Spin Chain Hamiltonians with Affine $U_q g$ symmetry

TL;DR

This paper constructs a family of spin chain Hamiltonians with affine quantum group symmetry, revealing their spectral properties and degeneracies related to affine and non-affine symmetries.

Contribution

It introduces a new class of spin chain Hamiltonians with affine $U_q g$ symmetry and analyzes their spectral degeneracies compared to non-affine cases.

Findings

Eigenvalues match those of non-affine $U_q g_0$ symmetric chains.

Degeneracy levels are characterized by affine $U_q g$ symmetry.

States are formed by tensor products of fully reducible representations.

Abstract

We construct the family of spin chain Hamiltonians, which have affine $U_q g$ guantum group symmetry. Their eigenvalues coincides with the eigenvalues of the usual spin chain Hamiltonians which have non-affine $U_q g_0$ quantum group symmetry, but have the degeneracy of levels, corresponding to affine $U_q g$. The space of states of these chaines are formed by the tensor product of the fully reducible representations.