Condensed Matter Physics

Copyright © 2000 by Akakii Melikidze:

**
A. Melikidze, Net Adv. Phys. Spec. Bibliog. 2:3 (2000).
**

Condensed Matter Theory

Dear Reader,

Below you will see a list of educational articles, of which most are availible on-line. Though, for obvious reasons, the selection of the topics can't fail to reflect my own reasearch 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 this page who have interests in condensed matter theory.

Akakii.

Condensed Matter Physics

STRONGLY INTERACTING SYSTEMS: General; --- MESOSCOPIC PHYSICS: General; --- QUANTUM HALL EFFECT: General; Chern-Simons-Landau-Ginzburg Theory; --- SUPERCONDUCTORS: General; Vortices; SO(5); --- DISORDER: General; Spin Glasses; --- METHODS IN PHYSICS: General; Integrable Models; Path Integrals and Field-Theoretic Techniques; Bosonization; Duality; Conformal Field Theory; Diagramatic Methods; Various; --- CROSS-DISCIPLINARY PHYSICS: Various;

**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.**

- 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 qauantum 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.

- 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.

- 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.

- 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.

- 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" (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!

- 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.**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).

- 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, "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).**

- The standard references are:
- 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":
- 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

- 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.

- 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).**

Creation Date: *October 20, 1997*

Last Modified:
*November 15, 2000*