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

Abstract

We study critical phenomena of the SU(3) symmetric spin-1 chains when adding the SU(3) asymmetric term. To investigate such phenomena, 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 on the basis of the conformal field theory (CFT). First of all, we discover soft modes at the wave number q = 0 and q = ±2π/3 for the PT point, and then the system is critical. Secondly, we find that the system at the PT point can be described by 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.

Critical phenomena around the SU(3) symmetric tricritical point of a spin-1 chain

“…Also, the universality class is BKT-like with c = 2 and x = 2/3 [13]. There are several numerical calculations [8,21,22,38,39] on this phase transition. Therefore, we do not do the numerical calculation in this paper.…”

Critical phenomena around the SU(3) symmetric tri-critical point of a spin-1 chain

“…Also, the universality class is the BKTlike with c = 2 and x = 2/3 [13]. There are several numerical calculations [8,18,20,39,40] on this phase transition. Therefore, we do not do the numerical calculation in this paper.…”

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

“…( 3) is composed only of the exchange operators, which conserves the number of spins, N1, N0, N−1 for each state S z = 1, 0, −1 respectively. Then, the full Hilbert space with 3 N dimensions is reduced to a subspace [6] with…”

“…As for the SU(3) symmetric spin-1 chains, there have been several studies investigating the critical phenomena and the universality class. It was found that the ground state is the critical trimer liquid (TL) state with no long-range order, in the cases of the Uimin-Lai-Sutherland (ULS) model [1][2][3][4] and the SU(3) symmetric Dimer-Trimer (DT) model [5,6]. In general, critical phases of SU(ν) symmetric quantum spin chains (ν: integer) is stabilized by the Zν symmetry [7,8], the center of the SU(ν) group.…”