Perturbative Tamm-Dancoff Renormalization

TL;DR

This paper introduces a novel two-step renormalization method combining perturbation theory and similarity transformation to derive an effective Hamiltonian for many-body systems, demonstrated on a simple example.

Contribution

It presents a new two-step renormalization procedure that simplifies many-body Hamiltonians by eliminating particle-number-changing interactions.

Findings

Effective Hamiltonian contains only particle-number-conserving interactions

Method successfully applied to a simple illustrative example

Provides a framework for numerical diagonalization of complex systems

Abstract

A new two-step renormalization procedure is proposed. In the first step, the effects of high-energy states are considered in the conventional (Feynman) perturbation theory. In the second step, the coupling to many-body states is eliminated by a similarity transformation. The resultant effective Hamiltonian contains only interactions which do not change particle number. It is subject to numerical diagonalization. We apply the general procedure to a simple example for the purpose of illustration.