This might be little geared towards physics but if anyone can help, it would so much helpful for me. So basically I want the matrix form of the following Hamiltonian ., where creates an electron at site i with spin σ which can be up (↑) or down (↓). For this I need the matrix form of the operators involved. For people who have been working with this type of Hamiltonian are aware that it follows aniti-commutation relations
What I can do now is that I can write the operators without the spin as below but i need help with the above when spin is also involved.
Is there anyway to do that. How should I go on to create the Hamiltonian for that. Are there any helpful packages to do that. Any help would be appreciated.