Fig. 2: PO connectivity as hyperspins.
We show here the connectivity for N = D = 2. The POs xj with j = 1, 2, 3, 4 form two spins labeled by q = 1, 2 (black labels) with two components μ = 1, 2 each (red labels), where the indexes are related as \(\mu=1+(j-1){{{{{{{\rm{mod}}}}}}}}(D)\) and q = 1 + ⌊(j − 1)/D⌋. The indexes j are then grouped as \({{\mathbb{S}}}_{1}=\{1,\,2\}\) and \({{\mathbb{S}}}_{2}=\{3,\,4\}\). The linear coupling term Cjl between xj and xl with j ≠ l is decomposed as C13 = J12G11, C14 = J12G12, C23 = J12G21, and C24 = J12G22 (see legend), while C12 = C34 = 0. The amplitudes \({X}_{1}\equiv {X}_{1}^{(1)}\) and \({X}_{2}\equiv {X}_{2}^{(1)}\), and \({X}_{3}\equiv {X}_{1}^{(2)}\) and \({X}_{4}\equiv {X}_{2}^{(2)}\) form the μ = 1, 2 components of the q = 1 and q = 2 hyperspins, respectively, \({\overrightarrow{S}}_{1}=({X}_{1},\,{X}_{2})\) and \({\overrightarrow{S}}_{2}=({X}_{3},\,{X}_{4})\).
