Related papers: The Density Matrix Renormalization Group, Quantum …
The free energy of the Coulomb Gap problem is expanded as a set of Feynman diagrams, using the standard diagrammatic methods of perturbation theory. The gap in the one-particle density of states due to long-ranged interactions corresponds…
We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a…
We extend the method of differential renormalization to massive quantum field theories treating in particular $\ph4$-theory and QED. As in the massless case, the method proves to be simple and powerful, and we are able to find, in…
An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining…
We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin-orbit coupling.…
I suggest that the current situation in quantum field theory (QFT) provides some reason to question the universal validity of ontological reductionism. I argue that the renormalization group flow is reversible except at fixed points, which…
We discuss Weyl anomaly and consistency conditions of local renormalization group in d=1+2 dimensional quantum field theories. We give a classification of the consistency conditions and ambiguities in most generality within the…
The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on…
We consider the double-scaling limit in matrix models for two-dimensional quantum gravity, and establish the nonperturbative functional Renormalization Group as a novel technique to compute the corresponding interacting fixed point of the…
We present an implementation of the relativistic quantum-chemical density matrix renormalization group (DMRG) approach based on a matrix-product formalism. Our approach allows us to optimize matrix product state (MPS) wave functions…
This is an elementary introduction to Wilson renormalization group and continuum effective field theories. We first review the idea of Wilsonian effective theory and derive the flow equation in a form that allows multiple insertion of…
A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by…
We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
A new operator formalism for the reduction of degrees of freedom in the evolution of discrete partial differential equations (PDE) via real space Renormalization Group is introduced, in which cell-overlapping is the key concept.…
We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations.…
Renormalization plays an important role in the theoretically and mathematically careful analysis of models in condensed-matter physics. I review selected results about correlated-fermion systems, ranging from mathematical theorems to…
We explore the implications of recent work by Br\'ezin and Zinn-Justin, applying the renormalization group techniques from critical phenomena to the scaling limit of matrix models in two-dimensional quantum gravity. They endeavor to get the…
Based only on simple principles of renormalization in coordinate space, we derive closed renormalized amplitudes and renormalization group constants at 1- and 2-loop orders for scalar field theories in general backgrounds. This is achieved…
This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum field theory over 2-dimensional quantum gravity up to algebraic…