Quantum Magnetism 2008, held May 2-4 at FTPI

At first sight the title of this Workshop might seem either paradoxical or self-evident. Thus, the exchange interactions that lead to collective magnetic behavior are a purely quantum-mechanical effect. Nevertheless, this underlying quantum nature has safely been ignored in describing, at least at the qualitative level, many magnetic phenomena of interest in the past. On the other hand, the investigation of magnetic systems and magnetic phenomena where the intrinsically quantal effects play a dominant role, and hence have to be accounted for in detail, has evolved in recent years to become a burgeoning area at the forefront of condensed matter theory.

From the experimental viewpoint, major impetus has come both from the discovery of high-temperature superconductors and, since then, from the ever-increasing ability of materials scientists to fabricate a by now bewildering array of magnetic systems of reduced dimensionality. While high-temperature superconductivity has raised the question of the link between the mechanism of superconductivity in the cuprates, for example, and spin fluctuations and magnetic order in one- and two-dimensional spin-half antiferromagnets, the new magnetic materials exhibit a wealth of new quantum phenomena of enormous interest in their own right. For example, in one-dimensional systems, the universal paradigm of Luttinger liquid behavior has occupied a key position of interest.

More generally, in all restricted geometries, the interplay between reduced dimensionality, competing interactions, and strong quantum fluctuations, generates a plethora of new states of condensed matter, beyond the usual states of quasiclassical long-range order. Examples, inter alia, include spin-Peierls states, magnetic plateau states, spin liquids, and valence bond solids. The investigation of such exotic phases and the quantum phase transitions between them has become a major frontier field in recent years, and the current Workshop QM08 was designed to provide a forum to review the current state-of-the-art.

As befitted a Workshop dedicated largely to low-dimensional materials, we began “in zero dimensions” with a discussion of the fascinating properties of magnetic molecules by Jürgen Schnack. The opening session proceeded via a tour-de-force description of the dynamic structure factor of the one-dimensional anisotropic (XXZ) Heisenberg chain by Alex Kamenev, to both experimental and theoretical talks, by Seung-Hun Lee and Leon Balents respectively, on the effects of fluctuations and frustration in the kagome and spinel classes of antiferromagnets.

The afternoon session of the first day picked up the pervasive theme of frustration in quantum magnetism, paying particular attention to how such diverse effects as quantum (and thermal) fluctuations and perturbations can lift the “accidental” degeneracy that is the hallmark of classical frustrated models. Two talks, by Shivaji Sondhi and Peter Holdsworth, focused specifically on the exotic spin-ice materials that are the magnetic analogs of the solid (ice) phase of water. They behave as collective paramagnets and display deconfined magnetic monopole states as excitations out of their otherwise topologically constrained states. Ashvin Vishwanath continued the overall theme by giving a masterful description of the novel types of magnetic order that can occur in frustrated spin and orbital systems. An experimental talk by Dan Stamper-Kurn described some of the beautiful effects, such as spontaneous magnetization, that can be studied in spinor Bose-Einstein condensates formed from super-cooled spin-1 quantum gases.

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