Condensed Matter Physics

Copyright © 2002 by Akakii Melikidze:

**A. Melikidze, Net Adv. Phys. Spec. Bibliog. 2:4 (2002). **

Condensed Matter Theory

Dear Reader,

Below you will see a list of educational articles, of which most are available on-line. Though, for obvious reasons, the selection of the topics can't fail to reflect my own research interests, I have tried to adhere to certain principles when compiling this list. These principles are:

- clarity of the style
- originality of presentation
- broadness of topics

I have used or am still using most of the articles in this list. Thus my idea was to share all these useful papers with those visitors of my page who have interests in condensed matter theory.

Akakii.

STRONGLY INTERACTING SYSTEMS: General; --- QUASI ONE-DIMENSIONAL CONDUCTORS: General; --- QUANTUM PHASE TRANSITIONS: General; Josephson Junctions; Metal-Insulator Transitions; --- MESOSCOPIC PHYSICS: General; --- QUANTUM HALL EFFECT: General; Chern-Simons-Landau-Ginzburg Theory; Stripes in Higher Landau Levels; --- SUPERCONDUCTORS: General; Vortices; Stripes; SO(5); --- DISORDER: General; Weak Localization and Beyond; Spin Glasses; --- METHODS IN PHYSICS: Models; Path Integrals and Field-Theoretic Techniques; Bosonization; Duality; Conformal Field Theory; Diagramatic Methods; Numerical Methods; Various; --- RELATED FIELDS: Quantum Optics; Bose-Einstein Condensation; Physics of Macromolecules; Various;

- General:
**H. J. Schulz, G. Cuniberti, P. Pieri, "Fermi Liquids and Luttinger Liquids",****cond-mat/9807366**An excellent set of lectures from Chia Laguna'97 about many topics, among which: Fermi Liquids, Renormalization, Luttinger Liquids, Heisenberg Model and Bethe Ansatz, Hubbard model, Metal-Insulator Transition, Spin-Charge Separation e.t.c.**C. M. Varma, Z. Nussinov, W. van Saarloos, "Singular Fermi Liquids", cond-mat/0103393, Phys. Rep. 361, 267 (2002).**A review of non-Fermi liquids and theories. Discusses heavy fermions and high-Tc's. This is the fullest and most recent account of the subject. See also:**A. J. Schofield, "Non-Fermi liquids", Contemp. Phys. 40, 95 (1999)**(**pdf file**from his**home page**).**A. Auerbach, "Interacting electrons and quantum magnetism" (Springer-Verlag, 1994).**I have seen this book designated as the principal textbook for one of the graduate courses; students in Santa Barbara and Princeton organized study groups to study it. See also:**I. Bose, "Quantum magnets: a brief overview", cond-mat/0107399.****E. Fradkin, "Field theories of condensed matter systems" (Addison-Wesley, 1991).**This book is about everything in condensed matter. A must-have. See also his**home page**for lecture notes.**P. M. Chaikin and T. C. Lubensky, "Principles of condensed matter physics" (Cambridge U. Press, 1995).**This book is about everything in soft condensed matter.**A. M. J. Schakel, "Boulevard of Broken Symmetries", cond-mat/9805152**A great set of lectures! Highly recommended.**Chetan Nayak, Piers Coleman, Matthew Dodgson, David Khmelnitskii**have lecture notes and problem sets for condensed matter courses on their web pages. Also, check out a great set of lectures from**Birmingham**.

**Quasi One-Dimensional Conductors:**

- General:
- Various:
**S. Biermann, A. Georges, T. Giamarchi, A. Lichtenstein, "Quasi-one-dimensional organic conductors: dimensional crossover and some puzzles", cond-mat/0201542**- recent Windsor'01 lectures.**J. Singleton, C. Mielke, "Quasi-two-dimensional organic superconductors: a review", cond-mat/0202442.****C. Bourbonnais, "Electronic phases of low-dimensional conductors", cond-mat/0204345**- Cargese'01 lectures.

- General:
**S. L. Sondhi et. al., "Continuous Quantum Phase Transitions",****Rev. Mod. Phys. 69, 315 (1997); cond-mat/9609279.**A very popular review article. One of my own favorites. An exposition of the theory of one special type of magnetic quantum phase transition, known as Hertz-Millis theory, can be found in these lectures:**M. Lavagna, "Quantum Phase Transitions", cond-mat/0102119.****Subir Sachdev**has published a book called**"Quantum Phase Transitions" (Cambridge U. Press, 2000)**. See also his recent Altenberg'2001 lectures:**"Quantum phase transitions of correlated electrons in two dimensions", cond-mat/0109419.**

- Josephson Junctions:
**J. E. Mooij, G. Schon, "Single charges in 2-dimensional junction arrays", in "Single charge tunneling", eds. H. Grabert and M. H. Devoret (Plenum, 1992).**Simple and comprehensive introduction to the phase diagram of 2D JJ arrays. See also:**R. Fazio, G. Schon, "Quantum Phase Transitions in Josephson Junction Arrays"**(**ps**file from G. Schon's**home page**) - Siena'97 lectures;**R. Fazio, H. van der Zant, "Quantum Phase Transitions and Vortex Dynamics in Superconducting Networks", cond-mat/0011152; Phys. Rep. 355, 235 (2001).**

