Quantum Magnetism

U Schollwöck (Editor), J Richter (Editor), DJJ Farnell (Editor), RF Bishop (Editor)

    Research output: Book/ReportAnthologypeer-review

    Abstract

    Putting the quantum into magnetism might, at first sight, seem like stating the obvious; the exchange interactions leading to collective magnetic behavior are, after all, a pure quantum effect. Yet, for many phenomena in magnetism this underlying quantum nature may be safely ignored at least on the qualitative level. The investigation of magnetic systems where quantum effects play a dominant role and have to be accounted for in detail has, over the last decades, evolved to be a field of very active research. On the experimental side, major boosts have come from the discovery of high-temperature superconductivity in the mid-eighties and the increasing ability of solid state chemists to fashion magnetic systems of restricted dimensionality. While high-temperature superconductivity has raised the question of the link between the mechanism of superconductivity in the cuprates and spin fluctuations and magnetic order in one- and two-dimensional spin-1/2 antiferromagnets, the new magnetic materials have exhibited a wealth of new quantum phenomena of interest in their own. In one-dimensional systems, the universal paradigm of Luttinger liquid behavior has come to the center of interest; in all restricted geometries, the interplay of low dimension, competing interactions and strong quantum fluctuations generates, beyond the usual long-range ordered states, a wealth of new states of condensed matter, such as valence bond solids, magnetic plateaux, spin liquid states or spin-Peierls states, to name but a few. The idea for this book arose during a Hereaus seminar on "Quantum Magnetism: Microscopic Techniques For Novel States of Matter" back in 2002, where it was realized that a set of extensive tutorial reviews would address the needs of both postgraduate students and researchers alike and fill a longstanding gap in the literature. The first three chapters set out to give an account of conceptual problems and insights related to classes of systems, namely one-dimensional (Mikeska and Kolezhuk), two-dimensional (Richter, Schulenburg and Honecker) and molecular magnets (Schnack). The following five chapters are intended to introduce the reader to methods used in the field of quantum magnetism, both for independent reading as well as a backup for the first chapters: this includes time-honored spin wave analysis (Ivanov and Sen), exact diagonalization (Laflorencie and Poilblanc), quantum field theory (Cabra and Pujol), coupled cluster methods (Farnell and Bishop) and the Bethe ansatz (Kl¨umper). To close, a more unified point of view is presented in a theoretical chapter on quantum phase transitions (Sachdev) and an experimentally oriented contribution (Lemmens and Millet), putting the wealth of phenomena into the solid state physics context of spins, orbitals and lattice topology.
    Original languageEnglish
    Place of PublicationBerlin
    PublisherSpringer Nature
    Number of pages481
    ISBN (Print)3-540-21422-4
    DOIs
    Publication statusPublished - 2004

    Publication series

    NameLecture Notes in Physics
    PublisherSpringer Verlag
    Volume645

    Keywords

    • * magnetic plateaux * quantum magnetism * quantum phase transition * spin liquid * valence bond solids

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