Interacting Electrons in Reduced Dimensions

399 Pages·1990·28.543 MB·English

by  Bill Sutherland (auth.), Dionys Baeriswyl, David K. Campbell (eds.)

Interacting Electrons
in Reduced
Dimensions
NATO ASI Series
Advanced Science Institutes Series
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Vo/ume212-Atoms in Strong Fields
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Vo/urne 213-lnteracting Electrons in Reduced Dimensions
edited by Dionys Baeriswyl and David K. Campbell
Vo/urne 214-Science and Engineering of One-and Zero-Dimensional
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edited by Steven P. Beaumont and Clivia M. Sotomayor Torres
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Se ries B: Physics
Interacting Electrons
in Reduced
Dimensions
Edited by
Dionys Baeriswyl
ETH
Zürich, Switzerland
and
David K. Campbell
Los Alamos National Laboratory
Los Alamos, New Mexico
Plenum Press
New York and London
Published in cooperation with NATO Scientific Affairs Division
Proceedings of a NATO Advanced Reseach Workshop (SOL Panel)
on Interacting Electrons in Reduced Dimensions,
held October 3-7, 1988,
in Turin, Italy
Llbrary of Congress Cataloglng-In-Publlcatlon Data
NATO Advaneed Research Workshop (SOL Panel) on Interaetlng Eleetrons
In Redueed Dimensions (1988 : Turln. Italy)
Interaetlng eleetrons in redueed dimensions I edlted by Dlonys
Baerlswyl and Davld K. Campbell.
p. em. -- (NATO ASI serles. Serles B. Physles ; vol. 2.13)
'Proeeedings of a NATO Advaneed Research Workshop (SOL Panel) on
Interaetlng Eleetrons In Redueed Dimensions. held Oetober 3-7. 1988.
In Turln. Italy"--T.p. verso.
Published In eooperatl.on wlth NATO Selentlfle Affalrs Division.
Ineludes blbliographieal referenees.
ISBN-13: 978-1-4612-7869-6 e-ISBN-13: 978-1-4613-0565-1
001: 10.1007/978-1-4613-0565-1
1. Solid state physles--Congresses. 2. Hubbard model--Congresses.
1. Baerlswyl. D. (DlonyS). 1944- 11. Campbell. David K.
111. North Atlantle Treaty Drganlzation. Selentlfle Affalrs
Division. IV. Tltle. V. Serles: NATO ASI series. Series B.
Physlcs ; v. 213.
CC176.A1N29 1988
530.4·1--de20 89-48931
CIP
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SPECIAL PROGRAM ON CONDENSED SYSTEMS
OF LOW DIMENSIONALITY
This book contains the proceedings of a NATO Advanced Research
Workshop held within the program of activities of the NATO
Special Program on Condensed Systems of Low Dimensionality,
running from 1983 to 1988 as part of the activities of the NATO
Science Committee.
Other books previously published as a result of the activities of
the Special Program are:
Volume 148 INTERCALATION IN LAYERED MATERIALS
edited by M. S. Dresselhaus
Volume 152 OPTICAL PROPERTIES OF NARROW-GAP LOW
DIMENSIONAL STRUCTURES
edited by C. M. Sotomayor Torres, J. C. Portal,
J. C. Maan, and R. A. Stradling
Volume 163 THIN FILM GROWTH TECHNIQUES FOR LOW
DIMENSIONAL STRUCTURES
edited by R. F. C. Farrow, S. S. P. Parkin,
P. J. Dobson, J. H. Neave, and A. S. Arrott
Volume 168 ORGANIC AND INORGANIC LOW-DIMENSIONAL
CRYSTALLINE MATERIALS
edited by Pierre Delhaes and Marc DrilIon
Volume 172 CHEMICAL PHYSICS OF INTERCALATION
edited by A. P. Legrand and S. Flandrois
Volume 182 PHYSICS, FABRICATION, AND APPLICATIONS OF
MULTI LAYERED STRUCTURES
edited by P. Dhez and C. Weisbuch
Volume 183 PROPERTIES OF IMPURITY STATES IN SUPERLATTICE
SEMICONDUCTORS
edited by C. Y. Fong, Inder P. Batra, and S. Ciraci
Volume 188 REFLECTION HIGH-ENERGY ELECTRON
DIFFRACTION AND REFLECTION ELECTRON
IMAGING OF SURFACES
edited by P. K. Larsen and P. J. Dobson
Volume 189 BAND STRUCTURE ENGINEERING IN
SEMICONDUCTOR MICROSTRUCTURES
edited by R. A. Abram and M. Jaros
Volume 194 OPTICALSWITCHING IN LOW-DIMENSIONALSYSTEMS
edited by H. Haug and L. Banyai
Volume 195 METALLIZATION AND METAL-SEMICONDUCTOR INTERFACES
edited by Inder P. Batra
