- #1
Amentia
- 110
- 5
Hello,
I am currently struggling to understand how one can write a Hamiltonian using group theory and change its form according to the symmetry of the system that is considered. The main issue is of course that I have no real experience in using group theory.
So to make my question a bit less general, take for example this article:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.6.3836
What I would like to understand is how we see that some matrices transform as a given representation, for example here they say the spin 1/2 matrices transform as Gamma 4 for the Td symmetry (3rd page). And how to use it to write the final Hamiltonian we want to obtain? I would like to be able to do that with any direction of magnetic field, stress or whatever applied to a given structure with any initial symmetry...
All the articles I try to understand that make use of group theory for such purposes just state the result as if there were obvious just by looking at the matrix of interest and the character table. Which must be the case but I do not see it.
I do not know if my question is clear. But any help is welcome.
Best regards!
I am currently struggling to understand how one can write a Hamiltonian using group theory and change its form according to the symmetry of the system that is considered. The main issue is of course that I have no real experience in using group theory.
So to make my question a bit less general, take for example this article:
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.6.3836
What I would like to understand is how we see that some matrices transform as a given representation, for example here they say the spin 1/2 matrices transform as Gamma 4 for the Td symmetry (3rd page). And how to use it to write the final Hamiltonian we want to obtain? I would like to be able to do that with any direction of magnetic field, stress or whatever applied to a given structure with any initial symmetry...
All the articles I try to understand that make use of group theory for such purposes just state the result as if there were obvious just by looking at the matrix of interest and the character table. Which must be the case but I do not see it.
I do not know if my question is clear. But any help is welcome.
Best regards!