The ordering of energy levels for image symmetric antiferromagnetic chains Original Research Article

The image symmetric antiferromagnetic finite chain with the fundamental representation and nearest-neighbor interaction is studied. A partial ordering between the lowest energy levels image in multiplet sectors corresponding to different Young tableaux image is established for the chains with arbitrary site-dependent couplings. For the open chains it is proved that image if image may be obtained from image moving down some of its boxes. In particular, the ground state of the chain belongs to the antisymmetric multiplet sector. For the rings the same condition is fulfilled if, in addition, all rows of image are of even or odd length. The ground state is image singlet if the chainʹs length is a multiple of n both for open and periodic chains. The results generalize the well known Lieb–Mattis theorem to chains with higher symmetries.