Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session Q57: The Fred Kavli Special Symposium: The Many Electron Problem -- Where are we now? |
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Sponsoring Units: APS Chair: Leon Balents, University of California, Santa Barbara Room: Four Seasons Ballroom |
Wednesday, March 5, 2014 2:30PM - 3:06PM |
Q57.00001: Magnetism as the emergent phenomena Invited Speaker: Yoshinori Tokura Versatile emergent phenomena have been observed in strongly correlated electron systems as a consequence of mutual strong coupling among the spin, orbital, and charge degrees of freedom. Here, we would overview the outcomes of topological spin textures in transport, dielectric, and optical properties of correlated systems; these include sciences of colossal magnetoresistance, multiferroics, skyrmions, and topological/quantum-anomalous Hall effects. Impacts of the emergent electric and magnetic fields acting on the electrons in a solid are discussed as well as their possible applications to future devices. [Preview Abstract] |
Wednesday, March 5, 2014 3:06PM - 3:42PM |
Q57.00002: Deciphering Electron Matter in Novel Superconductors Invited Speaker: Laura Greene Superconductors may be grouped into two major classes. The first is conventional metallic, whose pairing mechanism is explained by the BCS theory and electron-phonon coupling. The pairing mechanism of the second class, driven by electron correlations, is still to be completely worked out. These superconductors have electronic properties that are highly tunable, either by doping or pressure, from a non-superconducting ground state to a superconducting one, thus defining a superconducting ``dome'' in the phase diagram. More than 40 families of such superconductors, including high-temperature cuprate and iron-based, heavy fermion, organic, and transition-metal di-chalcogenide superconductors exhibit this ubiquitous phase diagram. All of these materials show intriguing correlated electron states above the dome, and researches agree that the understanding of this electron matter holds the key to the pairing mechanism, and ultimately predicative design of new superconductors, which hold great promise of revolutionary applications, including energy, information technology, and medicine. [Preview Abstract] |
Wednesday, March 5, 2014 3:42PM - 4:18PM |
Q57.00003: Correlated Electrons in Two Dimensions: The Fractional Quantum Hall Effect and More Invited Speaker: James Eisenstein A collection of electrons confined to move on a plane surface is surely one of the simplest many-body systems imaginable. But in spite of this apparent simplicity, a strong magnetic field applied perpendicular to the plane opens a door to a complex and beautiful world filled with many-body exotica. The magnetic field quenches the kinetic energy, leaving Coulomb interactions in control of the physics. The result has been a revolution in many-body physics comparable to that created by the discovery of superconductivity. Incompressible liquid ground states with fractionally charged quasiparticle excitations exhibit the quantized Hall effect at numerous discrete partial fillings of the lowest and first excited Landau level. The first examples of topological condensed matter, these many-body bulk insulators possess complex families of both conducting and neutral edge states at their boundaries. Highly correlated compressible phases of composite fermions also exist and may be viewed as progenitors of the various families of incompressible states. Multi-component two-dimensional systems with active discrete internal degrees of freedom (spin, layer, valley, etc.) display a wide array of broken symmetry states including ferromagnetism and exciton condensation. Now thirty years old, the field generically dubbed ``the fractional quantum Hall effect,'' remains extraordinarily vibrant. Once confined largely to GaAs/AlGaAs heterostructures, the fractional quantum Hall effect and its many relatives and offspring are now pursued in graphene, various oxide interfaces, and other materials. Some of the most fundamental aspects, including the exotic non-abelian quasiparticle statistics expected of some of the more subtle phases, have hardly been touched experimentally even as their potential for applications to quantum computation is alluring. In this talk, I will try to give a flavor of this enormous field, emphasizing current topics and possible future directions. [Preview Abstract] |
Wednesday, March 5, 2014 4:18PM - 4:54PM |
Q57.00004: Theoretical Approaches to Correlated Electron Problems Invited Speaker: Steven Kivelson Theoretical studies of the electronic properties of strongly correlated materials can rarely be both “realistic” and “controlled.” Despite the lack of a small parameter, astonishing success has been achieved by realistic approaches using various generalized forms of mean field theory including, most notably, local density approximation. I will instead discuss some of what has been learned by studying simple paradigmatic models, such as the Hubbard model, in limits in which the existence of a small parameter allows asymptotic control of the theory, and of “engineered” models, that are amenable to exact solution. This approach is ideal for establishing, as points of principle, what behaviors can exist. In some cases, invoking the principle of adiabatic continuity, the results can be extrapolated to a physically reasonable regime so that contact with experiment becomes plausible. [Preview Abstract] |
Wednesday, March 5, 2014 4:54PM - 5:30PM |
Q57.00005: Numerical studies of strongly correlated systems: beating the exponential growth in computation time Invited Speaker: Steven White In simulating strongly correlated systems, where approximate approaches based on small parameters are unreliable, the key problem is the exponential growth in computation time with system size, inverse temperature, or accuracy. For example, in exact diagonalization methods, the size of the vector describing the wavefunction has a length which is exponential in the number of sites. Progress in simulation methods has often involved removing this exponential for a certain class of problems. In quantum Monte Carlo, for example, for unfrustrated, half-filled Hubbard or Heisenberg models, the lack of a fermion sign problem eliminates the exponential, and large systems can be studied with high accuracy. In contrast, for most frustrated or doped systems, the expectation value of the sign falls exponentially and thus the computation time grows exponentially with the system size. The density matrix renormalization group eliminates the exponential for 1D systems. In this approach, the low entanglement of many-body ground states is exploited in a systematically improvable matrix product description of the wavefunction. For 2D systems, one is again faced with an exponential growth, but in a weaker form: an exponential of the width only, not the length. This weaker exponential has made DMRG the current method of choice for many 2D systems with a sign problem. Recently, the first approaches which appear to eliminate the exponential much more broadly have appeared, based on tensor networks such as projected entangled pair states (PEPS), which are closely related to DMRG. These methods also exploit the relatively low entanglement of ground states of realistic Hamiltonians. The computation time of these approaches, while non-exponential, is still quite high. Nevertheless, practical calculations with these methods are now becoming as good as DMRG and other approaches for 2D systems, and the methods are improving at a rapid rate. [Preview Abstract] |
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