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This introduces a small nuance that E i can no longer be treated as a scalar but must be considered as a matrix that depends on the initial and final spin states (but independent of the intermediate states). However, the off-diagonal terms of this matrix is of order t / U and hence negligible.
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j〉 for next- and next-next-nearest neighbors are needed. From the DSL ansatz these must be real, equal in magnitude, but vary in signs. We determine the signs using numerical calculations as a shortcut. It turns out that the cancellation holds separately for next-nearest neighbor terms and next-next-nearest ones. Thus the determination of signs is adequate for reaching our conclusion
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j〉 for next- and next-next-nearest neighbors are needed. From the DSL ansatz these must be real, equal in magnitude, but vary in signs. We determine the signs using numerical calculations as a shortcut. It turns out that the cancellation holds separately for next-nearest neighbor terms and next-next-nearest ones. Thus the determination of signs is adequate for reaching our conclusion.
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Since the photon momentum is small, we can ignore distances at the lattice scale. Thus, the precise definition of rijk do not concern us
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Since the photon momentum is small, we can ignore distances at the lattice scale. Thus, the precise definition of r i j k do not concern us.
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