the two-dimensional electron liquid may have the van Hove singularities observed experimentally in the copper-oxide superconductors. We find significant deviations…
Lifshitz transitions in two 2D systems with a single quadratic band touching point as the chemical potential is varied have been studied here. The effects of interactions have been studied using the renormalization group (RG) and it is…
We propose a modification of the non-perturbative renormalization-group (NPRG) which applies to lattice models. Contrary to the usual NPRG approach where the initial condition of the RG flow is the mean-field solution, the lattice NPRG uses…
Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ by Chatterjee \emph{et al.} [Nature Physics \textbf{6}, 99 (2010)], we perform a field-theoretical…
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of…
We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to…
The conceptual framework provided by the functional Renormalization Group (fRG) has become a formidable tool to study correlated electron systems on lattices which, in turn, provided great insights to our understanding of complex many-body…
Wilson's numerical renormalization group (NRG) method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean field theory at finite temperatures. We…
We introduce a new model for quasi one-dimensional materials, motivated by intriguing but not yet well-understood experiments that have shown two-dimensional polymer films to be promising materials for thermoelectric devices. We consider a…
Breakdown of Landau's hypothesis of adiabatic continuation from non-interacting to fully interacting electrons is commonly believed to bring about a violation of Luttinger's theorem. Here, we elucidate what may go wrong in the proof of…
The functional renormalization group (fRG) approach has the property that, in general, the flow equation for the two-particle vertex generates $\mathcal{O}(N^4)$ independent variables, where $N$ is the number of interacting states (e.g.…
The effects of doping on a one-dimensional wire in a charge density wave state are studied using the density-matrix renormalization group method. We show that for a finite number of extra electrons the ground state becomes conducting but…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
The renormalization group (RG) properties of quantum gravity are explored, using the vielbein and the spin connection as the fundamental field variables. The scale dependent effective action is required to be invariant both under space time…
We review some of our recent results concerning the relationship between the Real-Space Renormalization Group method and Quantum Groups. We show this relation by applying real-space RG methods to study two quantum group invariant…
We discuss a two-parameter renormalization group (RG) consideration of a phyllotaxis model in the framework of the ``energetic approach'' proposed by L. Levitov in 1991. Following L. Levitov, we consider an equilibrium distribution of…