Exact models for trimerization and tetramerization in spin chains

TL;DR

This paper introduces exact models for antiferromagnetic spin chains exhibiting trimerization and tetramerization, providing explicit Hamiltonians and ground states, and confirming their properties through numerical methods.

Contribution

It presents new exactly solvable models for spin chains with trimerization and tetramerization, extending the Majumdar-Ghosh model with explicit Hamiltonians and ground states.

Findings

Exact local Hamiltonians for trimerized and tetramerized chains

Degenerate ground state wavefunctions explicitly constructed

Numerical confirmation of model validity and analysis of excitations

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.