Quantum Phase Transitions
Lecture (MVSpec)
Wednesday, 11:1513:00; Friday, 09:1511:00; (starting on 22/04) INF 227 (KIP), SR 2.404. [LSF]
Exercises
Register and view group list and further information, and download material here. (More places available!)
Classes take place on Fridays, 14:1515:45 hrs, starting on 08/05: INF 227 (KIP), SR 3.403.
The lecture course provides an introduction to the theory of classical and quantum phase transitions, to positionspace as well as Wilson renormalisationgroup theory. Emphasis will be set on broadly used spin models as well as bosonic field theories relevant in particular for applications in the field of ultracold atomic gases. Methodologically, the lecture will build on the basics of the operator as well as the pathintegral approach to quantum field theory. Basic knowledge of quantum mechanics, statistical mechanics, and quantum field theory is presumed.

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
 Quantum Mechanics (PTP 3), Statistical Mechanics (PTP 4); Quantum Field Theory I or Quantum Field Theory of ManyBody Systems
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
 Luigi Amico, Rosario Fazio, Andreas Osterloh, and Vlatko Vedral, Entanglement in manybody systems. Rev. Mod. Phys. 80, 517 (2008). [arXiv:quantph/0703044v3]
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 (pdf online) ]
 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 ]
 The Weirdness of Water, by Rachel Brazil, Chem. World, 6 Apr 2020  on Russo et al., Waterlike anomalies as a function of tetrahedrality, PNAS 115, E3333 (2018).
 Experiments realising critical opalescence and supercritical fluidity in Water and Carbon Dioxide (further, commercial video with explanations).
 Applet simulating the 2D Ising model (You may have to adapt your Java settings to not block this page as well as isingApplet.html and isingText.html in the same path).
 2D Ising model MCsimulator by D. on Wolfram.
 Visualization of the realspace renormalisation group for a 2D Ising system by D. Ashton (Straight to video on youtube).
 Visualization of the scale invariance of critical fluctuations of a 2D Ising system
Exercises:
Exercises will be held in general (exceptions posted above) on Fridays, 14:1515:45 hrs, in SR 3.403, INF 227 (KIP), starting on 28/04/17. (Please register here.)
The problem sets will available for download here.
Credit Points:
Problem sets must be handed in and will be marked. Achieving a minimum of 50% will be the condition to obtain 8 CPs for the lecture.