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a) I would like to ask, if knowledge about eigenvectors in second quantization is important and what do they mean? Let's just say, I create Fock space [(NumberOfSites)x(Permutations) matrix], then I solve Hubbard Hamiltonian [(NumberOfSites)x(NumberOfSites) matrix]. After diagonalisation of this Hamiltonian I get eigenvalues [Energies] and eigenvectors.How should I interpret these eigenvectors?

b) How can I know/calculate what phase does system has? Basically, how is someone able to tell which phase does system has just from Hamiltonian?

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    $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Jun 22, 2022 at 13:00

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Eigenvectors in second quantization play the same role as in the first quantization - mainly determining the physical properties of the system. In particular, the ground state (i.e., the lowest energy eigenvectors) is the subject of many studies, books, articles, etc.:Why is the ground state important in condensed matter physics?

If by saying "phase" you refer to phase transitions, then Hamiltonian itself does not determine a phase - it is determined by the (thermodynamics) state of the system. E.g., the system may go from one phase to another when temperature changes, while the Hamiltonian remains the same.

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  • $\begingroup$ Thank you. Your answer really helped me. $\endgroup$
    – QMAmateur
    Commented Jun 22, 2022 at 17:39

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