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Hi guys! I am starting to study Hubbard model with application in DFT and I have some doubts how to solve the Hubbard Hamiltonian. I have the DFT modeled to Hubbard, where the homogeneous Hamiltonian is

$$ H = -t\sum_{\langle i,j \rangle}\sigma (\hat{c}_{i\sigma}^{\dagger}\hat{c}_{j\sigma} + H.c.) + \sum_i v_i^{eff} \hat{c}_{i\sigma}^{\dagger}\hat{c}_{i\sigma} $$

How do I diagonalize it?

Thanks in advance.

$$ H = -t\sum_{\langle i,j \rangle}\sigma (\hat{c}_{i\sigma}^{\dagger}\hat{c}_{j\sigma} + H.c.) + \sum_i v_i^{eff} \hat{c}_{i\sigma}^{\dagger}\hat{c}_{i\sigma} $$

How do I diagonalize it?

Thanks in advance.

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