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

TL;DR

This study explores the critical phenomena near an SU(3) symmetric tri-critical point in a spin-1 chain, revealing BKT-like universality and phase boundaries modeled by the self-dual sine-Gordon theory.

Contribution

It identifies the tri-critical point among Haldane, trimer, and trimer liquid phases and characterizes the critical phenomena with conformal field theory and renormalization group analysis.

Findings

Verification of the tri-critical point among three phases.

Critical phenomena exhibit BKT-like universality.

Phase boundary described by self-dual sine-Gordon model.

Abstract

We investigate critical phenomena of a spin-1 chain in the vicinity of the SU(3) symmetric critical point, which we already specified in the previous study. We numerically diagonalize a Hamiltonian combining the bilinear-biquadratic (BLBQ) Hamiltonian with the trimer Hamiltonian. We then discuss the numerical results based on the conformal field theory (CFT) and the renormalization group. As a result, we firstly verify that the critical point found in our previous study is the tri-critical point among the Haldane phase, trimer phase, and the trimer liquid (TL) phase. Secondly, with regard to the TL--trimer transition and TL--Haldane transition, we find that the critical phenomena around this tri-critical point belong to the Berezinskii--Kosterlitz--Thouless (BKT)-like universality class. We thirdly find the boundary between the Haldane phase and the trimer phase, which is illustrated by the massive self-dual sine-Gordon (SDSG) model.