Related papers: Internal Space Renormalization Group Methods for A…
We review some aspects of the renormalization group method for interacting fermions. Special emphasis is placed on the application of scaling theory to quasi-one-dimensional systems at non zero temperature. We begin by introducing the…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
This chapter presents the development of a density functional theory (DFT)-based method for accurate, reliable treatment of various resonances in atoms. Many of these are known to be notorious for their strong correlation, proximity to more…
We report on the current status of recent efforts to develop the Density Matrix Renormalization Group method for use in large-scale nuclear shell-model calculations.
When an electron or a hole is added into an orbital of an adsorbed molecule the substrate electrons will rearrange in order to screen the added charge. This results in a reduction of the electron addition/removal energies as compared to the…
Kohn-Sham (KS) formalism of Density Functional Theory is modified to include the systems with strong non-dynamic electron correlation. Unlike in extended KS and broken symmetry unrestricted KS formalisms, cases of both singlet-triplet and…
We formulate the Hartree-Fock method using a functional integral approach. Then we consider a nonperturbative component of the vacuum polarization. For the Dirac-Coulomb operator the renormalization flow of the vacuum polarization is…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries.…
The methods of the renormalization group and the $\varepsilon$-expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical…
We examine the vacuum polarization contribution in the renormalization scheme of QED. Normally, the quadratic divergence term is discarded under the condition that the counter term of the Lagrangian density should be gauge invariant. Here,…
We construct a new version of the effective average action together with its flow equation. The construction entails in particular the consistency of fluctuation field and background field equations of motion, even for finite…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
We employ the density matrix renormalization group (DMRG) and the wave function factorization method for the numerical solution of large scale nuclear structure problems. The DMRG exhibits an improved convergence for problems with realistic…
In close analogy to the Bloch-Feshbach formalism known from the theory of nuclear dynamics, I develop a mathematical framework that allows one to understand renormalization in terms of purely algebraic operations (projections, dilatations)…
The renormalization group (RG) is used in order to obtain the RG improved effective potential in curved spacetime. This potential is explicitly calculated for the Yukawa model and for scalar electrodynamics, i.e. theories with several…
We study a recently proposed quantum action depending on temperature. We construct a renormalisation group equation describing the flow of action parameters with temperature. At zero temperature the quantum action is obtained analytically…
We extend the density matrix renormalization group to compute exact ground states of continuum many-electron systems in one dimension with long-range interactions. We find the exact ground state of a chain of 100 strongly correlated…
We expand upon on an earlier renormalization group analysis of a non-Fermi liquid fixed point that plausibly govers the two dimensional electron liquid in a magnetic field near filling fraction $\nu=1/2$. We give a more complete description…