- Metal-Insulator Transitions:
**M. Imada, A. Fujimori, and Y. Tokura, "Metal-insulator transitions",****Rev. Mod. Phys. 70, 1039 (1998).**This is an extensive review article which discusses many approaches to the problem from a practical point of view.- For a more theoretical analysis of the problem see:
**D. Belitz, T. R. Kirkpatrick, "The Anderson-Mott transition", Rev. Mod. Phys. 66, 261 (1994).**See also their Leiden'98 lectures:**D. Belitz, T. R. Kirkpatrick, "Quantum phase transitions", cond-mat/9811058.** **A. Georges, G. Kotliar, W. Krauth, M. Rozenberg, "Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions", Rev. Mod. Phys. 68, 13 (1996).**A review of a powerful general approach to strongly interacting systems. Mott MIT has been one of the major applications of the approach.**E. Abrahams, S. V. Kravchenko, and M. P. Sarachik, "Metallic behavior and related phenomena in two dimensions", cond-mat/0006055, Rev. Mod. Phys. 73, 251 (2001).**This is a review of recently discoverd 2D MIT. Theoretical understanding of these phenomena is currently missing.

- General:
- Before reading this section you should consider reading a long-awaited
overview of the entire field:
**L. I. Glazman, "Resource Letter: MesP-1: Mesoscopic physics",****Am. J. Phys. 70, 376 (2002).** **Y. Imry, "Introduction to mesoscopic physics" (Oxford U. Press, 1997).**One of the most elementary introductions that I have seen. As a next step I would recommend:**T. Dittrich et. al., "Quantum transport and dissipation" (Wiley-VCH, 1998); H. Grabert and M. H. Devoret, eds., "Single charge tunneling" (Plenum 1992).**- Gerd Schon has given numerous lectures on the subject. Some of them can
be found on his
**home page**. - Les Houches'94 Summer session was devoted to mesoscopic physics:
**E. Akermans et. al., eds., "Mesoscopic quantum physics" (Elsevier 1995).** **G. Montambaux, "Spectral Fluctuations in Disordered Metals", cond-mat/9602071.**Les Houches'95 lectures. See also his recent Cargese'01 lectures:**E. Akkermans, G. Montambaux, "Coherent multiple scattering in disordered media", cond-mat/0104013.****C. W. J. Beenakker, "Random-Matrix Theory of Quantum Transport", cond-mat/9612179, Rev. Mod. Phys. 69, 731 (1997)**(see also his**home page**). A comprehensive review of RMT applications in disordered electronic systems. For an introduction to the techniques:**A. D. Mirlin, "Statistics of energy levels and eigenfunctions in disordered and chaotic systems: Supersymmetry approach", cond-mat/0006421; K. Efetov, "Supersymmetry in disorder and chaos" (Cambridge U. Press, 1997).**See also lectures at Les Houches'94 (above).**Ya. M. Blanter and M. Buttiker, "Shot Noise in Mesoscopic Conductors", cond-mat/9910158, Phys. Rep. 336, 1 (2000).**Shot noise is a very powerful technique to investigate correlations in electronic systems. The review is superbly written. There is also a book:**Sh. Kogan, "Electronic noise and fluctuations in solids" (Cambridge U. Press, New York, 1996)**, but I still have to check it out.**Y. Alhassid, "The Statistical Theory of Quantum Dots", cond-mat/0102268, Rev. Mod. Phys. 72, 895 (2000).**This is a recent review article.**S. Datta, "Electronic transport in mesoscopic systems", (Cambridge U. Press 1997).**A superbly written book!**Ben Simons**has a great set of lecture notes and review articles on his web site covering many topics in mesoscopic physics. Strongly recommended!**G. Hackenbroich, "Phase coherent transmission through interacting mesoscopic systems", cond-mat/0006361, Phys. Rep. 343, 463 (2001).**Seems to be a good review article.**I. L. Aleiner, P. W. Brouwer, L. I. Glazman, "Quantum Effects in Coulomb Blockade", cond-mat/0103008, Phys. Rep. 358, 309 (2002).**Quite a lengthy review of some recent work of the "gang of three". For a more elementary account see:**L. I. Glazman, "Single Electron Tunneling", J. Low Temp. Phys. 118, 247 (2000).****W. G. van der Wiel et al., "Electron transport through double quantum dots", cond-mat/0205350.**A review of the experimental situation.**J. von Delft, F. Braun, "Superconductivity in Ultrasmall Grains: Introduction to Richardson's Exact Solution", cond-mat/9911058.**Surprises in mesoscopic physics.

- Before reading this section you should consider reading a long-awaited
overview of the entire field:

- General:
- There are several good books on the QHE:
- R. Prange and S. Girvin, eds., "The quantum Hall effect" (Springer-Verlag, 1990);
- M. Stone, ed., "Quantum Hall effect" (World Scientific, 1992);
- J. Hajdu, ed., "Introduction to the theory of the integer quantum Hall effect" (VCH, 1994).

