Haldane-Shastry like spin chains with open boundary condition and related vertex models

Quantum integrable spin chains with long-range interaction have found applications in diverse topics of physics like generalized exclusion statistics, N=4 super Yang-Mills gauge theory, infinite matrix product states related to conformal field theory and recent experiments involving optical lattices of ultra cold Rydberg atoms. In this talk we shall discuss how the motifs, which are suitable combinations of binary digits like 0 and 1, determine all energy levels appearing in the spectra of Haldane-Shastry (HS) like spin chains with long-range interaction. In particular, we shall derive the exact spectra and partition functions of some su(m) invariant HS like integrable spin chains with open boundary condition, whose ground state wave functions are obtained from the chiral correlator of the c=m-1 free boson boundary conformal field theory. Subsequently, we shall introduce some classical vertex models which exactly reproduce the spectra of such HS like quantum spin chains.