Quantum Phase Transitions of Antiferromagnets and the Cuprate Superconductors

  • Subir SachdevEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 843)


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.


Fermi Surface Quantum Phase Transition Dirac Fermion Quantum Critical Point Spin Density Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of PhysicsHarvard UniversityCambridge,USA

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