Many Particle Strongly Interacting Systems.pdf


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Contents
1 Introduction

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Varieties of Green Functions
2.1 Temperature Green Functions . . . . . . . . . . . . . . . . .
2.2 Double-time Green Functions . . . . . . . . . . . . . . . . . .
2.3 Spectral Representations . . . . . . . . . . . . . . . . . . . . .

3 Irreducible Green Functions Method
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3.1 Outline of IGF Method . . . . . . . . . . . . . . . . . . . . . 11
4 Many-Particle Interacting Systems on a Lattice
4.1 Spin Systems on a Lattice . . . . . . . . . . . . .
4.1.1 Heisenberg Ferromagnet . . . . . . . . .
4.1.2 Heisenberg Antiferromagnet . . . . . . . .
4.2 Correlated Electrons on a Lattice . . . . . . . . .
4.2.1 Hubbard Model . . . . . . . . . . . . . .
4.2.2 Single Impurity Anderson Model (SIAM)
4.2.3 Periodic Anderson Model (PAM) . . . . .
4.2.4 Two-Impurity Anderson Model ( TIAM )
5 Effective and Generalized Mean Fields
5.1 Molecular Field Approximation . . . .
5.2 Effective Field Theories . . . . . . . .
5.3 Generalized Mean Fields . . . . . . . .
5.4 Symmetry Broken Solutions . . . . . .

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6 Quasi-Particle Many Body Dynamics
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6.1 Green Function Picture of Quasi-Particles . . . . . . . . . . . 36
6.2 Spin-Wave Scattering Effects in Heisenberg Ferromagnet . . . 39
7 Heisenberg Antiferromagnet at Finite Temperatures
7.1 Hamiltonian of the Model . . . . . . . . . . . . . . . . . . . .
7.2 Quasi-Particle Dynamics of Heisenberg Antiferromagnet . . .
7.3 Generalized Mean-Field GF . . . . . . . . . . . . . . . . . . .
7.4 Damping of Quasi-Particle Excitations . . . . . . . . . . . . .

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8 Quasi-Particle Dynamics of Lattice Fermion Models
8.1 Hubbard Model. Weak Correlation . . . . . . . . . . .
8.2 Hubbard Model. Strong Correlation . . . . . . . . . .
8.3 Correlations in Random Hubbard Model . . . . . . . .
8.4 Electron-Lattice Interaction and MTBA . . . . . . . .
8.5 Equations of Superconductivity . . . . . . . . . . . . .

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