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One possible correction comes, for example, from the three-site terms arising in the strong coupling-limit expansion of the Hubbard model and omitted in the simplest t-J Hamiltonian (1) (see, e.g., Ref. 7). I have verified that those terms do not significantly contribute to the convexity of the ground-state energy as a function of doping, and therefore they do not affect the qualitative results on phase separation obtained in the simplified model (1).
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