Topological quantum phase transition in an S=2 spin chain

We construct a model Hamiltonian for S = 2 spin chain, where a variable parameter $\alpha$ is introduced. The edge spin is S = 1 for $\alpha = 0$, and S = 3/2 for $\alpha = 1$. Due to the topological distinction of the edge states, these two phases must be separated by one or several topological quantum phase transitions. We investigate the nature of the quantum phase transition by DMRG calculation, and propose a phase diagram for this model.Comment: 5 pages, 4 figure