Universality Class around the SU(3) Symmetric Point of the Dimer-Trimer Spin-1 Chain

TL;DR

This study investigates the critical behavior of SU(3) symmetric spin-1 chains near the symmetric point, revealing a BKT-like phase transition characterized by conformal field theory with central charge c=2.

Contribution

It numerically analyzes the Dimer-Trimer model around the SU(3) symmetric point, identifying the universality class and critical properties using conformal field theory.

Findings

Critical modes at q=0 and q=2π/3

System at PT point belongs to CFT with c=2

Phase transition is BKT-like from massive to massless phase

Abstract

We study critical phenomena of the SU(3) symmetric spin-1 chains when adding the SU(3) asymmetric term. To investigate such system, we numerically diagonalize the Dimer-Trimer (DT) model Hamiltonian around the SU(3) symmetric point, named the pure trimer (PT) point. We analyze our numerical results with the conformal field theory (CFT). First of all, we discover soft modes at the wave number q = 0 and q = 2{\pi}/3 for the PT point, and then the system is critical. Secondly, we find that the system at the PT point belongs to the CFT with the central charge c = 2 and the scaling dimension x = 2/3. Finally, by investigating the eigenvalues of the Hamiltonian in the vicinity of the PT point, we find that there is a phase transition at the PT point from a massive phase to a massless phase. From these numerical results, the phase transition at the PT point belongs to the Berezinskii-Kosterlitz-Thouless (BKT)-like universality class that is explained by the level-1 SU(3) Wess-Zumino-Witten (SU(3) 1 WZW) model.