Afternoon Session: DMFT

From ALPS

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