Topology-adapted modes

The detailed derivation of iTeff is given in Ref. [53]. Here, two of the six modes (i.e., X and X2) are chosen as topology-adapted modes that span the branching plane for a chosen pair of electronic states (here, states 1 and 2). Each /th-order residual term now also comprises 6 modes,... 

Here, a topology-adapted representation [55] was chosen, where (Xi,X2) lift the degeneracy at the intersection and thus span the branching plane [74], These modes are obtained by orthogonalizing the modes (X, Xa) of Eq. (10). The third mode Xg is in turn orthogonal to (Xi, ) and carries information on the intersection space, i.e., the X+ component of Eqs. (9)-(10). Alternative construction schemes are possible in particular, the bilinear coupling terms can be eliminated within the three-mode subspace [54,72]. 

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