Exact models for trimerization and tetramerization in spin chains

Abstract

We present exact models for an antiferromagnetic $S=1$ spin chain describing trimerization as well as for an antiferromagnetic $S=3/2$ spin chain describing tetramerization. These models can be seen as generalizations of the Majumdar-Ghosh model. For both models, we provide a local Hamiltonian and its exact threefold or fourfold degenerate ground state wave functions, respectively. We numerically confirm the validity of both models using exact diagonalization and discuss the low-lying excitations.