Diagrammatic theory for Anderson impurity model

Abstract

A diagrammatic theory around atomic limit is proposed for the normal and superconducting states of the Anderson impurity model. The impurity electrons have strong Coulomb repulsion between them. This interaction is the main parameter of the theory. The new method is based on the ordinary Wick theorem for conduction electrons and generalized Wick theorem for strongly correlated impurity electrons. For the mean value of evolution operator the linked cluster theorem is proved and the Dyson-type equations for one-particle propagators of conduction and impurity electrons in the normal and superconducting states of the system have been established. The behavior of the impurity electron spectral function has been studied. The structure of the resonances and their properties are analyzed. We have proved that the thermodynamic potential of this strongly correlated system can be presented, after introduction of special integration by the constant of hybridization strength, as the functional of the full Green function of conduction electrons and its mass operator. The stationary property of this potential related to the changes of the mass operator has been demonstrated as well.

Предложена диаграммная теория в окрестности атомного предела в нормальном и сверхпроводящем состояниях для примесной модели Андерсона. Примесные электроны испытывают сильное кулоновское отталкивание между собой. Новый метод основан на обычной теореме Вика для электронов проводимости и на обобщенной теореме Вика для сильнокоррелированных примесных электронов.