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Quantum dimer model for the pseudogap metal

  1. Subir Sachdevd,e,1
  1. aInstitute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria;
  2. bInstitute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria;
  3. cPhysics Department, Ludwig-Maximilians-Universität München, 80333 Munich, Germany;
  4. dDepartment of Physics, Harvard University, Cambridge, MA 02138;
  5. ePerimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

  1. Contributed by Subir Sachdev, June 23, 2015 (sent for review May 14, 2015; reviewed by Antoine Georges and Masaki Oshikawa)

Significance

The most interesting states of the copper oxide compounds are not the superconductors with high critical temperatures. Instead, the novelty lies primarily in the higher temperature metallic “normal” states from which the superconductors descend. Here, we develop a simple, intuitive model for the physics of the metal at low carrier density, in the “pseudogap” regime. This model describes an exotic metal that is similar in many respects to simple metals like silver. However, the simple metallic character coexists with “topological order” and long-range quantum entanglement previously observed only in exotic insulators or fractional quantum Hall states in very high magnetic fields. Our model is compatible with many recent observations, and we discuss more definitive experimental tests.

Abstract

We propose a quantum dimer model for the metallic state of the hole-doped cuprates at low hole density, p. The Hilbert space is spanned by spinless, neutral, bosonic dimers and spin <mml:math><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mrow></mml:math>S=1/2, charge <mml:math><mml:mrow><mml:mo>+</mml:mo><mml:mi>e</mml:mi></mml:mrow></mml:math>+e fermionic dimers. The model realizes a “fractionalized Fermi liquid” with no symmetry breaking and small hole pocket Fermi surfaces enclosing a total area determined by p. Exact diagonalization, on lattices of sizes up to <mml:math><mml:mrow><mml:mn>8</mml:mn><mml:mo>×</mml:mo><mml:mn>8</mml:mn></mml:mrow></mml:math>8×8, shows anisotropic quasiparticle residue around the pocket Fermi surfaces. We discuss the relationship to experiments.

Footnotes

  • ↵1To whom correspondence should be addressed. Email: sachdev{at}g.harvard.edu.

  • Author contributions: M.P., A.A., and S.S. performed research; and M.P., A.A., and S.S. wrote the paper.

  • Reviewers: A.G., College de France; and M.O., Institute for Solid State Physics, University of Tokyo.

  • The authors declare no conflict of interest.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1512206112/-/DCSupplemental.

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