Quantum renormalization group

Renormalization Group in Quantum Mechanics

The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation. The harmonic oscillator and the propagation on curved spaces are presented as examples. The hamiltonian and the lagrangian scaling relations are obtained. These evolution equations are used to construct low energy effective models.

Renormalization Group in Quantum Mechanics

We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of the well known pathologies which appear in quantum field theory due to the sharp cutoff. We show that for an arbitrary background path the usual local form o...

Renormalization Group and Quantum Information

The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems defined on a chain, an optimal formulation is given by White’s “density matrix renormalization group”. This formulation can be shown to rely on concepts of the de...

Renormalization Group Renormalization Group

Basis Optimization Renormalization Group for Quantum Hamiltonian

A method of Hamiltonian diagonalization is suitable for calculating physical quantities associated with wavefunctions, such as structure functions and form factors. However, we cannot diagonalize Hamiltonian directly in quantum field theories because dimension of Hilbert space is generally infinite. To create effective Hamiltonian, we extend a technique of NRG (numerical renormalization group) ...