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The functional integral formulation of the Schrieffer-Wolff transformation

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Zamani,  Farzaneh
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Kirchner,  Stefan
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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フルテキスト (公開)

1605.02373
(プレプリント), 17KB

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引用

Zamani, F., Ribeiro, P., & Kirchner, S. (2016). The functional integral formulation of the Schrieffer-Wolff transformation. New Journal of Physics, 18:. doi:10.1088/1367-2630/18/6/063024.


引用: https://hdl.handle.net/11858/00-001M-0000-002B-1519-B
要旨
We revisit the Schrieffer-Wolff transformation and present a path integral version of this important canonical transformation. The equivalence between the low-energy sector of the Anderson model in the so-called local moment regime and the spin-isotropic Kondo model is usually established via a canonical transformation performed on the Hamiltonian, followed by a projection. Here we present a path integral formulation of the Schrieffer-Wolff transformation which relates the functional integral form of the partition function of the Anderson model to that of its effective low-energy model. The resulting functional integral assumes the form of a spin path integral and includes a geometric phase factor, i.e. a Berry phase. Our approach stresses the underlying symmetries of the model and allows for a straightforward generalization of the transformation to more involved models. It thus not only sheds new light on a classic problem, it also offers a systematic route of obtaining effective low-energy models and higher order corrections. This is demonstrated by obtaining the effective low-energy model of a quantum dot attached to two ferromagnetic leads.