Afternoon Session: DMFT

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Talks

  • Chair: Thomas Maier
  • Speakers
    • Thomas Meier
      • k-space formulation: makes no difference for single-site impurity
      • What state is obtained for the impurity model?
      • What's the debate about this phase diagram?
        • Short-range correlations increase towards larger cluster
        • Build cluster according to some criterion, which frustrates e.g. stripe order
      • Causality problems?
      • Where does it work?
        • Single-site DMFT in 2d: very bad -> always Kondo peak
        • Can be systematically improved to larger clusters, but that has bad sign problem
        • More test cases: ladders
        • Comparison to perturbation theory: fits nicely, e.g. 3d Hubbard
      • Is it giving the right answer somewhere?
        • 2d Hubbard model with regard to d-wave superconductivity
      • How does it compare to QMC directly on small lattices?
        • Weaker sign problem
        • Mean-field bath better than periodic system
      • Can it be generalized to spin models/bosons?
        • Spin model: Curie-Weiss MF
        • Frustration: cluster extensions
        • Bosons: not clear how it works; cannot be microscropically motivated
    • Matthias Troyer
    • Boris Svistunov
      • Always sign problem: even 1d and half filling
      • Extract energy from single-particle WF
      • Analytical expansion?
        • Usually only first order, maybe second
      • Error bars: DiagMC vs DMFT - better than DMFT?
        • Two guesses that agree
        • Some control in error bars, as opposed to DMFT
        • In 1d: compare to exact results; 2d?
      • Self-energy and k-dependence - check for DMFT?
      • Photoemission spectra?
        • Everything that can be expressed in diagrams
        • Dynamic quantities: one would want diagrams in frequency instead of imaginary time rep
    • Ian
      • Time comparison: minutes with QMC, hours with DMRG
      • Single impurity Anderson model -> Kondo physics, only in very large systems
        • Large number of sites in bath is possible (~120 right now)
        • Semi-infinite chain: infinite chain as boundary state
      • DMFT with ED: how does one get Kondo peak?
        • Broaden spectrum peaks -> looks like peak
      • Difference between 2d bath or 3d bath or infinity-d bath
        • Choice of momentum levels
        • Need evenly spaced levels for semi-infinite chain
      • Monte Carlo requires analytic continuation (MaxEnt)
      • Frequencies with DMRG are almost real, small continuation
      • How many states in continued-fraction-approach?
        • Probably in the hundreds...?
        • Many artefacts in spectral functions with this approach, no way of telling