Paramagnetic metal and extrapolation errors

In this example we simulate the Hubbard model on the Bethe lattice with interaction $U=3D/\sqrt{2}$ at a temperature $\beta =32 \sqrt{2}/D$ using a paramagnetic self-consistency. We will calculate the self-energy and compare it to Fig. 15 in the DMFT review by Georges it et al., where Hirsch-Fye and Exact Diagonalization results are shown for the same system. In contrast to the Hirsch-Fye algorithm the two Continuous time Monte Carlo algorithms CT-HYB and CT-INT do not suffer from discretization errors and reproduce the ED-results.

The parameter files and python scripts are located in the subdirectories hyb and int of the directory tutorials/dmft-06-paramagnet in your ALPS install directory. You can run the simulations by executing (for the hybridization expansion version)

alpspython tutorial6a.py


(vispython on Mac) and (for the interaction expansion version)

alpspython tutorial6b.py


At each DMFT iteration $i$ the self-energy is written to the file selfenergy_i. Plot the converged self-energy and compare your results to Fig. 15 in Georges it et al.. Alternatively you may use the python script for this task as it is done in the tutorial ALPS 2 Tutorials:DMFT-02 Hybridization.