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 three- or four-fold degenerate ground state wavefunctions, respectively. We numerically confirm the validity of both models using exact diagonalization and discuss the low lying excitations.

7 pages, 8 figures

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• Exact ground states for coupled spin trimers
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Covariance-based method for eigenstate factorization and generalized singlets
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