DMFT-07 Hirsch-Fye

Tutorial 07: Hirsch Fye Code

We start by running a discrete time Monte Carlo code: the Hirsch Fye code. As an example we reproduce Fig. 11 in the DMFT review by Georges it et al.. The series of six curves shows how the system, a Hubbard model on the Bethe lattice with interaction $U=3D/\sqrt{2}$ at half filling, enters an antiferromagnetic phase upon cooling.

The Hirsch Fye algorithm is described in here, and this review also provides an open source implementation for the codes. More information can also be found in Blümer’s PhD. While many improvements have been developed (see e.g. Alvarez08 or Nukala09), the algorithm has been replaced by continuous-time algorithms eliminating systematic discretization errors.

The Hirsch Fye simulation will run for about 20 seconds per iteration. The python scripts for running this simulation can be found in the directory tutorials/dmft-07-hirschfye, a short version tutorial7.py running simulations at 2 temperatures only (takes 5 minutes) or a version reproducing all 6 temperatures tutorial7_long.py. For evaluation you may use the same script tutorial2eval.py as it is described in the tutorial ALPS_2_Tutorials:DMFT-02_Hybridization.

The main parameters are same as those described in the tutorial ALPS_2_Tutorials:DMFT-02_Hybridization.

As a discrete time method, HF suffers from $\Delta\tau$ - errors. Pick a set of parameters and run it for sucessively larger N.

Tutorial by Emanuel - Please don’t hesitate to ask!

Contributors

-Emanuel Gull