## Basic Aspects of the Quantum Theory of Solids: Order and Elementary ExcitationsAimed at graduate students and researchers, this book covers the key aspects of the modern quantum theory of solids, including up-to-date ideas such as quantum fluctuations and strong electron correlations. It presents in the main concepts of the modern quantum theory of solids, as well as a general description of the essential theoretical methods required when working with these systems. Diverse topics such as general theory of phase transitions, harmonic and anharmonic lattices, Bose condensation and superfluidity, modern aspects of magnetism including resonating valence bonds, electrons in metals, and strong electron correlations are treated using unifying concepts of order and elementary excitations. The main theoretical tools used to treat these problems are introduced and explained in a simple way, and their applications are demonstrated through concrete examples. |

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### Contents

1 | |

2 General theory of phase transitions | 6 |

3 Bose and Fermi statistics | 31 |

4 Phonons in crystals | 34 |

5 General Bose systems | 54 |

6 Magnetism | 70 |

7 Electrons in metals | 127 |

8 Interacting electrons Green functions and Feynman diagrams methods of field theory in manyparticle physics | 133 |

9 Electrons with Coulomb interaction | 159 |

10 Fermiliquid theory and its generalizations | 175 |

11 Instabilities and phase transitions | 188 |

12 Strongly correlated electrons | 229 |

13 Magnetic impurities in metals Kondo effect heavy fermions and mixed valence | 272 |

296 | |

298 | |

### Other editions - View all

Basic Aspects of the Quantum Theory of Solids: Order and Elementary Excitations Daniel I. Khomskii No preview available - 2010 |

### Common terms and phrases

actually antiferromagnetic approximation atoms average band behaviour Bose condensation Chapter coefﬁcient conduction electrons conﬁguration correlations corresponding Coulomb interaction deﬁnition density described diagrams discussed distortion effective electron–hole electron–phonon elementary excitations energy gap entropy equation exchange interaction excitonic exist Fermi liquid Fermi surface ferromagnetic ﬁlled ﬁnd ﬁnite ﬁrst ﬁrst-order ﬂuctuations free energy Green function Hamiltonian hole hopping Hubbard model impurity instability insulators Kondo Kondo effect Landau lattice long-range order magnetic ﬁeld magnetic ordering magnons mean ﬁeld momentum Mott insulator Mott transition NŽeel obtain one-dimensional operators orbital order parameter particles Peierls phase transition phonon physics potential problem quantum quasiparticles result second-order phase transition Section shown in Fig similar singlet situation solitons solution speciﬁc heat spectrum structure sublattice superconductivity superﬂuid symmetry temperature term theory thermodynamic transition metal treatment usually wavefunction wavevector Wigner crystal xy model zero