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Superconductivity through Quantum Critical Fluctuations in the ...

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Theory of <strong>the</strong> Loop OrderPhysics beyond <strong>the</strong> Hubbard ModelThree-Orbital Model with on-site and nearest neighbor Interactions.oocuUse Operator identity:Vn i n j = V/2 |J ij | 2 + n i + n j ).J ij = ic + i c j + H.C. ⇥ current operator <strong>in</strong> <strong>the</strong> l<strong>in</strong>k (i j)SupposeV2 < J ij >= x ij .Then effective k<strong>in</strong>etic energy parameter on <strong>the</strong> l<strong>in</strong>k (i j) ist ij + ix ij = |˜t ij |e ia ij.This is equivalent to a vector potentiala ijon <strong>the</strong> l<strong>in</strong>k (i j).

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