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Volumn 79, Issue 23, 2009, Pages

Low-energy theory of the t- t′ - T″ -U Hubbard model at half-filling: Interaction strengths in cuprate superconductors and an effective spin-only description of La2 CuO4

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EID: 68949104364     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.235130     Document Type: Article
Times cited : (71)

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    • Proof. [T1, MH†] =- t 2N i,j,k,σ, σ′ [ni σ̄ c iσ † cjσ hj σ̄, σ σ′] (-1) k, [T1, MH†] = - t 2N i,j,k,σ, σ′ ni σ̄ { [c iσ †, nk, σ′] cjσ + c iσ † [cjσ, nk, σ′] } × hj σ̄ σ σ, σ′ z (-1) k, hence, [T1, MH†] =- t 2N i,j,σ ni σ̄ c iσ † cjσ hj σ̄ [- (-1) i + (- 1j)] σ σ,σ z. Since (-1) i =- (-1) j for nearest neighbors, we get the final result and can generalize it for T-1 and T0.
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    • Proof. Same calculation as in Eqs. 48 49 50, but for second or third nearest neighbors, (-1) i = (-1) j.
    • Proof. Same calculation as in Eqs. 48 49 50, but for second or third nearest neighbors, (-1) i = (-1) j.
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    • We remark that a spin-only Hamiltonian can also be obtained for the three-band model [see Ref. and M. Roger and J. M. Delrieu, Phys. Rev. B 39, 2299 (1989)].
    • We remark that a spin-only Hamiltonian can also be obtained for the three-band model [see Ref. and M. Roger and J. M. Delrieu, Phys. Rev. B 39, 2299 (1989)].
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