Instanton approximation to the graded nonlinear sigma model for the integer quantum hall effect |
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| Affiliation: | 1. Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, Carretera Emiliano Zapata, Km. 8, Rancho San Francisco, 29050, Tuxtla Gutiérrez, Chiapas, Mexico;2. Instituto de Fisica, Universidad Nacional Autónoma de México, Apartado Postal 20-364,01000, Ciudad de México, Mexico;1. Max-Planck-Institut für Physik, Föhringer Ring 6, D-80805 Munich, Germany;2. Steklov Mathematical Institute of Russ. Acad. Sci., Gubkina str. 8, 119991 Moscow, Russia;1. Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel;2. Department of Physics, Oakland University, Rochester, MI 48309-4451, USA;1. Department of Materials Science and Engineering, Nanchang University, 999 Xuefu Avenue, Nanchang 330031, China;2. Institute of Photovoltaics, Nanchang University, 999 Xuefu Avenue, Nanchang 330031, China |
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| Abstract: | We construct the multi-instanton solutions for the graded nonlinear σ model with symmetry U(1,1/2)/U(1/1) ⊗ U(1/1), and we calculate the quantum fluctuations around these solutions. The determinant of the fluctuation operator for a fixed multi-instanton solution turns out to be UV finite. However, the integration over instanton parameters contains an integral, ∫d|a| |a|−3, over the size, |a|, of each instanton, which is quadratically singular at |a|=0. It is shown that these quadratic divergences cancel exactly in the calculation of all Green functions. The applicability of the present results to the integer quantum Hall effect is discussed. |
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