Local dynamical lattice instabilities: Prerequisites for resonant pairing superconductivity

Fluctuating local diamagnetic pairs of electrons, embedded in a Fermi sea, are candidates for non-phonon-mediated superconductors without the stringent conditions on Tc which arise in phonon-mediated BCS classical low-Tc superconductors. The local accumulations of charge, from which such diamagnetic fluctuations originate, are irrevocably coupled to local dynamical lattice instabilities and form composite charge-lattice excitations of the system. For a superconducting phase to be realized, such excitations must be itinerant spatially phase-coherent modes. This can be achieved by resonant pair tunneling in and out of polaronic cation-ligand sites. Materials in which superconductivity driven by such local lattice instability can be expected, have a Tc which is controlled by the phase stiffness rather than the amplitude of the diamagnetic pair fluctuations. Above Tc, a pseudogap phase will be maintained up to a T*, where this pairing amplitude disappears. We discuss the characteristic local charge and lattice properties which characterize this pseudogap phase and which form the prerequisites for establishing a phase-coherent macroscopic superconducting state.Comment: 15 pages, 13 figure

The quantum phases of matter

I present a selective survey of the phases of quantum matter with varieties of many-particle quantum entanglement. I classify the phases as gapped, conformal, or compressible quantum matter. Gapped quantum matter is illustrated by a simple discussion of the Z_2 spin liquid, and connections are made to topological field theories. I discuss how conformal matter is realized at quantum critical points of realistic lattice models, and make connections to a number of experimental systems. Recent progress in our understanding of compressible quantum phases which are not Fermi liquids is summarized. Finally, I discuss how the strongly-coupled phases of quantum matter may be described by gauge-gravity duality. The structure of the large N limit of SU(N) gauge theory, coupled to adjoint fermion matter at non-zero density, suggests aspects of gravitational duals of compressible quantum matter.Comment: 35 pages, 21 figures; Rapporteur presentation at the 25th Solvay Conference on Physics, "The Theory of the Quantum World", Brussels, Oct 2011; (v2+v3+v4) expanded holographic discussion and referencin

Resonating singlet valence plaquettes

We consider the simplest generalizations of the valence bond physics of SU(2) singlets to SU(N) singlets that comprise objects with N sites -- these are SU(N) singlet plaquettes with N=3 and N=4 in three spatial dimensions. Specifically, we search for a quantum mechanical liquid of such objects -- a resonating singlet valence plaquette phase that generalizes the celebrated resonating valence bond phase for SU(2) spins. We extend the Rokhsar-Kivelson construction of the quantum dimer model to the simplest SU(4) model for valence plaquette dynamics on a cubic lattice. The phase diagram of the resulting quantum plaquette model is analyzed both analytically and numerically. We find that the ground state is solid everywhere, including at the Rokhsar-Kivelson point where the ground state is an equal amplitude sum. By contrast, the equal amplitude sum of SU(3) singlet triangular plaquettes on the face centered cubic lattice is liquid and thus a candidate for describing a resonating single valence plaquette phase, given a suitably defined local Hamiltonian.Comment: 12 pages, 15 figures, minor changes, references added, Phys Rev B versio

Two-dimensional quantum antiferromagnets

This review presents some theoretical advances in the field of quantum magnetism in two-dimensional systems, and quantum spin liquids in particular. It is to be published as a chapter in the second edition of the book "Frustrated spin systems", edited by H. T. Diep (World-Scientific). The section (Sec. 7) devoted to the kagome antiferromagnet has been completely rewritten/updated, as well as the concluding section (Sec. 8). The other sections (Secs. 1-6) are unchanged from the first edition of the book (published in 2005)Comment: 87 pages. 396 references. To be published as a chapter in the second edition of the book "Frustrated spin systems", edited by H. T. Diep (World-Scientific

Magnetization plateaus of an easy-axis Kagom\'e antiferromagnet with extended interactions

We investigate the properties in finite magnetic field of an extended anisotropic XXZ spin-1/2 model on the Kagome lattice, originally introduced by Balents, Fisher, and Girvin [Phys. Rev. B, 65, 224412 (2002)]. The magnetization curve displays plateaus at magnetization m=1/6 and 1/3 when the anisotropy is large. Using low-energy effective constrained models (quantum loop and quantum dimer models), we discuss the nature of the plateau phases, found to be crystals that break discrete rotation and/or translation symmetries. Large-scale quantum Monte-Carlo simulations were carried out in particular for the m=1/6 plateau. We first map out the phase diagram of the effective quantum loop model with an additional loop-loop interaction to find stripe order around the point relevant for the original model as well as a topological Z2 spin liquid. The existence of a stripe crystalline phase is further evidenced by measuring both standard structure factor and entanglement entropy of the original microscopic model.Comment: 14 pages, 14 figure