Ground-state study of the spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice using tensor networks

• Published in: Physical review. B 2018-06, Vol.97 (24), Article 245146
• Main Authors: Niesen, Ido, Corboz, Philippe
• Format: Article
• Language: English
• Subjects: Ferromagnetism; Heisenberg theory; Phase diagrams; Phase transitions; Statistical models
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.97.245146

Making use of infinite projected entangled pair states, we investigate the ground-state phase diagram of the nearest-neighbor spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice. In agreement with previous studies, we find the ferromagnetic, 120∘ magnetically ordered, ferroquadrupolar and antiferroquadrupolar phases, and confirm that all corresponding phase transitions are first order. Moreover, we provide an accurate estimate of the location of the ferroquadrupolar to 120∘ magnetically ordered phase transition, thereby fully establishing the phase diagram. Also, we do not encounter any signs of the existence of a quantum paramagnetic phase. In particular, contrary to the equivalent square lattice model, we demonstrate that on the triangular lattice the one-dimensional Haldane phase does not reach all the way up to the two-dimensional limit. Finally, we investigate the possibility of an intermediate partially magnetic partially quadrupolar phase close to θ=π/2, and we show that, also contrary to the square lattice case, this phase is not present on the triangular lattice.