Lowest-energy states in parity-transformation eigenspaces of SO(N)SO(N) spin chain

We expand the symmetry of the open finite-size SO(N)SO(N) symmetric spin chain to O(N)O(N). We partition its space of states into the eigenspaces of the parity transformations in the flavor space, generating the subgroup Z2×(N−1). It is proven that the lowest-energy states in these eigenspaces are nondegenerate and assemble in antisymmetric tensors or pseudotensors. At the valence-bond solid point, they constitute the 2N−12N−1-fold degenerate ground state with fully broken parity-transformation symmetry.