# Schrieffer-Wolff transformation of Anderson Models

## TL;DR

This paper provides a pedagogical review of the Schrieffer-Wolff transformation, a key method for deriving low-energy effective Hamiltonians in quantum many-body physics, focusing on the Anderson Impurity Model and its lattice generalization.

## Contribution

It offers a clear, educational overview of the Schrieffer-Wolff transformation applied to Anderson models, enhancing understanding of this important technique.

## Key findings

- Clarifies the derivation of effective Hamiltonians
- Explains the transformation for SIAM and PAM models
- Provides insights into low-energy physics of quantum impurity systems

## Abstract

Schrieffer-Wolff transformation is one of the very important transformations in the study of quantum many body physics. It is used to arrive at the low energy effective hamiltonian of Quantum many-body hamiltonians, which are not generally analytically tractable. In this paper we give a pedagogical review of this transformation for Anderson Impurity model(SIAM) and its lattice generlaization called, the Periodic Anderson Model(PAM).