**A. Karlhede, S. A. Kivelson and S. L. Sondhi, "The quantum Hall effect", in "Correlated electron systems", ed. V. J. Emery (World Scientific 1993).**One of the first good reviews on the QHE. Jerusalem'92 lectures.**A. H. MacDonald, "Introduction to the physics of the Quantum Hall regime",****cond-mat/9410047**This is the best among elementary introductions to the QHE that can be found on the Net.**Steven M. Girvin, "The Quantum Hall Effect: Novel Excitations and Broken Symmetries", cond-mat/9907002**Great lectures! Highly recommended.**R. Shankar, "Theories of the Fractional Quantum Hall Effect", cond-mat/0108271.**Cargese'2001 lectures. See also:**G. Murthy and R. Shankar, "Hamiltonian Theory of the FQHE", cond-mat/0205326.**A review article submitted to the Rev. Mod. Phys.- Much information on the edge states in the QHE can be found on
**X.-G. Wen's home page**. **X.-G. Wen and A. Zee, "Superfluidity and Superconductivity in Double-Layered Quantum Hall state", cond-mat/0110007.**Conceptual introduction to double-layer quantum Hall systems.

- There are several good books on the QHE:
- Chern-Simons-Landau-Ginzburg Theory:
**S. C. Zhang, "The Chern-Simons-Landau-Ginzburg Theory of the Fractional Quantum Hall Effect", Int. J. Mod. Phys. B, Vol. 6, 25 (1992).**This is the article that one is usually referred to about the composite boson theory of Quantum Hall Effect.**G. Dunne, "Aspects of Chern-Simons Theory",****hep-th/9902115.**Les Houches'98 lectures. Surprisingly enough, though written by a field-theorist, these lectures turned out to be quite accessible and informative.**Steven H. Simon, "The Chern-Simons Fermi Liquid Description of Fractional Quantum Hall States", cond-mat/9812186**A review of*nu=1/2*problem.

- Stripes in higher Landau levels:
**Michael M. Fogler, "Stripe and bubble phases in quantum Hall systems",****cond-mat/0111001.**This is a nice review of the recently discovered stripe phases.

**Superconductors:**

- General:
**P. W. Anderson, "THE theory of superconductivity in the high-Tc cuprates" (Princeton U. Press, 1997).**As prof. Anderson says, "90% of the theory is known, left are the details".**M. P. A. Fisher, "Mott Insulators, Spin Liquids and Quantum Disordered Superconductivity",****cond-mat/9806164**Lectures in Les Houches, 1998. They introduce the reader into one of the recent phenomenological theories of High-Tc superconductors. This approach eventually lead to what is now called "Z_{2}gauge theory":**T. Senthil, M. P. A. Fisher, "Z**See also:_{2}Gauge Theory of Electron Fractionalization in Strongly Correlated Systems", cond-mat/9910224.**R. Moessner, S. L. Sondhi, E. Fradkin, "Short-ranged RVB physics, quantum dimer models and Ising gauge theories", cond-mat/0103396; C. Lhuillier, G. Misguich, "Frustrated quantum magnets", cond-mat/0109146,**Cargese'01 lectures.- For a chronological introduction to the spin liquids try:
**X.-G. Wen, "Mean Field theory of Spin Liquid States and Topological Orders"**(**pdf**from his**home page**) - Cargese'90 lectures. **The Boulder'2000 school**was devoted to superconductivity.**F. Marsiglio, J.P. Carbotte, "Electron - Phonon Superconductivity", cond-mat/0106143**. Review of the Migdal-Eliashberg theory - strong coupling extension of the BCS theory. Fluctuation phenomena that become important in this regime are thoroughly covered in this great review:**A.I. Larkin, A.A.Varlamov, "Fluctuation Phenomena in Superconductors", cond-mat/0109177.**

- Vortices:
**G. Blatter et. al., "Vortices in High-Temperature Superconductors",****Rev. Mod. Phys., 66, 1125 (1994).**Almost everything you have ever wanted to know about vortices in High-Tc's.**E. H. Brandt, "The Flux-Line Lattice in Superconductors", supr-con/9506003**Quite a lengthy review article; I haven't gotten to read it yet. For a recent review see:**T. Giamarchi, S. Bhattacharya, "Vortex phases", cond-mat/0111052****D. R. Nelson, "Vortex line fluctuations in superconductors from elementary quanum mechanics"**, in**"Phase transitions and relaxation in systems with competing energy scales", eds. T. Riste and D. Sherington (Kluwer, 1993).**Geilo'93 lectures. Great set, highly recommended!**E. Akkermans and K. Mallick, "Geometrical description of vortices in Ginzburg-Landau billiards", cond-mat/9907441.**A crash course in topology followed by an application to the dual point of Ginzburg-Landau equations. Les Houches'98 lectures.

