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In the slightly more than thirty years since its formulation, the
Hubbard model has become a central component of modern many-body
physics. It provides a paradigm for strongly correlated,
interacting electronic systems and offers insights not only into
the general underlying mathematical structure of many-body systems
but also into the experimental behavior of many novel electronic
materials. In condensed matter physics, the Hubbard model
represents the simplest theoret ical framework for describing
interacting electrons in a crystal lattice. Containing only two
explicit parameters - the ratio ("Ujt") between the Coulomb
repulsion and the kinetic energy of the electrons, and the filling
(p) of the available electronic band - and one implicit parameter -
the structure of the underlying lattice - it appears nonetheless
capable of capturing behavior ranging from metallic to insulating
and from magnetism to superconductivity. Introduced originally as a
model of magnetism of transition met als, the Hubbard model has
seen a spectacular recent renaissance in connection with possible
applications to high-Tc superconductivity, for which particular
emphasis has been placed on the phase diagram of the
two-dimensional variant of the model. In mathematical physics, the
Hubbard model has also had an essential role. The solution by Lieb
and Wu of the one-dimensional Hubbard model by Bethe Ansatz
provided the stimulus for a broad and continuing effort to study
"solvable" many-body models. In higher dimensions, there have been
important but isolated exact results (e. g., N agoaka's Theorem)."
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 invalidate
mean-field results.
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Nonlinearity in Condensed Matter - Proceedings of the Sixth Annual Conference, Center for Nonlinear Studies, Los Alamos, New Mexico, 5-9 May, 1986 (Paperback, Softcover reprint of the original 1st ed. 1987)
Alan R. Bishop, David K. Campbell, Steven E. Trullinger, Pradeep Kumar
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R3,036
Discovery Miles 30 360
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Ships in 10 - 15 working days
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The Sixth Annual Conference of the Center for Nonlinear Studies at
the Los Alamos National Laboratory was held May 5-9, 1986, on the
topic "Nonlinearity in Condensed Matter: Lessons from the Past and
Prospects for the Future. " As conference organizers, we felt that
the study of non linear phenomena in condensed matter had matured
to the point where it made sense to take stock of the numerous
lessons to be learned from a variety of contexts where nonlinearity
plays a fundamental role and to evaluate the prospects for the
growth of this general discipline. The successful 1978 Oxford
Symposium on nonlinear (soliton) struc ture and dynamics in
condensed matter (Springer Ser. Solid-State Sci., Vol. 8) was held
at a time when the ubiquity of solitons was just begin ning to be
appreciated by the condensed matter community; in subsequent years
the soliton paradigm has provided a rather useful framework for in
vestigating a large number of phenomena, particularly in
low-dimensional systems. Nevertheless, we felt that the importance
of nonlinearity in wider arenas than "solitonics" merited a
significant expansion in the scope of the conference over that of
the 1978 symposium. Indeed, many of the lessons are quite general
and their potential for cross-fertilization of otherwise poorly
connected disciplines was certainly one of the prime motivations
for this conference. Thus, while these proceedings contain many
contribu tions pertaining to soliton behavior in different
contexts, the reader will find much more as well, particularly in
the later chapters."
ill the past three decades there has been enonnous progress in
identifying the es sential role that "nonlinearity" plays in
physical systems. Classical nonlinear wave equations can support
localized, stable "soliton" solutions, and nonlinearities in
quantum systems can lead to self-trapped excitations, such as
polarons. Since these nonlinear excitations often dominate the
transport and response properties of the systems in which they
exist, accurate modeling of their effects is essential to
interpreting a wide range of physical phenomena. Further, the
dramatic de velopments in "deterministic chaos", including the
recognition that even simple nonlinear dynamical systems can
produce seemingly random temporal evolution, have similarly
demonstrated that an understanding of chaotic dynamics is vital to
an accurate interpretation of the behavior of many physical
systems. As a conse quence of these two developments, the study of
nonlinear phenomena has emerged as a subject in its own right.
During these same three decades, similar progress has occurred in
understand ing the effects of "disorder". Stimulated by Anderson's
pioneering work on "dis ordered" quantum solid state materials,
this effort has also grown into a field that now includes a variety
of classical and quantum systems and treats "disorder" arising from
many sources, including impurities, random spatial structures, and
stochastic applied fields. Significantly, these two developments
have occurred rather independently, with relatively little
overlapping research.
In the slightly more than thirty years since its formulation, the
Hubbard model has become a central component of modern many-body
physics. It provides a paradigm for strongly correlated,
interacting electronic systems and offers insights not only into
the general underlying mathematical structure of many-body systems
but also into the experimental behavior of many novel electronic
materials. In condensed matter physics, the Hubbard model
represents the simplest theoret ical framework for describing
interacting electrons in a crystal lattice. Containing only two
explicit parameters - the ratio ("Ujt") between the Coulomb
repulsion and the kinetic energy of the electrons, and the filling
(p) of the available electronic band - and one implicit parameter -
the structure of the underlying lattice - it appears nonetheless
capable of capturing behavior ranging from metallic to insulating
and from magnetism to superconductivity. Introduced originally as a
model of magnetism of transition met als, the Hubbard model has
seen a spectacular recent renaissance in connection with possible
applications to high-Tc superconductivity, for which particular
emphasis has been placed on the phase diagram of the
two-dimensional variant of the model. In mathematical physics, the
Hubbard model has also had an essential role. The solution by Lieb
and Wu of the one-dimensional Hubbard model by Bethe Ansatz
provided the stimulus for a broad and continuing effort to study
"solvable" many-body models. In higher dimensions, there have been
important but isolated exact results (e. g., N agoaka's Theorem)."
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