Critical intermediate phase and phase transitions in a triangular-lattice three-spin interaction model: Level-spectroscopy approach

TL;DR

This paper studies infinite-order phase transitions in a triangular-lattice three-spin interaction model using field theory, renormalization-group analysis, and numerical verification to understand critical behavior and universal relations.

Contribution

It introduces a level-spectroscopy approach combined with field theory and numerical analysis to characterize phase transitions and symmetry enhancement in the model.

Findings

Identification of criteria for transition points

Universal relations among excitation levels

Verification of predictions via transfer matrix analysis

Abstract

We investigate infinite-order phase transitions like the Berezinskii-Kosterlitz-Thouless transition observed in a triangular-lattice three-spin interaction model. Based on a field theoretical description and the operator-production-expansion technique, we perform the renormalization-group analysis, and then clarify properties of marginal operators near the phase transition points. The results are utilized to establish criteria to determine the transition points and some universal relations among excitation levels to characterize the transitions. We verify these predictions via the numerical analysis on eigenvalue structures of the transfer matrix. Also, we discuss an enhancement of symmetry at the end points of a critical intermediate phase in connection with a transition observed in the ground state of the bilinear-biquadratic spin-1 chain.