Schrieffer–Wolff transformation

The Schrieffer–Wolff transformation is a unitary transformation which projects out the high energy excitations and hence enabls one to obtain effective low energy physics from a given quantum many-body Hamiltonian like Hubbard model or Anderson impurity model.^[1] This transformation was first used to obtain Kondo model from single impurity Anderson model by J.R. Schrieffer and P.A. Wolff.^[2]. Using Schrieffer-Wolff transformation,the high energy charge excitations present in Anderson impurity model are projected out and the low energy effective Hamiltonian is obtained which has only virtual charge fluctuations. One important feature of Schrieffer-Wolff transformations is that it provides a controlled perturbative way to study the strong coupling regime of quantum-many body Hamiltonians. For the Anderson impurity model case, Schrieffer-Wolff transformation showed that Kondo model lies in the strong coupling regime of Anderson impurity model,which gave important insight to understand both these models better.

References

Further reading

• Phillips, Philip (2012). Advanced Solid State Physics (Second ed.). New York: Cambridge University Press. pp. 109–114. ISBN 978-1-107-49346-9.