Volume 198 MECHANISMS OF REACTIONS OF ORGANOMETALLIC
COMPOUNDS WITH SURFACES
edited by D. J. Cole-Hamilton and J. O. Williams
SPECIAL PROGRAM ON CONDENSED SYSTEMS
OF LOW DIMENSIONALITY
Volume 199 SCIENCE AND TECHNOLOGY OF FAST ION CONDUCTORS
edited by Harry L. Tuller and Minko Balkanski
Volume 200 GROWTH AND OPTICAL PROPERTIES OF WIDE-GAP li-VI
LOW-DIMENSIONAL SEMICONDUCTORS
edited by T. C. McGill, C. M. Sotomayor Torres,
and W. Gebhardt
Volume 202 POINT AND EXTENDED DEFECTS IN SEMICONDUCTORS
edited by G. Benedek, A. Cavallini, and W. Schröter
Volume 203 EVALUATION OF ADVANCED SEMICONDUCTOR MATERIALS
BY ELECTRON MICROSCOPY
edited by David Cherns
Volume 206 SPECTROSCOPY OF SEMICONDUCTOR MICROSTRUCTURES
edited by Gerhard Fasol, Annalisa Fasolino,
and Paolo Lugli
PREFACE
As its name suggests, the 1988 workshop on "Interacting Electrons in Reduced Dimen
sions" focused on the wide variety of physical effects that are associated with (possibly
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 invalidate mean-field results.
By convening a group of leading experts in theoretical methods ranging from rigorous
analytical approaches ("bosonization" and Bethe Ansatz) for infinite systems through nu
merical algorithms, both "exact" for small systems (valence bond and Lanczos methods)
and "stochastic" for intermediate systems (Quantum Monte Carlo (QMC)) to renormaliza
tion group and variational methods, the workshop was able to survey critically essentially
the entire spectrum of relevant theoretical methods. As a result, the limitations of the
various approaches were clearly exposed and a number of critical issues for future study
were identified.
Both the formal presentations, recorded in these proceedings, and the informal discus
sions reflected the excitement that the confluence of analytic and computational approaches
and the ever-increasing number of novel materials have brought to this topic. Among the
particularly exciting new results were advances in QMC methodology, stimulated by work
of the Trieste group, which offer substantial promise for fermionic QMC calculations in two
(and higher !) dimensions. In another important area for numerical calculations - relating
vii
results for (smali) finite-size clusters to the behavior of infinite systems - two new develop
ments were presented, first the concept of "effective dispersion relations" and second the
idea of "phase randomization/boundary condition averaging." Considerable discussion was
devoted to holes in antiferromagnets, especially in the framework of the two-dimensional
t-J model and its variants. Unfortunately (but unsurprisingly I), the intricate issue of
superconductivity in these models was not answered in a definitive way. Similarly, llQ gen
erally accepted "recipe" for describing materials as chemically and structurally complex as
the high-temperature superconductors within the framework of simple model Hamiltonians
was given. However, recent developments in "ab initio" methods (e.g. improvements of the
local density approximation) may open the way for a semi-quantitative determination from
the actual materials of certain crucial parameters in the models. We hope that the success
of the conference, as measured by the level of interaction, discussion, and excitement at
the meeting, is apparent to the readers of these proceedings.
The success of the conference owed much to the ambience of the Institute for Scientific
Interchange (ISI) in Torino, Italy, and to the superb efforts of the staff, Tiziana Bertoletti,
Carmen Novella, and Marinella Prato. As organizers we are also grateful to the President
of the ISI, Prof. Thllio Regge, and its Director, Prof. Mario Rasetti, for their intellectual
and financial support and are pleased to thank the NATO Office of Scientific Affairs for
its support of the meeting under the NATO Advanced Research Workshop program.
