General remarks on the Hubbard model in the strong coupling limit

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Karim Chahine

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Karim Chahine Asks: General remarks on the Hubbard model in the strong coupling limit
Some results are known for the Fermi-Hubbard model under certain assumptions. For instance, it is known that at half-filling and in the strong coupling limit, the Hubbard model reduces to a Heisenberg antiferromagnet. For reference, the Hubbard model is: \begin{equation} H = -t\sum_{\langle ij \rangle\sigma}c^\dagger_{i\sigma}c_{j\sigma}+U\sum_i n_{i\uparrow}n_{i\downarrow} \end{equation}

I'm wondering: is it possible to make general remarks on how the ground state of the system behaves by increasing the on-site interaction $U$? What I'm looking for is some basic predictions on, say, how the densities on a given lattice might evolve if $U/t$ gets higher regardless of the filling or the specific lattice.

In general, $U$ favours having a non-zero spin on each site and thus one might expect that for any lattice and any filling a sort of antiferromagnetic configuration emerges as the ground state at high $U$. Is it fair to say so? Can we say anything else? I hope the question isn't too generic.

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SolveForum.com may not be responsible for the answers or solutions given to any question asked by the users. All Answers or responses are user generated answers and we do not have proof of its validity or correctness. Please vote for the answer that helped you in order to help others find out which is the most helpful answer. Questions labeled as solved may be solved or may not be solved depending on the type of question and the date posted for some posts may be scheduled to be deleted periodically. Do not hesitate to share your thoughts here to help others.

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Code:
plt.ioff()
fig = plt.figure(figsize=(50, 25))

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Thanks in advance

SolveForum.com may not be responsible for the answers or solutions given to any question asked by the users. All Answers or responses are user generated answers and we do not have proof of its validity or correctness. Please vote for the answer that helped you in order to help others find out which is the most helpful answer. Questions labeled as solved may be solved or may not be solved depending on the type of question and the date posted for some posts may be scheduled to be deleted periodically. Do not hesitate to share your thoughts here to help others.

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