


Quantum Phase Transitions, SUPA Doctoral Training Center, @StAndrews
 Course Outline and Lecture Notes
Chapter1:
Introduction 
 What are QuantumPhase Transitions?
 Basic Concepts of Phase Transitions and Critical Behavior
 Critical Exponents, Scaling and Hyperscaling
 How Important is Quantum Mechanics?
 Sketch of the QuantumtoClassical Mapping
 What's Different about QuantumPhase Transitions?

Chapter2:
Ising Chain in a Transversal Field 
 Quantum Ising Model
 Strong Coupling
 Weak Coupling
 Exact Spectrum from JordanWigner Transformation
 Equal Time Correlations of Order Parameter
 Finite Temperature Crossovers
 QuantumtoClassical Mapping
 Quantum Field Theory

Chapter3:
BoseHubbard Model

 Hamiltonian and MottInsulator/Superfluid Transition
 Coherent States for Bosons
 CoherentState Path Integral Representation of the Partition
Function
 HubbardStratonovich Transformation
 MeanField Phase Diagram
 Dynamical Critical Exponent and
Upper Critiacal Dimension

Chapter4(a),
Chapter4(b):
Frustrated Quantum Antiferromagnets 
 Hamiltonian, Classical Groundstates and Linear
SpinWave Theory
 Classical NonLinear Sigma Model
 RenormalizationGroup (RG) Analysis
 SpinCoherent States
 CoherentState Path Integral for a Single Quantum Spin
 Quantum NonLinear Sigma Model and Berry Phases
 RG of Quantum NonLinear Sigma Model
 Phase Diagrams for d=2 and d=3
 Finite Temperature Crossovers
 Crucial Role of Berry Phases

 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



