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As we know, the Zeeman splitting by magnetic field causes the energy difference between |↑> and |↓>, therefore states like |T+>=|↑↑> have a different energy from others. But why states like |S>=(|↑↓>-|↓↑>)/sqrt(2) and |T0>=(|↑↓>+|↓↑>)/sqrt(2) have energy differences? In this picture, T(0,2) must be in |T0> state, and it have different energy than |S(0,2)>.

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We are talking here about two-electron states, which means that we need to account for the Coulomb interaction. This interaction results in exchange energy, which means that the energy of the triplet states is different from the energy of the singlet even in absence of a magnetic field.

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  • $\begingroup$ Why coulomb interaction play a role here? |S(2,0)>and |T(2,0)> are both 2 electrons in the same dot here $\endgroup$
    – Lucas
    Commented May 20, 2021 at 15:17
  • $\begingroup$ Electrons are negatively charged and repel each other - one cannot ignore this interaction. Also, you have at least two orbital states here, spread between the two dots - but these do not appear in your expression for the singlet and the triplet states. $\endgroup$
    – Roger V.
    Commented May 20, 2021 at 15:31

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