Phase transition of an SU(3) symmetric spin-1 chain

Abstract

We investigate a phase transition in an SU(3) symmetric spin-1 chain. To study this transition, we numerically diagonalize an SU(3) symmetric Hamiltonian combining the Uimin-Lai-Sutherland (ULS) model Hamiltonian with the Hamiltonian of the exact trimer ground state (${\mathbb{Z}}_{3}$ symmetry breaking). Our numerical results are discussed on the basis of the conformal field theory (CFT) and the renormalization group (RG). We then show the phase transition between a trimer liquid phase (massless, no long-range order) and a trimer phase (spontaneously ${\mathbb{Z}}_{3}$ symmetry breaking). Next, we find the central charge $c=2$ in the massless phase, and $c<2$ in the ${\mathbb{Z}}_{3}$ symmetry broken phase. From these results, we identify the universality class of the critical trimer liquid phase, as well as the phase boundary between these two phases.