# 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

- Thomas Meier