Flow Equations and Normal Ordering. A Survey

TL;DR

This survey reviews the flow equation method for Hamiltonian diagonalization, its application to the Hubbard model, and how symmetry breaking can be incorporated through normal ordering adjustments.

Contribution

It provides a comprehensive overview of flow equations, highlighting their use in analyzing complex quantum models and introducing symmetry breaking via normal ordering.

Findings

Flow equations effectively diagonalize Hamiltonians.

Application to the 2D Hubbard model demonstrates practical utility.

Normal ordering symmetry breaking offers a novel approach.

Abstract

First we give an introduction to the method of diagonalizing or block-diagonalizing continuously a Hamiltonian and explain how this procedure can be used to analyze the two-dimensional Hubbard model. Then we give a short survey on applications of this flow equation on other models. Finally we outline, how symmetry breaking can be introduced by means of a symmetry breaking of the normal ordering, not of the Hamiltonian.