An Explicit Method for Schrieffer-Wolff Transformation

TL;DR

This paper introduces an explicit, non-perturbative method to compute the generator of the Schrieffer-Wolff transformation directly from the Hamiltonian, applied to key models in condensed matter physics.

Contribution

The paper presents a novel explicit method for calculating the Schrieffer-Wolff transformation generator directly from the Hamiltonian, avoiding perturbative approximations.

Findings

Generator computed for SIAM and PAM models

Method yields full generator, not just perturbative expansion

Applicable to general Hamiltonians in condensed matter

Abstract

Schrieffer-Wolff transformation is a very important transformation in Quantum Many Body physics. Yet, there isn't an explicit method in the literature to calculate the generator of this unitary transformation directly from the hamiltonian. In this paper we present an explicit method to compute the generator of the Schrieffer-Wolff transformation in general and then calculate the same for two very important hamiltonians in condensed matter physics, the Single Impurity Anderson model (SIAM) and its lattice generalization , the Periodic Anderson Model (PAM). Our method can be used to carry out the transformation directly from the hamiltonian and the generator of the transformation can be obtained without any recourse to perturbative expansion or intuitive guesswork. In fact here, the full generator is calculated rather than its expansion to first two orders which is usually the case.