Optimization of renormalization group flow

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 flow of hexatic membranes.

We investigate hexatic membranes embedded in Euclidean D-dimensional space using a reparametrization invariant formulation combined with exact renormalization group equations. An XY model coupled to a fluid membrane, when integrated out, induces long-range interactions between curvatures described by a Polyakov term in the effective action. We evaluate the contributions of this term to the runn...

Renormalization group flow of reduced string actions

It has been argued that certain reduced actions play a role in AdS/CFT when comparing fast moving strings to long single trace operators in gauge theories. Such actions arise in two ways: as a limit of the string action and as a description of long single trace field theory operators. They are non-relativistic sigma models with the target space usually being a Kähler manifold. They are non-reno...

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) ...