- Stripes Theory:
- A comprehensive account of the stripes paradigm can be found in:
**E. W. Carlson, V. J. Emery, S. A. Kivelson, and D. Orgad, "Concepts in High Temperature Superconductivity",****cond-mat/0206217.**

- A comprehensive account of the stripes paradigm can be found in:
- SO(5) Theory:
**S.-C. Zhang, "The SO(5) theory of high-Tc superconductors",****cond-mat/9704135**This is a short simply-written version of the article which appeared in "Science". The idea was to combine spin-SU(2) and charge-U(1) symmetries to describe phenomenology of High-Tc's. There is an ongoing debate about it, see e.g. :**G. Baskaran, P. W. Anderson, "On an SO(5) unification attempt for the cuprates", cond-mat/9706076**

- General:
**T. Giamarchi and E. Orignac, "Disordered Quantum Solids",****cond-mat/0005220;**Montreal'00 Lectures. See also:**T. Giamarchi, "Disordered Wigner crystals", cond-mat/0205099;**Windsor'01 lectures.**M. Kardar, "Directed Paths in Random Media", cond-mat/9411022**Les Houches'94 lectures.**D. S. Fisher, "Collective transport: from superconductors to earthquakes", cond-mat/9711179**Les Houches'94 lectures.- Although this it is not a review, this article is considered the
cornerstone of our understanding of localization of interacting electrons in
1D:
**T. Giamarchi, H. J. Schulz, "Anderson localization and interactions in one-dimensional metals", Phys. Rev. B 37, 325 (1988).** **P. Van Mieghem, "Theory of band tails in heavily doped semiconductors", Rev. Mod. Phys. 64, 755 (1992).****M. V. Sadovskii, "Superconductivity and localization", cond-mat/9308018**Seems interesting, but I haven't read it yet.**N. Hatano, "Localization in non-Hermitian quantum mechanics and flux-line pinning in superconductors", cond-mat/9801283**A review article on non-hermitian localization. For detailed calculations see:**J. Feinberg, A. Zee, "Non-Hermitean Localization and De-Localization", cond-mat/9706218**

- Weak localization and beyond:
For an introduction to the subject see tutorial references in the section on mesoscopics (above). There are four major approaches to the problem of treating interacting electrons in the presence of disorder. In their chronological order they are:

*Diagrams*. This approach is described in the section devoted to diagrammatic techniques (see below)*Replica sigma-models*. For a recent set of lectures on this see:**Igor V. Lerner, "Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions",****cond-mat/0205555;**Windsor'01 lectures. For more on replicas see the following section on spin glasses.*Supersymmetric sigma-models*. The standard reference is:**K. Efetov, "Supersymmetry in Disorder and Chaos" (Cambridge U. Press, 1999).**See also Bernard's lectures below.*Keldysh technique*. References can be found in the section on path-integral techniques below.

- Spin Glasses:
**V. S. Dotsenko, "Introduction to the theory of spin glasses and neural networks" (World Scientific, 1995).**In my opinion this is simply the best text on spin glasses.**D. Sherrington, "Spin Glasses",****cond-mat/9806289.**I haven't read this one yet.**G. Parisi, "Slow dynamics of glassy systems", cond-mat/9705312**Varenna lectures, 1996.**M. Mezard, "Random systems and replica field theory", cond-mat/9503056.**Les Houches'94 lectures.

**Methods:**

- Models:
- The solution of the 2D Ising model through the introduction of Majorana
fermions can be looked up in many current textbooks (see e.g. Itzykson and
Drouffe's book in the CFT section below). The original reference is:
**T. D. Schultz, D. C. Mattis, and E. H. Lieb, "Two-Dimensional Ising Model as a Soluble Problem of Many Fermions",****Rev. Mod. Phys. 36, 856 (1964).**More about the modern (RG) view on the Ising model in 1, 2 and 3 dimensions can be found in:**N. Goldenfeld, "Lectures on phase transitions and the renormalization group" (Addison-Wesley, 1992).** - The Kosterlitz-Thouless transition in the 2D XY model is treated in many
textbooks, see e.g. Chaikin and Lubensky's book (above) and Girvin's
lectures at
**Boulder'00**. The critical properties of this model are those of the 1+1D sine-Gordon model (see the same book above), and the latter is "renormalized" in many field theory textbooks (see e.g. Gogolin, Nersesyan, Tsvelik). A very good discussion of the 2D XY model and the physical systems it describes can be found in these Les Houches'94 lectures:**D. R. Nelson, "Defects in superfluids, superconductors and membranes", cond-mat/9502114.** - The Kondo model is one of the central models of condensed matter theory.
Piers Coleman has recently written up a great set of lectures on the
subject:
**P. Coleman, "Local moment physics in heavy electron systems", cond-mat/0206003.**The standard reference is:**A. C. Hewson, "The Kondo Problem to Heavy Fermions" (Cambridge U. Press, 1997).**The "modern" approach is described in**I. Affleck, "Conformal Field Theory Approach to the Kondo Effect", cond-mat/9512099**. - A few general reviews of field-theoretic models of interest to a
condensed matter physicist can be found in the Reviews of Modern Physics:
**J. B. Kogut, "An introduction to lattice gauge theory and spin systems", Rev. Mod. Phys. 51, 659 (1979); H. B. Thacker, "Exact integrability in quantum field theory and statistical systems", Rev. Mod. Phys. 53, 253 (1981); R. Savit, "Duality in field theory and statistical systems", Rev. Mod. Phys. 52, 453 (1980).**A brilliant exposition of this field can be found in:**A. M. Polyakov, "Gauge fields and strings" (Harwood, 1987).** **A. P. Polychronakos, "Generalized Statistics In One Dimension", hep-th/9902157**Les Houches'98 lectures. See also:**R. B. Laughlin et. al., "Quantum Number Fractionalization in Antiferromagnets", cond-mat/9802135.**Chia Laguna'97 lectures.**N. Andrei, "Integrable Models in Condensed Matter Physics", cond-mat/9408101**These lectures describe in detail Bethe Ansatz solutions of many solvable models. Highly mathematical in style.**M. Takahashi, "Thermodynamical Bethe Ansatz and condensed matter", cond-mat/9708087**A comprehensive description of the TBA solution of many low-dimensional models.**H. Tasaki, "The Hubbard model: introduction and some rigorous results", cond-mat/9512169**An excellent review of exact results on Hubbard model. Written for a general physics audience.**N. M. R. Peres, "The many-Electron Problem in Novel Low-Dimensional Materials", cond-mat/9802240**This is a full-length description of the algebraic solution of 1D Hubbard model.

