Condensed Matter Physics

Copyright © 2000 by Akakii Melikidze:

**
A. Melikidze, Net Adv. Phys. Spec. Bibliog. 2 (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; --- QUANTUM HALL EFFECT: General; Chern-Simons-Landau-Ginzburg Theory; --- SUPERCONDUCTORS: General; Vortices; SO(5); --- MODELS: General; Hubbard; Tomonaga-Luttinger; --- DISORDER AND CHAOS: General; Spin Glasses; --- METHODS IN PHYSICS: General; Conformal Invariance; Diagramatic Methods; --- 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 them: Fermi Liquids, Renormalization, Littinger Liquids, Heisenberg Model and Bethe Ansatz, Hubbard Model, Metal-Insulator Transition, Spin-Charge Separation etc. Les Houches '94.**A. Auerbach, "Quantum magnetism approaches to strongly correlated electrons", lecture notes, cond-mat/9801294**A well written set of lectures. There is also a book with a similar title by the same author in which these and other issues are considered in more detail.**S. L. Sondhi et. al., "Quantum Phase Transitions", Rev. Mod. Phys. 69, 315 (1997).**A very popular review article. One of my own favorites.**A. M. J. Schakel, "Boulevard of Broken Symmetries",****cond-mat/9805152**A great set of lectures! Deals with mathematically involved questions in a very physical way. Very recommended.**G. E. Volovik, "Exotic Properties of ^3He", World Scientific.**Everything that any condensed matter physicist has to know about topology and ^3He.

**Quantum Hall Effect:**

- General:
**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.**J. Froehlich, U. M. Studer, E. Thiran, "Quantum Theory of Large Systems of Non-Relativistic Matter" cond-mat/9508062**In these Les Houches '94 lectures a field-theoretic approach to the problem is presented. Quite a difficult text to read, however informative.**G. Murphy, R. Shankar, "Field Theory of the Fractional Quantum Hall Effect-I", cond-mat/9802244**Still have to check this out.

- 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, No. 1 (1992) 25-28.**This is the article that one is usually referred to if one wants to understand what a composite boson theory of Quantum Hall Effect is.**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 the*nu=1/2*problem.

**Superconductors:**

- General:
**M. P. A. Fisher, "Mott Insulators, Spin Liquids and Quantum Disordered Superconductivity",****cond-mat/9806164**Lectures in Les Houches, 1998. At the moment when these lines are written (January 2000), this article is extremely popular. Being clearly written it introduces a reader into one of the recent phenomenological theories of d-wave superconductors.**M. B. Maple, "High Temperature Superconductivity", cond-mat/9802202**A view of an experimentalist on the current status of research in High-Tc's**R. B. Laughlin, "A critique of two metals", cond-mat/9709195**This is how Nobel Laureat Prof. Robert Laughlin understands the fundamental problems facing the theory of High-Tc's. And here's what other people think about it :**P. W. Anderson, G.Baskaran, "A critique of 'A critique of two metals'", cond-mat/9711197**

- Vortices:
**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.

- 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.

**Models:**

- General:
**N.Andrei, "Integrable Models in Condensed Matter Physics",****cond-mat/9408101**These lectures describe analytic solutions of most of the important models of strongly interacting systems in*all details*so that you don't even have to use a workbook, just follow the text. Highly mathematical in style.

- Hubbard Model:
**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 the 1D Hubbard model.**A. B. Eriksson, T. Einarsson, S. Ostlund, "Symmetries and MF phases of the extended Hubbard model", cond-mat/9411071**This is an attempt to analyze the 2D Hubbard model at Mean Field level.

- Tomonaga-Luttinger Model:
**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.**A. O. Gogolin, "Selcted Topics in the Theory of 1D Quantum Wires", cond-mat/9407103**Written for a general physics audience. Contains a simple discussion of a wide range of 1D physics.

**Disorder and Chaos:**

- General:
**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.**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.**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.

**Methods in Physics:**

- General:
**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!".**M. Kiometzis, H. Kleinert, A. M. J. Schakel, "Dual description of the Superconducting Phase Transition", cond-mat/9508142**A new approach to the old problem. This is, in fact, an expanded version of one of the chapters in Schakel's book.**P. A. Marchetti, "Bosonization and Duality in Condensed Matter Systems", hep-th/9511100**This was the article from which I learned what the field-theoretic duality is.**R. S. Markiewicz, M. T. Vaughn, "Higher Symmetries in Condensed Matter Physics", cond-mat/9809119**A very nice and enjoyable talk.**C. W. J. Beenakker, "Random-Matrix Theory of Quantum Transport", cond-mat/9612179**One of the best tutorials on Random-Matrix Theory availible on the Net. Often referenced in many physics research papers.**M. Takahashi, "Thermodynamical Bethe Ansatz and condensed matter", cond-mat/9708087**A comprehensive descpription of the TBA solution of many low-dimensional models. Although highly mathematical in style, the level of this tutorial is not very difficult.**R. Rajamaran, "Solitons and Instantons", North Holland 1989.**An instant classic. However, it is quite self-focused, therefore best used as a reference.**J. Spencer, "Random Graphs", lecture notes**Pure math, however enjoyable.**M. P. Nightingale, C. J. Umrigar, "Monte Carlo Eigenvalue Methods in Quantum Mechanics and Statistical Mechanics", cond-mat/9804288**Experts review Monte Carlo methods.

- Conformal Invariance:
**J. Cardy, "Conformal Invariance", in "Phase Transitions", Vol. 11 (1987), Academic Press.**A bit superficial; however, an extensive review.**D. Bernard, "(Perturbed) Conformal Field Theory Applied to 2D Disordered Systems : an Introduction",****hep-th/9509137**Also a bit superficial, but even more extensive. Topics discussed include supersymmetry methods, replica methods etc.

- Diagrammatic Techniques:
**L.S. Levitov, A. V. Shytov, "Diagramnye metody v zadachah" (in russian),****ftp archive**The famous course.**A. MacKinnon, "Transport and Disorder", lecture notes**Explains the diagrammatic techniques for disorder. Few applications.

**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.**D. R. Nelson, "Defects in superfluids, superconductors and membranes", cond-mat/9502114**Les Houches lectures on well-settled topics.**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****M. Baake, "A Guide to Mathematical Quasicrystals", math-ph/9901014**Haven't checked it out yet.**S. Nechaev, "Statistics of Knots and Entangled Rnadom Walks", cond-mat/9812205**Lectures of the guy whom I heard at LSU '97.**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!

Creation Date: *October 20, 1997*

Last Modified:
*January 10, 2000*