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Quantum Phase Transitions, SUPA Doctoral Training Center, @StAndrews
- Course Outline and Lecture Notes
Chapter1:
Introduction |
- What are Quantum-Phase Transitions?
- Basic Concepts of Phase Transitions and Critical Behavior
- Critical Exponents, Scaling and Hyperscaling
- How Important is Quantum Mechanics?
- Sketch of the Quantum-to-Classical Mapping
- What's Different about Quantum-Phase Transitions?
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Chapter2:
Ising Chain in a Transversal Field |
- Quantum Ising Model
- Strong Coupling
- Weak Coupling
- Exact Spectrum from Jordan-Wigner Transformation
- Equal Time Correlations of Order Parameter
- Finite Temperature Crossovers
- Quantum-to-Classical Mapping
- Quantum Field Theory
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Chapter3:
Bose-Hubbard Model
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- Hamiltonian and Mott-Insulator/Superfluid Transition
- Coherent States for Bosons
- Coherent-State Path Integral Representation of the Partition
Function
- Hubbard-Stratonovich Transformation
- Mean-Field Phase Diagram
- Dynamical Critical Exponent and
Upper Critiacal Dimension
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Chapter4(a),
Chapter4(b):
Frustrated Quantum Antiferromagnets |
- Hamiltonian, Classical Groundstates and Linear
Spin-Wave Theory
- Classical Non-Linear Sigma Model
- Renormalization-Group (RG) Analysis
- Spin-Coherent States
- Coherent-State Path Integral for a Single Quantum Spin
- Quantum Non-Linear Sigma Model and Berry Phases
- RG of Quantum Non-Linear Sigma Model
- Phase Diagrams for d=2 and d=3
- Finite Temperature Crossovers
- Crucial Role of Berry Phases
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- Assessment is based on three homework problem sets (set1, set2, set3).
- Books recommended background reading
- Quantum Phase Transitions, Subir Sachdev, Cambridge Univ. Press
Very nice book. In particular the first chapters give a very nice introduction.
- A Modern Approach to Critical Phenomena, Igor Herbut, Cambridge Univ. Press
Short and to the point.
- Scaling and Renormalization in Statistical Physics, John Cardy, Cambridge Univ. Press
Excellent introduction to the renormalization group
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