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Introduction to Frustrated Magnetism pp 23–41Cite as

Introduction to Quantum Spin Liquids

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Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 164))

Abstract

In SU(2)-invariant spin models with frustrated interactions and low spin quantum number, long-ranged magnetic order and breaking of the SU(2) symmetry is not the most general situation, especially in low dimensions. Many such systems are, loosely speaking, “quantum paramagnets” down to zero temperature, states conveniently represented in terms of spins paired into rotationally invariant singlets, or “valence bonds” (VBs). In this large family of states, at least two very different physical phases should be distinguished, valence bond crystals (or solids) and resonating-valence-bond (RVB) liquids.

This chapter provides a basic introduction to the concept of short-range resonating-valence-bond (srRVB) states, and emphasizes the qualitative differences between VB crystals and RVB liquids. We explain in simple terms why the former sustain only integer-spin excitations while the latter possess \(\rm spin-\frac{1} {2}\) excitations (the property of fractionalization). We then elaborate qualitatively on the notion of macroscopic quantum resonances, which are behind the ‘R’ of the RVB spin liquid, to motivate the idea that spin liquids are not disordered systems but possess instead hidden quantum order parameters. After giving a brief list of models and materials of current interest as candidate spin liquids, we conclude by mentioning the role of the parity of the net spin in the unit cell (half-odd-integer or integer) in spin-liquid formation, by recalling the contrasting results for kagomé and pyrochlore lattices.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, case courrier 121, 4 place Jussieu, 75252, Paris cedex 05, France

    Claire Lhuillier

  2. Institut de Physique Théorique, Orme des Merisiers batiment 774, Point courrier 136, CEA/DSM/IPhT, CEA/Saclay, 91191, Gif-sur-Yvette Cedex, France

    Grégoire Misguich

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  1. Claire Lhuillier
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Correspondence to Claire Lhuillier .

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Editors and Affiliations

  1. Laboratoire Louis Néel, CNRS, Grenoble CX, France

    Claudine Lacroix

  2. CNRS, Labo. Physique Solides, Université Paris-Sud XI, Orsay CX, 91405, France

    Philippe Mendels

  3. Inst. Physique Théorique, Ecole Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland

    Frédéric Mila

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Lhuillier, C., Misguich, G. (2011). Introduction to Quantum Spin Liquids. In: Lacroix, C., Mendels, P., Mila, F. (eds) Introduction to Frustrated Magnetism. Springer Series in Solid-State Sciences, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10589-0_2

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