The functional integral formulation of the Schrieffer–Wolff transformation. (22nd June 2016)

• Record Type: Journal Article
• Authors: Zamani, Farzaneh; Ribeiro, Pedro; Kirchner, Stefan
• Is Part Of: New journal of physics. Volume 18:Number 6(2016:Jun.)
• Publication Date: 2016-06-22
• Subjects: Schrieffer–Wolff transformation -- spin dynamics -- magnetic transistor -- Kondo physics -- Berry phase -- path integral; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/18/6/063024
• Languages: English
• ISSNs: 1367-2630

Abstract

Abstract: 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.