Renormalization of Hamiltonians

TL;DR

This paper develops a perturbative similarity renormalization group method to solve Hamiltonians in asymptotically free theories, achieving accurate bound state energies and proposing a framework for applying similar techniques to QCD.

Contribution

It introduces a perturbative similarity renormalization approach for Hamiltonians and demonstrates its effectiveness in calculating bound states with high accuracy.

Findings

Achieved ~10% accuracy in bound state energy calculations.

Developed a small effective Hamiltonian via perturbative expansion.

Outlined a method for applying similar techniques to QCD Hamiltonians.

Abstract

A matrix model of an asymptotically free theory with a bound state is solved using a perturbative similarity renormalization group for hamiltonians. An effective hamiltonian with a small width, calculated including the first three terms in the perturbative expansion, is projected on a small set of effective basis states. The resulting small hamiltonian matrix is diagonalized and the exact bound state energy is obtained with accuracy of order 10%. Then, a brief description and an elementary illustration are given for a related light-front Fock space operator method which aims at carrying out analogous steps for hamiltonians of QCD and other theories.