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IOS Press , Società Italiana di Fisica eBooks

The electron liquid paradigm in condensed matter physics : Varenna on Lake Como, Villa Monastero, 29 July - 8 August 2003

Gabriele F. Giuliani, Giovanni Vignale

Published Jan 1, 2004• 0 citations

Abstract

The electron liquid paradigm is at the basis of most of our current understanding of the physical properties of electronic systems. Quite remarkably, the latter are nowadays at the intersection of the most exciting areas of science: materials science, quantum chemistry, nano-electronics, biology, and quantum computation. Accordingly, its importance can hardly be overestimated. During the past 20 years the field has witnessed momentous developments, which are partly covered in this new volume. Advances in semiconductor technology have allowed the realizations of ultra-pure electron liquids whose density, unlike that of the ones spontaneously occurring in nature, can be tuned by electrical means, allowing a systematic exploration of both strongly and weakly correlated regimes. Most of these system are two- or even one-dimensional, and can be coupled together in the form of multi-layers or multi-wires, opening vast observational possibilities. On the theoretical side, quantum Monte Carlo methods have allowed an essentially exact determination of the ground-state energy of the electron liquid, and have provided partial answers to the still open question of the structure of its phase diagram. Starting from the 1980s some truly revolutionary concepts have emerged, which are well represented in this volume.

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•Jan 1, 2002•0 citations

The electron liquid paradigm is at the basis of most of our current understanding of the physical properties of electronic systems. Quite remarkably, the latter are nowadays at the intersection of the most exciting areas of science: materials science, quantum chemistry, nano-electronics, biology, and quantum computation. Accordingly, its importance can hardly be overestimated. During the past 20 years the field has witnessed momentous developments, which are partly covered in this new volume. Advances in semiconductor technology have allowed the realizations of ultra-pure electron liquids whose density, unlike that of the ones spontaneously occurring in nature, can be tuned by electrical means, allowing a systematic exploration of both strongly and weakly correlated regimes. Most of these system are two- or even one-dimensional, and can be coupled together in the form of multi-layers or multi-wires, opening vast observational possibilities. On the theoretical side, quantum Monte Carlo methods have allowed an essentially exact determination of the ground-state energy of the electron liquid, and have provided partial answers to the still open question of the structure of its phase diagram. Starting from the 1980s some truly revolutionary concepts have emerged, which are well represented in this volume.

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature, including a notion that unifies light and electrons. Topics covered include dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological/quantum order, and spin liquid and string-net condensation. Methods discussed include the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, projective construction, and exactly soluble models beyond one-dimension.

An enormous theoretical effort has been made to treat electron-phonon coupled systems, with particular emphasis on Many Body aspects for dense electron systems, taking into account continuum as well as lattice polaron effects. Treating such aspects of polaron theory has been made possible because of powerful Many Body techniques which include: Exact Diagonalization techniques, Quantum Monte Carlo approaches, Density Matrix renormalization group and Dynamical Mean Field Theory. All these advances in polaron theory needed to be accompanied by: an equally important advance in material research which produced many new materials such as the high Tc cuprates, the manganites and nickelates and the fullerines; as well as significant advances in the refinement of experimental analysis and, in particular, the spectroscopic means such as Angel Resolved Photoemission Spectroscopy, X Ray Absorption Spectroscopy (EXAFS, XANES), Pulsed Neutron Diffraction measurements allowing to study the local dynamical lattice de-formations and optical spectroscopy including time resolved measurements. The scope and purpose of this publication is to review both these theoretical and experimental advances which occurred over the last few decades and to introduce the study of such systems, where both strong electron-electron correlations and large electron-phonon coupling strengths play important roles.

Preface (R.A. Broglia and J.R. Schrieffer). 50 years of the Mott phenomenon: insulators, magnets, solids and superconductors as aspects of strong-repulsion theory (P.W. Anderson). Collective motion in Fermi droplets (G. Bertsch). The quantum Hall effect (R. Schrieffer and D.P. Arovas). Quantum effects in heavy-ion reactions (D.M. Brink). Heavy fermions (T.M. Rice). Theory of relaxation, phase transitions and tunnelling in nuclei (R.A. Broglia). The quantum mechanics of a macroscopic variable: some recent results and current issues (A.J. Leggett). Moments at the relativistic borderline: nuclei and rotation superconductors (G. Baym). Numerical simulations of many-electron condensed-matter systems (D.J. Scalapino). The lattice strong interactions: an introduction (E. Marinari).

An understanding of the effects of electronic correlations in quantum systems is one of the most challenging problems in physics, partly due to the relevance in modern high technology. Yet there exist hardly any books on the subject which try to give a comprehensive overview on the field covering insulators, semiconductors, as well as metals. The present book tries to fill that gap. It intends to provide graduate students and researchers a comprehensive survey of electron correlations, weak and strong, in insulators, semiconductors and metals. This topic is a central one in condensed matter and beyond that in theoretical physics. The reader will have a better understanding of the great progress which has been made in the field over the past few decades.

This Fermi Summer School of Physics on Experimental Quantum Information and Computing represents a primer in an expanding area in physics. In this part, the interest in quantum information (QI) science is due to the discovery that a computer operating on quantum mechanical principles can solve certain important computational problems exponentially faster than any conceivable classical computer. But this interest is also due to the interdisciplinary nature of the field: the rapid growth is attributable, in part, to the stimulating confluence of researchers and ideas from physics, chemistry, mathematics, information theory, and computer science. The lectures cover Quantum Information (QI) processing, spanning quantum optics and laser physics, atomic and molecular physics, physical chemistry, and condensed-matter physics.