1. One-Dimensional Fermi liquids

Author: Johannes Voit
Comments: uuencoded Latex files and postscript figures, one Readme-file approx 160 pages + 13 figures; to be published by Reports on Progress in Physics

     I attempt to give a pedagogical overview of the progress which has occurred during the past decade in the description of one-dimensional correlated fermions. Fermi liquid theory based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence and because of charge-spin separation. It is replaced by a Luttinger liquid whose elementary excitations are collective charge and spin modes, based on the exactly solvable Luttinger model. I review this model and various solutions with emphasis on bosonization (and its equivalence to conformal field theory), and its physical properties. The notion of a Luttinger liquid implies that all gapless 1D systems share these properties at low energies. Chapters 1 and 2 of the article contain an introduction and a discussion of the breakdown of Fermi liquid theory. Chapter 3 describes in detail the solution of the Luttinger model both by bosonization and by Green's functions methods and summarizes the properties of the model, expressed thorugh correlation functions. The relation to conformal field theory is discussed. Chapter 4 of the article introduces the notion of a Luttinger liquid. It describes in much detail the various mappings applied to realistic models of 1D correlated fermions, onto the Luttinger model, as well as important corrections to the Luttinger
model properties discussed in Ch.3. Chapter 5 describes situations where the Luttinger liquid is not a stable fixed point, and where spin or charge gaps open  in at least one channel. Chapter 6 discusses multi-band and multichain problems, in particular the stability of a Luttinger liquid with respect to interchain hopping. Ch. 7 gives a brief summary of experimental efforts to uncover Luttinger liquid correlations in quasi-1D materials.

2. Fermi liquids and Luttinger liquids

Authors: H.J. Schulz, G. Cuniberti, P. Pieri
Comments: Lecture notes of the Chia Laguna (Italy) summer school, september 1997, 62 pages references updated, typos corrected
Subj-class: Strongly Correlated Electrons
Journal-ref: In `Field Theories for Low-Dimensional Condensed Matter Systems'. G. Morandi et al. Eds. Springer (2000). ISBN: 3540671773

     In these lecture notes, the basic physics of Fermi liquids and Luttinger liquids is presented. Fermi liquids are discussed both from a phenomenological viewpoint, in relation to microscopic approaches, and as renormalization group fixed points. Luttinger liquids are introduced using the bosonization formalism, and their essential differences with Fermi liquids are pointed out. Applications to transport effects, the effect of disorder, quantum spin chains, and spin ladders, both insulating and metallic, are given.

3. Fermi liquids and non--Fermi liquids

Author: H. J. Schulz
Comments: 1994 Les Houches lecture notes, 59 pages, RexTeX 3.0, uuencoded, together with postscript figures, needs epsf, you want to compile houches_send.tex
(small corrections to original submission)
Journal-ref: in "Proceedings of Les Houches Summer School LXI", ed. E. Akkermans, G. Montambaux, J. Pichard, et J. Zinn-Justin (Elsevier, Amsterdam, 1995),
p.533.

     Contents
     I. Introduction
     II. Fermi Liquids
     III. Renormalization group for interacting fermions
     IV. Luttinger liquids
     V. Transport in a Luttinger liquid
     VI. The Bethe ansatz: a pedestrian introduction
     VII. Conclusion and outlookLuttinger revisted-the renormalization group approach

4. Luttinger revisted-the renormalization group approach

Authors: R. Shankar (Yale)
Comments: Latex 4 figures Sumbitted to the Luttinger Memorial Issue J. Stat. Phys
Subj-class: Mesoscopic Systems and Quantum Hall Effect

     Luttinger's contributions abound in different parts of many-body physics. Here I review the ones that appear when one uses the Renormalization Group (RG) to study the subject: the Luttinger Liquid, Luttinger's Theorem (on the volume of the Fermi surface) and the Kohn-Luttinger Theorem on the superconducting instability of all metals as one approaches absolute zero.