Ordering of Energy Levels for Extended SU(N) Hubbard Chain

The Lieb-Mattis theorem on the antiferromagnetic ordering of energy levels is generalized to SU(N) extended Hubbard model with Heisenberg exchange and pair-hopping terms. It is proved that the minimum energy levels among the states from equivalent representations are nondegenerate and ordered according to the dominance order of corresponding Young diagrams. In particular, the ground states form a unique antisymmetric multiplet. The relation with the similar ordering among the spatial wavefunctions with different symmetry classes of ordinary quantum mechanics is discussed also

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

We expand the symmetry of the open finite-size SO(N) symmetric spin chain to O(N). We partition its space of states into the eigenspaces of the parity transformations in the flavor space, generating the subgroup $Z_2^{\times(N-1)}$. 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 $2^{N-1}$-fold degenerate ground state with fully broken parity-transformation symmetry.Comment: 11 pages, final versio

On Dunkl angular momenta algebra

We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincare-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N) version of the subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.Comment: 27 pages; small changes, concluding remarks expande