Quantum Field Theory of ManyBody Systems
Introduction to Quantum Phase Transitions
Lecture (MVSpec)
Thomas Gasenzer
Tuesday, 11:1513:00 (starting on 14/04);
Thursday, 11:1513:00 (during odd weeks, starting on 23/04);
INF 227 (KIP), SR 1.404.
[
LSF]
Note:
Exam: Tue, 28/07, 11:0013:00 hrs, INF 227, SR 1.404
Exercises
Tutor:
Asier Piñeiro Orioli
Register and view group list here.
Classes take place in general during even weeks on Thursdays, 11:1512:45 hrs, starting on 30/04: INF 227 (KIP), SR 1.404.
Written exam on Tue., 28/07/15, 11:0013:00 hrs, INF 227 (KIP), SR 1.404.
Content 
Prerequisites 
Script 
Literature 
Supplementary materials 
Exercises 
Exam
The lecture course provides an introduction to field theoretic methods for systems with many degrees of freedom.
A focus will be set on quantum phase transitions, with special emphasis on applications to ultracold, mostly bosonic, atomic gases as they are the subject of many forefront presentday experiments.
The course will introduce to the basis of the theory of classical and quantum phase transitions, with a special emphasis on simple model applications.
Methodologically, the lecture will build on the basics of the operator as well as the pathintegral approach to quantum field theory.
Knowledge of the basics of quantum mechanics, statistical mechanics, and quantum field theory is presumed.
Content:

Introduction
 Classical phase transitions
 phase diagram of water
 Ehrenfest classification
 continuous phase transitions
 quantum phase transitions

Phase transition in the classical Ising model
 Ising Hamiltonian
 Spontaneous symmetry breaking
 Thermodynamic properties
 Phase transitions in the Ising model
 Landau meanfield theory
 Meanfield critical exponents
 Correlation functions
 Hubbard Stratonovich transformation
 Functionalintegral representation
 GinzburgLandauWilson functional
 Saddlepoint approximation and Gaussian effective action
 Ginzburg criterion

Renormalisationgroup theory in position space
 Blockspin transformation
 Transfermatrix solution of the 1D Ising chain
 RG stepping for the 1D and 2D Ising models
 Critical point
 RG fixed points
 Relevant and irrelevant couplings
 Universality and universality class
 Renormalisationgroup flows
 Scaling properties of the free energy and of the twopoint correlation function
 Scaling relations between critical exponents
 The scaling hypothesis

Wilson's Renormalisation Group
 Perturbation theory
 LinkedCluster and Wick's theorems
 Dyson equation
 Oneloop critical properties
 Dimensional analysis
 Momentumscale RG
 Gaussian fixed point
 WilsonFisher fixed point
 Epsilonexpansion
 Critical exponents
 Wave function renormalisation and anomalous dimension
 Suppl. Mat.: Asymptotic expansions

Quantum phase transitions
 Quantum Ising model
 Mapping of the classical Ising chain to a quantum spin model
 Universal scaling behaviour
 Thermal as timeordered correlators
 Quantum to classical mapping
 Perturbative spectrum of the transversefield Ising model
 Jordan Wigner transformation and exact spectrum
 Universal crossover functions near the quantum critical point
 Anomalous scaling dimension
 Lowtemperature and quantum critical regimes
 Conformal mapping
 Spectral properties close to criticality
 Structure factor, susceptibility, and linear response
 Relaxational response in the quantum critical regime
Prerequisites:
Skriptum :

The notes are available for download above, separately for each chapter.

The Script of the lecture on QFT of ManyBody Systems in WT 14/15 (with a different focus) can be found
here.
Literature:
Textbooks on critical phenomena and (quantum) phase transitions

D. Belitz und T.R. Kirkpatrick, in J. Karkheck (Hrsg.),
Dynamics: Models and kinetic methods for nonequilibrium manybody systems.
Kluwer, Dordrecht (2000).
[ Google books
 HEIDI
]

John Cardy,
Scaling and renormalization in statistical physics.
CUP, Cambridge, 2003.
[ Google books
 HEIDI
]

Peter Kopietz, Lorenz Bartosch, Florian Schütz,
Introduction to the Functional Renormalization Group.
Springer, Berlin Heidelberg, 2010.
[ Google books
 HEIDI (online)
 Errata and Addenda
]

Lincoln D. Carr (Ed.),
Understanding quantum phase transitions.
CRCPress, Boca Raton, 2011.
[ Google books
 HEIDI
]

Nigel Goldenfeld,
Lectures on phase transitions and the renormalization group.
AddisonWesley, Reading, 1992.
[ Google books
 HEIDI
]

Igor Herbut,
A modern approach to critical phenomena.
CUP, Cambridge, 2007.
[ Google books
 HEIDI
]

Subir Sachdev,
Quantum Phase Transitions.
CUP, Cambridge, 2011.
[ Google books
 HEIDI (incl. online)
]

S. L. Sondhi, S. M. Girvin, J. P. Carini, and D. Shahar,
Continuous quantum phase transitions.
Rev. Mod. Phys. 69, 315 (1997).
[ arXiv:condmat/9609279
]

Jean ZinnJustin,
Quantum field theory and critical phenomena.
Clarendon, Oxford, 2004.
[ Google books
 HEIDI
]
Reviews on critical phenomena and (quantum) phase transitions
General texts on statistical mechanics

Kerson Huang,
Statistical Mechanics.
Wiley, 1987.
[ Google books
 HEIDI
]

Linda E. Reichl,
A Modern Course in Statistical Physics.
Wiley Interscience, 2nd edition 1998.
[ Google books (3rd ed.)
 HEIDI
]

Frederick Reif,
Fundamentals of Statistical and Thermal Physics
McGrawHill, New York, 1987.
[ Google books
 HEIDI
]

Franz Schwabl,
Statistische Mechanik.
Springer, Heidelberg, 2000.
[ Google books
 HEIDI
]

M. Toda, R. Kubo, N. Saito,
Statistical Physics, Equilibrium Statistical Mechanics,
Springer, 2nd edition 1992.
[ Google books
 HEIDI
]
General texts on quantum field theory

Brian Hatfield,
Quantum Field Theory of Point Particles and Strings.
Addison Wesley, Oxford, 2010.
[ Google books
 HEIDI
]

Michael E. Peskin, Daniel V. Schroeder
An introduction to quantum field theory.
Westview, Boulder, 2006.
[ Google books
 HEIDI
]

XiaoGang Wen,
Quantum Field Theory of ManyBody Systems.
OUP, Oxford, 2010.
[ Google books
 HEIDI
]
Additional material
Exercises:
Exercises will be held in general (exceptions posted above) on Thursdays during even weeks, 11:1512:45 hrs, in SR 1.404, INF 227 (KIP), starting on 30/04/15. Tutor: Asier Piñeiro Orioli
(Please
register here.)
Exam:
Passing the written exam, which will prospectively take place on
Tue, 28/07/15, 11:0013:00 hrs, INF 227 (KIP), SR 1.404,
will be the condition to obtain
6 CPs for the lecture.
Rules for the exam: You are allowed to use one A4 twosided and handwritten sheet. No electronic devices of any kind are permitted. The exam lasts 120 mins. Please bring enough paper to be able to start every problem on a new sheet of paper.