Interacting Electrons in Reduced Dimensions

1. Front Matter

   Pages i-xi

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2. Methods

   1. Solvable Models and Analytic Results

      1. Brief History of a One-Dimensional Ground State Wave Function

         • Bill Sutherland

         Pages 1-9

      2. Two Theorems on the Hubbard Model

         • Elliott H. Lieb

         Pages 11-16

      3. A Model of Crystallization: A Variation on the Hubbard Model

         • Elliott H. Lieb

         Pages 17-26

      4. The Fermi-Linearized Hubbard Model: Dimer Ground State

         • Arianna Montorsi, Mario Rasetti, Allan I. Solomon

         Pages 27-34

      5. Superconductivity of Itinerant Electrons Coupled to Spin Chains

         • R. Shankar

         Pages 35-41

      6. Valence Bond Spin Models: Ground States and Excitations

         • Elliott H. Lieb

         Pages 43-46

   2. Quantum Monte Carlo and Numerical Diagonalization Methods

      1. Numerical Simulation of the Two Dimensional Hubbard Model

         • S. Sorella, M. Parrinello

         Pages 47-54

      2. Stable Matrix-Multiplication Algorithms for Low-Temperature Numerical Simulations of Fermions

         • E. Y. Loh Jr., J. E. Gubernatis, R. T. Scalettar, R. L. Sugar, S. R. White

         Pages 55-60

      3. Numerical Simulations of the Two-Dimensional Hubbard Model

         • I. Morgenstern

         Pages 61-68

      4. Monte Carlo Simulation of a Three-Band Model for High-Tc Superconductors

         • G. Dopf, J. Rahm, A. Muramatsu

         Pages 69-77

      5. Exact Valence-Bond Approach to Quantum Cell Models

         • Z. G. Soos, S. Ramasesha, G. W. Hayden

         Pages 79-90

      6. Lanczos Diagonalizations of the 1-D Peierls-Hubbard Model

         • E. Y. Loh Jr., D. K. Campbell, J. Tinka Gammel

         Pages 91-105

   3. Variational and Perturbation Theoretic Methods

      1. Variational Wave Functions for Correlated Lattice Fermions

         • Dieter Vollhardt

         Pages 107-121

      2. Variational Approach to Correlation Functions and to the Periodic Anderson Model in Infinite Dimensions

         • Florian Gebhard, Dieter Vollhardt

         Pages 123-128

      3. The Hubbard Model in Infinite Dimensions

         • Walter Metzner, Dieter Vollhardt

         Pages 129-134

      4. Correlation Functions for the Two-Dimensional Hubbard Model

         • José Carmelo, Dionys Baeriswyl, Xenophon Zotos

         Pages 135-138

   4. Density Funstional Theory

      1. Density Functional Calculations for Strongly Correlated Systems

         • O. Gunnarsson, O. K. Andersen, A. Svane

         Pages 139-150

      2. Dimensionality Effects in <i>trans</i>-(CH)_<i>x</i>

         • P. Vogl, D. K. Campbell

         Pages 151-164

3. Quasi-One Dimensional Models and Materials

   1. Applicability of Hubbard-Type Models

      1. The Hubbard Model for One-Dimensional Solids

         • Anna Painelli, Alberto Girlando

         Pages 165-170

As its name suggests, the 1988 workshop on "Interacting Electrons in Reduced Dimen­ the wide variety of physical effects that are associated with (possibly sions" focused on strongly) correlated electrons interacting in quasi-one- and quasi-two-dimensional mate­ rials. Among the phenomena discussed were superconductivity, magnetic ordering, the metal-insulator transition, localization, the fractional Quantum Hall effect (QHE), Peierls and spin-Peierls transitions, conductance fluctuations and sliding charge-density (CDW) and spin-density (SDW) waves. That these effects appear most pronounced in systems of reduced dimensionality was amply demonstrated at the meeting. Indeed, when concrete illustrations were presented, they typically involved chain-like materials such as conjugated polymers, inorganic CDW systems and organie conductors, or layered materials such as high-temperature copper-oxide superconductors, certain of the organic superconductors, and the QHE samples, or devices where the electrons are confined to a restricted region of sample, e. g. , the depletion layer of a MOSFET. To enable this broad subject to be covered in thirty-five lectures (and ab out half as many posters), the workshop was deliberately focused on theoretical models for these phenomena and on methods for describing as faithfully as possible the "true" behav­ ior of these models. This latter emphasis was especially important, since the inherently many-body nature of problems involving interacting electrons renders conventional effec­ tive single-particle/mean-field methods (e. g. , Hartree-Fock or the local-density approxi­ mation in density-functional theory) highly suspect. Again, this is particularly true in reduced dimensions, where strong quantum fluctuations can invalidatemean-field results.

• Helium-Atom-Streuung
• crystal
• liquid
• particles
• polymer

• ETH, Zürich, Switzerland

  Dionys Baeriswyl

• Los Alamos National Laboratory, Los Alamos, USA

  David K. Campbell

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