A novel class of translationally invariant spin chains with long-range interactions

Abstract

We introduce a new class of open, translationally invariant spin chains with long-range interactions depending on both spin permutation and polarized spin reversal operators, which includes the Haldane-Shastry chain as a degenerate case. The new class is characterized by the fact that the Hamiltonian is invariant under "twisted" translations, combining an ordinary translation with a spin flip at one end of the chain. When the spin-spin interactions depend on the inverse square of the distance, we are able to compute in closed form the model's partition function and hence study several statistical properties of its spectrum. In particular, we show that this model possesses a highly degenerate spectrum, which suggests the existence of an underlying twisted Yangian symmetry.

Elliptic generalisation of integrable q-deformed anisotropic Haldane–Shastry long-range spin chain

“…A similar idea will be used in this paper for the case of supersymmetric R-matrices. There are extensions of the Haldane-Shastry model to different root systems [4] although we do not discuss them in this paper.…”