Related papers: Renormalization group based implicit function appr…
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
A numerical algorithm for studying strongly correlated electron systems is proposed. The groundstate wavefunction is projected out after numerical renormalization procedure in the path integral formalism. The wavefunction is expressed from…
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…
In this work, we introduce a new class of non-convex functions, called implicit concave functions, which are compositions of a concave function with a continuously differentiable mapping. We analyze the properties of their minimization by…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
Criticality and symmetry, studied by the renormalization groups, lie at the heart of modern physics theories of matters and complex systems. However, surveying these properties with massive experimental data is bottlenecked by the…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
Large-$N$ renormalization group equations for one- and two-matrix models are derived. The exact renormalization group equation involving infinitely many induced interactions can be rewritten in a form that has a finite number of coupling…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
We give a comprehensive review of the renormalization group method for global and asymptotic analysis, putting an emphasis on the relevance to the classical theory of envelopes and the existence of invariant manifolds of the dynamics under…
We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective…
Uniformly regular equilibrium problems are natural generalizations of abstract equilibrium prob lems and they are defined over the uniformly prox-regular nonconvex sets. Some new efficient implicit methods for solving uniformly regular…
Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states.…
The renormalization group (RG) is an essential technique in statistical physics and quantum field theory, which considers scale-invariant properties of physical theories and how these theories' parameters change with scaling. Deep learning…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
The paper contains generalization of the renormgroup algorithm for boundary value problems of mathematical physics and related concept of the renormgroup symmetry, formulated earlier by authors with reference to models based on differential…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
Implicit regularization (IR) has been shown as an useful momentum space tool for perturbative calculations in dimension specific theories, such as chiral gauge, topological and supersymmetric quantum field theoretical models at one loop…