Some progress in Excitons

[muralidhar-nalabothula]

Key Additions:

• Introduced exciton_X_matelem function to compute generic exciton matrix elements of the form in a highly optimized way:
  $$\langle S, k+q | O | k, S' \rangle$$
  where $( O )$ represents an operator.

  • If $( O )$ corresponds to dvscf, this function will be used for exciton-phonon (ExPh) interactions.
  • If $( O )$ represents $( S_z )$, it computes the exciton spin.

• Currently, exciton spin calculations are implemented. The structure allows for easy extension to exciton-phonon interactions in future updates.

Future Work:

• Physical observables such as exciton representations and optical spectroscopies are not yet implemented but will be added in a later update. But basic functions such exction wfc rotations is implemented. So it is almost done

Additional Changes:

• Added new functions in the Letz database to support lazy loading from files, improving efficiency when handling large databases.
• Added a function get_Akcv in Exctiondb to convert from(neig,BS_table) format to meaningful (neig,k,c,v) format.

Example

import numpy as np
from yambopy.bse.exciton_spin import compute_exc_spin_iqpt

# Total spin
Sz_exe = compute_exc_spin_iqpt(bse_dir='GW_BSE', nstates=2)
print(Sz_exe)
## One could use a more general one incase they already loaded dbs 
## compute_exciton_spin(lattice, excdb, wfdb, elec_sz, contribution='b',diagonal=False)
#Compute only the electron spin contribution:

Sz_exe = compute_exc_spin_iqpt(bse_dir='GW_BSE', nstates=2, contribution='e')

#Compute only the hole spin contribution:

Sz_exe = compute_exc_spin_iqpt(bse_dir='GW_BSE', nstates=2, contribution='h')

[muralidhar-nalabothula]

Will reopen once everything is done

[muralidhar-nalabothula]

Following the discussion in #70 Reopened. Ready to be merged from my side. Please go ahead if every thing looks fine for you. This PR does not contain any exph implementation

1. Added full spin support too. all cases should work out of the box.

[palful]

Ok merged. Thank you. Thank you for also including the Crystal_Symmetries class, very instructive.