Dionys Baeriswyl
David Campbell
viii
CONTENTS
I. METHODS
A. Solvable Models and Analytic Results
Brief History of a One-Dimensional Ground State Wave Function
Bill Sutherland .................................................. 1
Two Theorems on the Hubbard Model
Elliott H. Lieb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11
A Model of Crystallization: A Variation on the Hubbard Model
Elliott H. Lieb .................................................. 17
The Fermi-Linearized Hubbard Model: Dimer Ground State
Arianna Montorsi, Mario Rasetti, and Allan 1. Solomon ............. 27
Superconductivity of Itinerant Electrons Coupled to Spin Chains
R. Shankar .................................................... 35
Valence Bond Spin Models: Ground States and Excitations
E. Lieb ........................................................ 43
B. Quantum Monte Carlo and Numerical Diagonalization Methods
Numerical Simulation of the Two Dimensional Hubbard Model
S. Sorella and M. Parrinello ..................................... 47
Stable Matrix-Multiplication Algorithms for Low Temperature
N umerical Simulations of Fermions
E. Y. Loh, Jr., J. E. Gubernatis, R. T. Scalettar, R. L. Sugar,
and S. R. White ................................................ 55
Numerical Simulations of the Two-Dimensional Hubbard Model
1. Morgenstern .................................................. 61
Monte Carlo Simulation of a Three-Band Model for High-Tc
Superconductors
G. Dopt, J. Rahm, and A. Muramatsu ............................. 69
Exact Valence-Bond Approach to Quantum Cell Models
Z. G. Soos, S. Ramasesha, and G. W. Hayden ...................... 79
Lanczos Diagonalizations of the 1-D Peierls-Hubbard Model
E. Y. Loh, Jr., D. K. Campbell, and J. Tinka Gammel ............... 91
C. Variational and Perturbation Theoretic Methods
Variational Wave Functions for Correlated Lattice Fermions
Dieter Vollhardt .....•......................................... 107
ix
Variational Approach to Correlation Functions and to the Periodic
Anderson Model in Infinite Dimensions
Florian Gebhard and Dieter Vollhardt ............................. 123
The Hubbard Model in Infinite Dimensions
Walter Metzner and Dieter Vollhardt ............................. 129
Correlation Functions for the Two-Dimensional Hubbard Model
J. Carmelo, D. Baeriswyl, and X. Zotos ........................... 135
D. Density Functional Theory
Density Functional Calculations for Strongly Correlated Systems
O. Gunnarsson, O. K. Andersen, and A. Svane .................... 139
Dimensionality Effects in trans-( CH).,
P. Vogl and D. K. Campbell ..................................... 151
H. QUASI-ONE DIMENSIONAL MODELS AND MATERIALS
A. ApplicabiIity of Hubbard-Type Models
The Hubbard Model for One-Dimensional Solids
Anna Painelli and Alberto Girlando .............................. 165
Off-Diagonal Coulomb Interactions in the Extended Peierls-Hubbard
Model: Exact Diagonalization Results
David K. Camp bell, J. Tinka Gammel, and Eugene Y. Loh, Jr. ..... " 171
Electron Correlation and Peierls Instability
Xin Sun, Jun Li, and Chang-qin Wu ............................. 179
B. Organic Conductors and Conjugated Polymers
Instabilities in Half-Filled One-Dimensional Systems: Valence Bond
Analysis
Anna Painelli and Alberto Girlando .............................. 189
Quantum Monte Carlo Study of Neutral-Ionic Transition
Naoto Nagaosa ................................................ 201
Diagonal and Off-Diagonal Electronic Interactions and Phonon
Dynamics in an Extended Model of Polyacetylene
Johannes Voit ............................................... " 207
Phonons and Quantum Fluctuations in a Dimerized Electron-Phonon
Chain
G. C. Psaltakis and N. Papanicolaou ............................. 219
Scaling Approach to Electronic Correlations in Organic Conductors
Claude Bourbonnais ............................................ 227
Peierls Instability in Weakly Non-Ideal One-Dimensional Systems
V. Ya. Krivnov and A. A. Ovchinnikov ........................... 241
Use of the Spin Hamiltonian to Study the Spin-Peierls Instability
and Magnetism in Conjugated Polymers
L. N. Bulaevskii ............................................... 253
A Two Band Model for Halogen-Bridged Transition Metal Linear
Chain Complexes
A. R. Bishop, J. Tinka Gammel, E. Y. Loh,Jr., S. R. Phillpot,
and S. M. Weber-Milbrodt ....................................... 267
x