- The solution of the 2D Ising model through the introduction of Majorana
fermions can be looked up in many current textbooks (see e.g. Itzykson and
Drouffe's book in the CFT section below). The original reference is:
- Path Integrals and Field-Theoretic Techniques:
- For single-particle path integrals and applications the best reference
is:
**D. C. Khandekar, S. V. Lawande and K. V. Bhagwat, "Path-integral methods and their applications" (World Scientific, 1993).**The best on-line introduction so far is:**R. MacKenzie, "Path Integral Methods and Applications",****quant-ph/0004090.** - For fermionic path integrals and RG techniques see:
**R. Shankar, "Renormalization Group Approach to Interacting Fermions", Rev. Mod. Phys. 66, 129 (1994); cond-mat/9307009.** - The universal reference for field theoretic techniques and models is:
**J. Zinn-Justin, "Quantum field theory and critical phenomena" (Oxford U. Press, 1996).**See also:**J. Zinn-Justin, "Vector models in the large N limit: a few applications", hep-th/9810198**These lectures constitute an updated and extended version of several chapters in Zinn-Justin's book. - The Shwinger-Keldysh or "double-time" path integral formalism is
described in:
**A. Kamenev, "Keldysh and Doi-Peliti Techniques for out-of-Equilibrium Systems", cond-mat/0109316.**Windsor'01 lectures. For a more elementary introduction to reaction-diffusion problems see:**M. R. Evans, R. A. Blythe, "Nonequilibrium Dynamics in Low Dimensional Systems", cond-mat/0110630,**Altenberg'01 lectures. - A review of the applications of the Keldysh technique to the transport
theory can be found in:
**J. Rammer, "Quantum transport theory of electrons in solids: A single-particle approach", Rev. Mod. Phys. 63, 781 (1991); J. Rammer, H. Smith, "Quantum field-theoretical methods in transport theory of metals", Rev. Mod. Phys. 58, 323 (1986).**Rammer also has a book out:**J. Rammer, "Quantum Transport Theory" (Perseus, 1998),**but I haven't had a chance to have a look at it yet. **R. Rajaraman, "Solitons and Instantons" (North Holland, 1989).**An instant classic!

- For single-particle path integrals and applications the best reference
is:
- Bosonization:
- The "Bible" of bosonization is:
**A. O. Gogolin, A. A. Nersesyan and A. M. Tsvelik, "Bosonization and strongly correlated systems" (Cambridge U. Press, 1998)**. **R. Shankar, "Bosonization: how to make it work for you in Condensed Matter", Acta Phys. Pol. B 26, 1835 (1995).**An introduction to bosonization techniques in condensed matter along with some applications.**K. Schonhammer, V. Meden, "Fermion-Boson Transmutation ...",****cond-mat/9606018**Can you explain what bosonization is to a freshman? These authors answer: "Yes, we can!".**K. Schonhammer, "Interacting fermions in 1D: Tomonaga-Luttinger liquid", cond-mat/9710330**Contains a short description of the standard solution of Tomonaga-Luttinger model by bosonization.**D. Senechal, "An introduction to bosonization", cond-mat/9908262.**Great review, simply the best!**J. von Delft, H. Schoeller, "Bosonization for Beginners --- Refermionization for Experts", cond-mat/9805275.**The most detailed exposition I have seen.**H. Grabert, "Transport in Single Channel Quantum Wires", cond-mat/0107175.**Recent tutorial.**A. Houghton, H.-J. Kwon, J. B. Marston, "Multidimensional Bosonization", cond-mat/9810388.**See also:**P. Kopietz, "Bosonization of interacting fermions in arbitrary dimensions" (Springer-Verlag, Berlin 1997).**

