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Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors

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Modern Theories of Many-Particle Systems in Condensed Matter Physics

Part of the book series: Lecture Notes in Physics ((LNP,volume 843))

Abstract

I begin with a proposed global phase diagram of the cuprate superconductors as a function of carrier concentration, magnetic field, and temperature, and highlight its connection to numerous recent experiments. The phase diagram is then used as a point of departure for a pedagogical review of various quantum phases and phase transitions of insulators, superconductors, and metals. The bond operator method is used to describe the transition of dimerized antiferromagnetic insulators between magnetically ordered states and spin-gap states. The Schwinger boson method is applied to frustrated square lattice antiferromagnets: phase diagrams containing collinear and spirally ordered magnetic states, \(Z_2\) spin liquids, and valence bond solids are presented, and described by an effective gauge theory of spinons. Insights from these theories of insulators are then applied to a variety of symmetry breaking transitions in d-wave superconductors. The latter systems also contain fermionic quasiparticles with a massless Dirac spectrum, and their influence on the order parameter fluctuations and quantum criticality is carefully discussed. I conclude with an introduction to strong coupling problems associated with symmetry breaking transitions in two-dimensional metals, where the order parameter fluctuations couple to a gapless line of fermionic excitations along the Fermi surface.

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Acknowledgments

I thank Eun Gook Moon for valuable comments on the manuscript and for a collaboration [3] which led to Fig. 1.1, R. Fernandes, J. Flouquet, G. Knebel, and J. Schmalian, for providing the plots shown in Fig. 1.2, C. Ruegg for the plot shown in Fig. 1.7, and the participants of the schools for their interest, and for stimulating discussions. This research was supported by the National Science Foundation under grant DMR-0757145, by the FQXi foundation, and by a MURI grant from AFOSR.

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  1. Department of Physics, Harvard University, Cambridge,, MA, 02138,, USA

    Subir Sachdev

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  1. Subir Sachdev
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  1. , Departamento de Física/IFLP, Universidad Nacional de La Plata, La Plata, 1900, Argentina

    Daniel C. Cabra

  2. , Institut für Theoretische Physik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, Göttingen, 37077, Germany

    Andreas Honecker

  3. , Laboratoire de Physique Théorique, Université Paul Sabatier, Route de Narbonne 118, Toulouse Cedex 4, 31062, France

    Pierre Pujol

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Sachdev, S. (2012). Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors. In: Cabra, D., Honecker, A., Pujol, P. (eds) Modern Theories of Many-Particle Systems in Condensed Matter Physics. Lecture Notes in Physics, vol 843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10449-7_1

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