Comment on "Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain"

TL;DR

This paper revisits the phase diagram of a spin-1 chain with complex interactions, confirming three phases and revealing new insights into the nature of phase transitions using advanced numerical and theoretical methods.

Contribution

It provides new evidence for the continuous nature of certain phase transitions and clarifies the universality class of the tri-critical point in the model.

Findings

Confirmed three phases: Haldane, NNN-Haldane, and dimerized.

Identified a continuous Ising transition between NNN-Haldane and dimerized phases.

Established the tri-critical end point's universality class as SU(2) level 2 WZW.

Abstract

The phase diagram of the spin-1 chain with bilinear-biquadratic and next-nearest neighbor inter- actions, recently investigated by Pixley, Shashi and Nevidomskyy [Phys. Rev. B 90, 214426 (2014)], has been revisited in the light of results we have recently obtained on a similar model. Combining extensive Density Matrix Renormalization Group (DMRG) simulations with conformal-field theory arguments, we confirm the presence of the three phases identified by Pixley et al, a Haldane phase, a next-nearest neighbor (NNN) Haldane phase, and a dimerized phase, but we come to significantly different conclusions regarding the nature of the phase transitions to the dimerized phase: i) We provide numerical evidence of a continuous Ising transition between the NNN-Haldane phase and the dimerized phase; ii) We show that the tri-critical end point, where the continuous transition between the Haldane phase and the dimerized phase turns into a first order transition, is distinct from the triple point where the three phases meet; iii) Finally, we demonstrate that the tri-critical end point is in the same Wess-Zumino-Witten (WZW) SU(2) level 2 universality class as the continuous transition line that ends at this point