- The "Bible" of bosonization is:
- Duality:
**S. E. Hjelmeland, U. Lindstrvm, "Duality for the Non-Specialist",****hep-th/9705122.**Introduction to the duality in field theory. For extensions into Yang-Mills theories see also:**S. T. Tsou, "Concepts in Gauge Theory Leading to Electric-Magnetic Duality", hep-th/0006178,**and**H. M. Chan, "Yang-Mills Duality and the Generation Puzzle", hep-th/0007016.****P. A. Marchetti, "Bosonization and Duality in Condensed Matter Systems", hep-th/9511100**Explains the essence of bosonization and dualities in condensed matter physics. See also:**I. Yurkevich, "Bosonization as the Hubbard-Stratonovich Transformation", cond-mat/0112270.****M. Kiometzis, H. Kleinert, A. M. J. Schakel, "Dual description of the Superconducting Phase Transition", cond-mat/9508142**Duality in action. This is, in fact, an expanded version of one of the chapters in Schakel's book (see top). See also Les Houches'99 lectures:**A. M. J. Schakel, "Time-Dependent Ginzburg-Landau Theory and Duality", cond-mat/9904092,**and Cracow'00 lectures:**A. M. J. Schakel, "Superconductor-Insulator Quantum Phase Transitions", cond-mat/0011030.**

- Conformal Field Theory:
- It all started with this article:
**A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, "Infinite conformal symmetry in two-dimensional quantum field theory", Nucl. Phys. B 241, 333 (1984), (****KEK Library)**. - Two of the old (and still the most popular) introductory reviews of CFT
are:
**P. Ginsparg, "Applied conformal invariance", ( KEK Library)**, and**J. L. Cardy, "Conformal invariance and statistical mechanics"**(these and other Cardy's lectures can be found on his**web site**). Both are Les Houches'88 lectures, published in**"Fields, strings and critical phenomena", eds. E. Brezin and J. Zinn-Justin**. The ultimate reference on CFT is:**P. Di Francesco, P. Mathieu and D. Senechal, "Conformal field theory" (Springer 1997)**. See also:**C. Itzykson and J.-M. Drouffe, "Statistical field theory", v. 2 (Cambridge U. Press, 1989)**. **J. Cardy, "Conformal Invariance and Percolation", math-ph/0103018.**Cardy's recent set of lectures given in Tokyo'01.- There are books which manage to present complicated issues in an
essentially natural way (those who have read Polyakov's book know what I'm
talking about). One such book that dwells on conformal field theory is:
**A. O. Gogolin, A. A. Nersesyan and A. M. Tsvelik, "Bosonization and strongly correlated systems" (Cambridge U. Press, 1998)**. **C.J. Efthimiou, D.A. Spector, "A Collection of Exercises in Two-Dimensional Physics, Part 1", hep-th/0003190.**The best way to learn is to solve problems!**D. Bernard, "(Perturbed) Conformal Field Theory Applied to 2D Disordered Systems : an Introduction", hep-th/9509137**Discusses disorder in 2D and Wess-Zumino-Novikov-Witten model. More on the WZNW model can be found in the book by Gogolin, Nersesyan and Tsvelik (see above).**I. Affleck, "Conformal Field Theory Approach to the Kondo Effect", cond-mat/9512099**Ian Affleck is one of the guys who have developed the modern conformal methods for condensed matter. This review can serve as an introduction.**H. Saleur, "Lectures on Non-Perturbative Field Theory and Quantum Impurity Problems", cond-mat/9812110**These Les Houches'98 lectures are similar in spirit to Affleck's review (see above).

- It all started with this article:
- Diagramatic Techniques:
- The standard references are:
**A. A. Abrikosov, L. P. Gorkov and I. E. Dzyaloshinski, "Methods of quantum field theory in statistical physics" (Dover 1975); G. D. Mahan, "Many-particle physics" (Plenum 1990).**A recent monograph with an excellent set of current applications is:**A M. Zagoskin, "Quantum theory of many-body systems" (Springer 1998).** **L.S. Levitov, A. V. Shytov, "Zadachi po teoreticheskoj fizike s reshenijami" ("Problems in theoretical physics with solutions", in russian),****unpublished.**I would learn russian just to read this book.**A. MacKinnon, "Transport and Disorder", lecture notes**Explains the diagramatic techniques for disorder. Few applications. The standard references are:**P. A. Lee and T. V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985); B. L. Altshuler and A. G. Aronov in "Electron-electron interactions in disordered systems", A. L. Effros and M. Pollak, eds. (North-Holland 1985).**

- The standard references are:
- Numerical methods:
- In 1998 Cornell University hosted a
**school**devoted to quantum Monte Carlo methods. See also:**W. M. C. Foulkes, L. Mitas, R. J. Needs and G. Rajagopal, "Quantum Monte Carlo simulations of solids", Rev. Mod. Phys. 73, 33 (2001).** **K. Binder, "Applications of Monte Carlo methods to statistical physics", Rep. Prog. Phys. 60, 487 (1997).**Looks like a very good review article. There is also a book:**D. P. Landau and K. Binder, "A Guide to Monte Carlo Simulations in Statistical Physics" (Cambridge U. Press, 2000).****A. K. Hartmann, H. Rieger, "A practical guide to computer simulations", cond-mat/0111531.**A survey of computer tools used by physicists.

