Question

Why doublons and holons are not bounded in spin-1/2 Hubbard chain?

Answer 1

The Hubbard model reads

H=−t∑⟨ij⟩,σc†jσciσ+U∑ini↑ni↓

In the large U limit and at half-filling, the Hubbard model tranforms to t-J model

H=−t∑⟨ij⟩,σc†jσciσ+J∑⟨ij⟩Si⋅Sj

where J=4t2/U. Obviously, ground state favors anti-parallel spin configurations but it is not obvious to see whether it is the Neel state (↑↓↑↓...)−(↓↑↓↑...) or the dimerized state (↑↓)(↑↓)... where (↑↓)=↑↓−↓↑. Calculation shows, in 1-D, dimerized state has lower energy (I'm not very clear about the calculation.)

It is also known that holon and doublon are not bounded in 1D (absence of Mott transition, Lieb-Wu's analytic result + VMC simulations). While in higher dimensions, Mott transitions do occur and dimerization is suppressed.

Answer 2

Heya...

See here for your answer...

===== In above attachment...

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