Optimization Algorithms Based on Renormalization Group

Optimization Algorithms Based on Renormalization Group Application to 2D Edwards-Anderson Spin Glass

Global changes of states are of crucial importance in optimization algorithms. We review some heuristic algorithms in which global updates are realized by a sort of real-space renormalization group transformation. Emphasis is on the relationship between the structure of low-energy excitations and “block-spins” appearing in the algorithms. We also discuss the implication of existence of a finite...

Density-matrix renormalization group algorithms

The Density Matrix Renormalization Group (DMRG) was developed by White [1, 2] in 1992 to overcome the problems arising in the application of real-space renormalization groups to quantum lattice many-body systems in solid-state physics. Since then the approach has been extended to a great variety of problems in all fields of physics and even in quantum chemistry. The numerous applications of DMR...

Optimization of Renormalization Group Transformations

This thesis examines the optimization of renormaiization group transformations. To do this I have examined simple spin models where some understanding of the problems which arise and particularly the systematic errors can be acquired. In the first chapter I have given a brief description of critical phenomena which provides the motivation for the study of the renormalization group in this rest ...

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) ...