Introduction¶

ctmo stands for Continuous time multi-orbital.

Sorry the docs are pretty bad for now.

Conventions¶

Comments¶

We use the convention “$” for the start of a shell command and “#” for commenting shell commands, etc.

Ex:: $ cd path/to/thing # change to the path of thing.

Executable names¶

There are two main executables: ctmo and ctmo_dca. The first executable uses the Cluster Dynamical mean field theory, whereas the second executable uses Dynamical mean field theory.

Hamiltonian¶

The hamiltonian is a density-density type hamiltonian with phonon coupling (Notice the + sign for the hopping term):

$H = \sum_{\rho \rho' \sigma} t_{\rho \rho'} c^\dagger_{\rho\sigma} c_{\rho'\sigma} + \sum_{r, \nu} U_{\nu, \nu} n_{r \nu \uparrow} n_{r \nu \downarrow} + \sum_{r \sigma, \nu < \nu'} U'_{\nu, \nu'} n_{r \nu \sigma} n_{r \nu' \bar{\sigma}} + \\ \sum_{r \sigma, \nu < \nu'} \left( U'_{\nu, \nu'} - J^H_{\nu, \nu'} \right) n_{r \nu \sigma} n_{r \nu' \sigma} + H_{\text{Phonons} }$

Important notes for the actual implementation:

For now, we permit a relatively generic hopping matrix.

The value of the interactions are not general yet, only one U, U’ and J_H are permitted for now.

Only one value (independant of the orbital index) is permitted for the phonon frequency and electron-phonon coupling.