Frequently Asked Questions

• What type of Coulomb repulsion uses the code? How do I check if the form is what I think it is?
  Answer: Here is a note on the Coulomb repulsion, which should help. cdmft
• How is self-energy computed in CTQMC?
  Answer: We use the property of the two particle vertex function and its relation to the self-energy, when using "S" mode. "G" mode uses Dyson equation, and computes self-energy just from the knowledge of the Greens function.
  The high frequency moments are computed by high frequency expansion.
• How is the two particle vertex implemented in CTQMC
  Answer: Here is a short documentation of the two particle vertex function
  
  
• What is the exact double-counting, and how is it implemented?
  Answer: The exact double-counting can be derived from the DFT+DMFT Luttinger-Ward functional. If one applies both the LDA and the DMFT approximation on the exact Luttinger-Ward functional, one obtains the intersection, which is the exact double-counting. This was derived in PRL 115, 196403 (2015).
  To understand this point better, here is a very short presentation with some equations.
  Finally, to implement the exact double-counting, one needs to solve the electron-gas problem, which interacts with the screened Coulomb repulsion. The best would be to solve this with Monte Carlo, but in the absence of MC results, the GW results can be used as a reasonable approximation (but only for the ration between the unscreened and screened correlation). The results of such a GW calculations, can be found here:
  • Step 1: Solution of the electron gas (jellium model) with GW (G0W0).
  • Step 2: Computing the correlation energy from the solution of GW problem for electron gas.
  • Step 3: Fit of the correlation energy to an analytic expression.