Orbital dependent dynamical part of two body interaction

[johanjoensson]

Hello!

I was wondering if there is a way to include a orbital dependent dynamical two body interaction?

Is there a way of doing something similar to how the hybridisation function is set up?

Best regards
Johan Jönsson

[cmelni]

Hello Johan,

ComCTQMC can construct dynamical two-body interactions out of quantum number operators of the form

Q = \sum_i q_i c^\dagger_i c_i

where c^\dagger_i c_i is the number operator for orbital i and q_i is the associated quantum number. We require these commute with the Hamiltonian, i.e., are conserved in every sector of the Hilbert space. The user guide Eqs. (4-5), (9-11) provide some additional detail. Of course, this is typically much more restrictive than the hybridization functions, which are constructed directly from the creation and annihilation operators of the orbitals.

More concretely, one can always generate dynamical two-body interactions which depend on the total number of particles N, and often on S or J / J^2 (in a non spin orbit coupled or a spin orbit coupled basis, respectively; depending on the precise details of your basis and Hamiltonian). With no off-diagonal elements in the one-body Hamiltonian and a density-density static two-body interaction, I think it would be possible to make a fully orbital dependent and dynamical two-body interaction (which is also restricted to density-density terms). However, I have no experience trying to do this and I'm not sure if its been attempted. If you try to do so and encounter problems, let me know and I can take a closer look.

Cheers,
Corey

[johanjoensson]

Thank you very much for this great answer!

If I encounter any problems, I will contact you again.

Regards
Johan