強相関電子論の基礎(集中講義:北海道大学理学部・大学院理学院): 2017年 冬学期

12月20日
1. Introduction
 1.1. Aim of materials science
 1.2. Electrons in solids
 1.3. Strongly correlated electron systems
 1.4. Examples
2. Mott transition
 2.1. Hubbard model
 2.2. Metal-insulator transition driven by electron correlation
 2.3. Brinkman-Rice theory
12月21日
 2.4. Brinkman-Rice theory
 2.5. Mean-field phase diagram
 2.6. Dynamical mean-field theory
3. Magnetism in Mott insulators
 3.1. Magnetism of independent magnetic moments
 3.2. Exchange interactions
  3.2.1. Kinetic exchange
  3.2.2. Direct exchange
  3.2.3. Super-exchange
  3.2.4. Other exchange interactions
12月22日
 3.3. Localized spin models
 3.4. Magnetic order
  3.4.1. Ground state in classical spin systems
  3.4.2. Phase transition and critical phenomena by mean-field approximation
  3.4.3. Landau theory
12月25日
4. Orbital degree of freedom
 4.1. Orbital degeneracy and crystal field splitting
 4.2. Jahn-Teller effect
 4.3. Spin-orbit coupling
 4.4. Multi-orbital Hubbard model
 4.5. Mott transition in multi-orbital systems
 4.6. Spin and orbital order in multi-orbital systems
  4.6.1. Mean-field phase diagram
  4.6.2. Strong-coupling limit: Kugel-Khomskii model
  4.6.3. Orbital order in multi-orbital Mott insulators
  4.6.4. Spin-orbit coupled Mott insulator
12月26日
5. Frustration
 5.1. What is frustration?
 5.2. General aspects of frustrated systems
  5.2.1. Suppression of long-range ordering
  5.2.2. Extensive degeneracy
  5.2.3. Order by disorder
 5.3. Spin ice
  5.3.1. Water ice
  5.3.2. Spin ice: materials and model
  5.3.3. Spin ice state
 5.4. Spin liquid
  5.4.1. Classical examples
  5.4.2. Quantum spin liquids
成績評価について
  • 出席とレポート。