- In 1998 Cornell University hosted a
- Various:
- The topic of "non-commutative geometry" has become a hot one among
string theorists in the past couple of years. From the condensed matter
point of view noncommutativity is just the effect of magnetic field.
Anticipating mutual interest of the people in the two areas, I decided to
compile a list of "tour guides" for tourists travelling to
"non-commuteland":
There is also a great review article:- D. Bigatti, hep-th/0006012
- L. Castellani, hep-th/0005210
- J. Ambjorn et. al., hep-th/0004147
- R. Gopakumar et. al., hep-th/0003160
- S. S. Gubser and S. L. Sondhi, hep-th/0006119

**Richard J. Szabo, "Quantum Field Theory on Noncommutative Spaces", hep-th/0109162.**See also:**M. R. Douglas and N. A. Nekrasov, "Noncommutative field theory", hep-th/0106048, Rev. Mod. Phys. 73, 977 (2001).** - In 1996/97 the Institute for Advanced Study in Princeton held a program
called
**"Quantum Field Theory for Mathematicians"**with lectures by E. Witten (Field Theory), K. Gawedzki (Conformal Field Theory) and many others. **Dimitry Vvedensky**has written a very good set of lectures on group theory and its application to quantum mechanics.- Several field theory courses are now available on-line:
**W. Siegel, "Fields", hep-th/9912205; P. van Baal, A course in field theory;**see also**lectures**from the NIKHEF in Netherlands. For courses on non-relativistic quantum mechanics see:**H.C. Rosu, "Elementary Nonrelativistic Quantum Mechanics", physics/0004072; S. Pratt, Quantum Mechanics; N. Cooper, Theoretical Physics 2.**While we are on the subject of prerequisite material take a look also at the**draft**of**H. Gould and J. Tobochnik, "Thermal and Statistical Physics".**

- The topic of "non-commutative geometry" has become a hot one among
string theorists in the past couple of years. From the condensed matter
point of view noncommutativity is just the effect of magnetic field.
Anticipating mutual interest of the people in the two areas, I decided to
compile a list of "tour guides" for tourists travelling to
"non-commuteland":

**Related Fields:**

- Quantum optics:
**P. L. Knight, "Quantum fluctuations in optical systems",****ps**(no figures),**P. Zoller, C. W. Gardiner, "Quantum Noise in Quantum Optics: the Stochastic Schrodinger Equation", quant-ph/9702030.**Les Houches'95 lectures.**M. B. Plenio, P. L. Knight, "The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics", quant-ph/9702007, Rev. Mod. Phys. 70, 101 (1998).**A review of a powerful technique.**B.-S. Skagerstam, "Topics in Modern Quantum Optics", quant-ph/9909086.**Read about one of the most exciting areas of modern quantum physics.**H. M. Wiseman, "Quantum trajectories and feedback", Ph. D. thesis (home page).**See also his course:**Advanced statistical mechanics**.- Take a look at a couple of courses:
**N. Kylstra, "Quantum optics" ; Y. Yamamoto, "Quantum optics and measurements" .** **H. J. Carmichael, "Quantum Fluctuations of Light: A Modern Perspective on Wave/Particle Duality", quant-ph/0104073.**Great introductory article. See also:**L. Mandel, "Quantum effects in one-photon and two-photon interference", Rev. Mod. Phys. 71, s274 (1999)**;**A. Zeilinger, "Experiment and the foundations of quantum physics", Rev. Mod. Phys. 71, s288 (1999).****Luiz Davidovich, "Quantum Optics in Cavities, Phase Space Representations, and the Classical Limit of Quantum Mechanics" (pdf)**- Ushuaia'2000 lectures;**"Sub-Poissonian processes in quantum optics", Rev. Mod. Phys. 68, 127 (1996)**- review article on which the Les Houches'95 lectures (see above) were based.**J. M. Raimond, M. Brune, and S. Haroche, "Manipulating quantum entanglement with atoms and photons in a cavity", Rev. Mod. Phys. 73, 565 (2001).**This is a recent review of cavity QED.

