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

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

arXiv comment4 pages, 6 figures

References in corpus (6)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Entanglement entropy and conformal field theory
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Dimerization transitions in spin-1 chains
• Frustration and Multicriticality in the Antiferromagnetic Spin-1 Chain

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