Physics Literature  Condensed Matter Theory

Below you will see a list of educational articles, of which most are available on-line. I like the clarity, originality and broadness of presentation  due to  which they have been selected in the list. I am mentioning the list to those who are interested in theoretical condensed matter physics.

Strongly Interacting Systems:

• General:

  • • • H. J. Schulz, "Fermi Liquids and Luttinger Liquids", cond-mat/9807366 An excellent set of lectures about many topics, among which: Fermi Liquids, Renormalization, Littinger Liquids, Heisenberg Model and Bethe Ansatz, Hubbard model, Metal-Insulator Transition, Spin-Charge Separation e.t.c. Les Houches'94 lectures.

      • R. Shankar, "Renormalization Group Approach to Interacting Fermions", Rev. Mod. Phys. 66, 129 (1994); cond-mat/9307009. You can learn fermionic path integrals and RG techniques from this review.

      • 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.

      • E. Fradkin, "Field theories of condensed matter systems" (Addison-Wesley, 1991). This book is about everything in condensed matter. A must-have.

      • P. M. Chaikin and T. C. Lubensky, "Principles of condensed matter physics" (Cam. U. Press, 1995). This book is about everything in soft condensed matter.

      • 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.

      • A. M. J. Schakel, "Boulvard of Broken Symmetries", cond-mat/9805152 A great set of lectures! Very recommended.

      • G. E. Volovik, "Exotic Properties of ^3He", World Scientific. Everything that any condensed matter physicist has to know about topology and ^3He. 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, "3He and Universe parallelism", cond-mat/9902171.

Mesoscopic Physics:

• • General

    • • 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).

      • Les Houches'94 Summer session was devoted to mesoscopic physics: E. Akermans et. al., eds., "Mesoscopic quantum physics" (Elsevier 1995).

      • L. S. Levitov, A. V. Shytov, "Coulomb blocking of tunneling: from zero-bias anomaly to coulomb gap", cond-mat/9607136 What is a Coulomb blockade? Find the answer in this paper.

      • G. Montambaux, "Spectral Fluctuations in Disordered Metals", cond-mat/9602071. Les Houches'95 lectures.

      • C. W. J. Beenakker, "Random-Matrix Theory of Quantum Transport", cond-mat/9612179. 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" (Cam. 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. Shot noise is a very powerful technique to investigate correlations in electronic systems. This article is a review rather than a tutorial, yet it's all I could find on the Net. There is also a book: Sh. Kogan, "Electronic noise and fluctuations in solids" (Cambridge Univ. Press, New York, 1996), but I still have to check it out.

Quantum Hall Effect:

• 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 qunatum 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.

• • 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.

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 a 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".

  • Vortices:

    • • G. Blatter et. al., "Vortices in High-Temperature Superconductors", Rev. Mod. Phys., Vol. 6, 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 havn't gotten to read it yet.

  • 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. However, the theory seems to be fundamentally flawed; 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 Currently, there are many articles on the Net which deal with this theory, most of them falling into two classes: those which use SO(5) to predict new phenomena and those which try to justify (disprove) the very existence of SO(5) symmetry. You can easily retrieve all of them just searching for the word "SO(5)" or "SO(8)" in the abstract.

Disorder:

• • General:

    • • T. Giamarchi and E. Orignac, "Disordered Quantum Solids", cond-mat/0005220. Montreal'00 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.

      • M. V. Sadovskii, "Superconductivity and localization", cond-mat/9308018 Seems interesting, but I havn'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

  • Spin Glasses:

    • • V. S. Dotsenko, "Introduction to the theory of spin glasses and neural networks", World Scientific. In my humble opinion this is simply the best text on spin glasses.

      • D. Sherrington, "Spin Glasses", cond-mat/9806289 I havn'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:

• • Integrable Models:

    • • 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 descpription 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. Wrtitten for a general physics audience. The author is a leading expert in the field.

      • 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.

  • 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.

  • Bosonization:

    • • The "Bible" of bosonization is: A. O. Gogolin, A. A. Nersesyan and A. M. Tsvelik, "Bosonization and strongly correlated systems" (Cam. U. Press, 1998).

      • R. Shankar, "Bosonization: how to make it work for you in Condensed Matter", in "Modern Trends in Condensed Matter". 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 bozonization 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!

  • Duality:

    • • S. E. Hjelmeland, U. Lindstrvm, "Duality for the Non-Specialist", hep-th/9705122. Introduction to the duality in field theory.

      • P. A. Marchetti, "Bosonization and Duality in Condensed Matter Systems", hep-th/9511100 Explains the essense of bosonization and dualities in condensed matter physics.

      • 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". 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).

      • There are books which menage 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" (Cam. 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 developped 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).

  • 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, "Diagramnye metody v zadachah" ("Diagramatic methods through problems", in russian). The first edition of the book is coming out soon.

      • 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).

  • Various:

    • • R. Rajamaran, "Solitons and Instantons", North Holland 1989. An instant classic!

      • D. R. Nelson, "Defects in superfluids, superconductors and membranes", cond-mat/9502114 Les Houches lectures on well-settled topics.

      • 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.

• • • 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":

• • • • 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.

Cross-Disciplinary Physics:

• • Various:

    • • 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.

      • R. Dickman et. al., "Paths to Self-Organized Criticality", cond-mat/9910454 Looks like a good tutorial. I havn't checked it out yet. See also: D. Dhar, "Studying Self-Organized Criticality with Exactly Solved Models", cond-mat/9909009

      • M. Baake, "A Guide to Mathematical Quasicrystals", math-ph/9901014 Havn'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)! This is the area that I work in. 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); and U. Weiss, "Quantum dissipative systems" (World Scientific, 1993).

• • • • 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

Useful References (print):

• ”Methods of Quantum Field Theory in Statistical Physics” by Abrikosov, Gorkov and Dzyalozinskii. (Dover Paperback) - Classic text from the sixties, known usually as AGD.

• “A guide to Feynman Diagrams in the Many-Body problem” by R. D. Mattuck. (Dover Paperback) A light introduction to the subject.

• “Many Particle Physics”, by G. Mahan (Plenum Press), an exhaustive treatise.

• “Quantum Theory of Many Particle Systems”, by Fetter and Walecka (Dover paperback). A formal exposition.

• “Green's Functions and Condensed Matter”, by Rickayzen. A nice discussion of Green functions, and many-body theory.

• “Quantum Field-theoretical method in Transport Theory of Metals”, by J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986).

• “Keldysh and Doi-Peliti Techniques for out-of-Equilibrium Systems” Alex Kamenev, preprint, cond-matt/0109316.

• “Ab Initio modeling of quantum transport...”, by J. Taylor, H. Guo and J. Wang, PRB 63 245407.

• ''Quantum Kinetics in Transport and Optics of Semi-conductors'', H. Haug and A.-P. Jauho.

• ''Quantum Statistical Mechanics'', L.P. Kadanoff and G. Baym (1962).

• L.P. Keldysh, JETP 20, 1018 (1965).