- Bose-Einstein condensation:
**Y. Castin, "Bose-Einstein condensates in atomic gases: simple theoretical results",****cond-mat/0105058**. Les Houches'99 lectures. See also:**Ph. W. Courteille, V. S. Bagnato, V. I. Yukalov, "Bose-Einstein Condensation of Trapped Atomic Gases", cond-mat/0109421.**

- Physics of macromolecules:
**T. Garel, H. Orland, E. Pitard, "Protein Folding and Heteropolymers",****cond-mat/9706125**A great tutorial! Best starting point for everyone who is about to embark on research in protein folding. See also:**J. Banavar et al., "Geometrical aspects of protein folding", cond-mat/0105209**. Varenna'01 lectures;**V. S. Pande, A. Yu. Grosberg, and T. Tanaka, "Heteropolymer freezing and design: Towards physical models of protein folding", Rev. Mod. Phys. 72, 259 (2000).****Sergei Nechaev, "Statistics of knots and entangled random walks", cond-mat/9812205.**Les Houches'98 lectures. A gentle introduction to polymer physics can be found on**Yong Mao's home page**. See also:**T. A. Witten, "Polymer solutions: A geometric introduction", Rev. Mod. Phys. 70, 1531 (1998)**and**Polymers and Liquid Crystals**.- The mathematical aspects of the subject are reviewed in:
**R. D. Kamien, "The Geometry of Soft Materials: A Primer", cond-mat/0203127.**.

- Various:
**William Bialek, "Thinking about the brain",****physics/0205030;**Les Houches'01. Recent lectures on the "theory of learning" - an exciting new extension of Shannon's theory of information.- The concept of information in the quantum context is discussed in:
**M. B. Plenio, V. Vitelli, "The physics of forgetting: Landauer's erasure principle and information theory", quant-ph/0103108; V. Vedral, "The Role of Relative Entropy in Quantum Information Theory", quant-ph/0102094.** **G. E. Volovik, "Exotic Properties of**Everything that any condensed matter physicist has to know about topology and^{3}He" (World Scientific, 1992).^{3}He. An interested reader may want to continue by reading a recent review:**"Superfluid analogies of cosmological phenomena", gr-qc/0005091;**see also Les Houches'99 lectures:**G. E. Volovik, "**Aslo, a draft version of Volovik's forthcoming book is available from his^{3}He and Universe parallelism", cond-mat/9902171.**home page.****G. Falkovich, K. Gawedzki, M. Vergassola, "Particles and fields in fluid turbulence", cond-mat/0105199**. Review article for Rev. Mod. Phys.**R. Dickman et. al., "Paths to Self-Organized Criticality", cond-mat/9910454**Looks like a good tutorial. I haven't checked it out yet. See also:**D. Dhar, "Studying Self-Organized Criticality with Exactly Solved Models", cond-mat/9909009****J. Anandan, J, Christian and K. Wanelik, "Resource Letter GPP-1: Geometric Phases in Physics", quant-ph/9702011**. A large collection of references to work dealing with geometrical phases. Reprints of many of the early works can be also found in:**F. Wilczek and A. Shapere, "Geometric phases in physics" (World Scientific, Singapore 1989)**.**M. Baake, "A Guide to Mathematical Quasicrystals", math-ph/9901014**Haven't checked it out yet.**V. S. Olkhovsky, E. Recami, "Tunneling Times and "Superluminal" Tunneling: A brief Review", cond-mat/9802162**This is not a Sci-Fi book!**C. Kiefer, E. Joos, "Decoherence: Concepts and Examples", quant-ph/9803052.**Great introductory review (it's a part of the review which appeared in the book by Giulini et. al., see below)! See also:**J. P. Paz, W. H. Zurek, "Environment-Induced Decoherence and the Transition From Quantum to Classical", quant-ph/0010011.**Some aspects are covered in the books:**D. Giulini et. al., "Decoherence and the appearance of a classical world in quantum theory" (Springer 1996)**;**P. Blanchard, "Decoherence: Theoretical, Experimental, and Conceptual Problems" ( Springer-Link)**and**U. Weiss, "Quantum dissipative systems" (World Scientific, 1993).****A. Eckert et. al., "Basic concepts in quantum computation", quant-ph/0011013**Les Houches'99 lectures. Another great place to start is**PHY 219/CS 219, "Quantum Computation"**, a course taught in Caltech by**John Preskill**. For introduction into one of the most exciting areas see:**N. Gisin et al., "Quantum cryptography", quant-ph/0101098**. The center of the "Quantum Computing Universe" is**Qubit.Org**.**L. O'Raifeartaigh, N. Straumann, "Early History of Gauge Theories and Kaluza-Klein Theories, with a Glance at Recent Developments", hep-ph/9810524.**This article appeared in the APS Centennial issue of Rev. Mod. Phys. Another interesting article is**N. Straumann, "Reflections on Gravity", astro-ph/0006423.****R. Jackiw, "A Particle Field Theorist's Lectures on Supersymmetric, Non-Abelian Fluid Mechanics and d-Branes", physics/0010042.**Montreal'00 lectures.**D. Bigatti, L. Susskind, "TASI lectures on the Holographic Principle", hep-th/0002044.**See also**'t Hooft**'s Erice lectures:**"Determinism and Dissipation in Quantum Gravity", hep-th/0003005,**and**"The Holographic Principle", hep-th/0003004.**By the way, 't Hooft has published a book on general relativity. A draft version of this book is available from his**web site**

Creation Date: *October 20, 1997*

Last Modified: *July 14,
2002*