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

TL;DR

This study uses tensor network methods to map the ground state phases of the spin-1 bilinear-biquadratic Heisenberg model on a triangular lattice, confirming known phases and clarifying phase boundaries without evidence of a quantum paramagnetic phase.

Contribution

It provides a comprehensive phase diagram of the model on the triangular lattice, accurately locating phase transitions and ruling out certain intermediate phases, advancing understanding of lattice-dependent quantum magnetism.

Findings

Confirmed ferromagnetic, 120° magnetic, ferroquadrupolar, and antiferroquadrupolar phases.

Established first-order phase transitions between these phases.

Found no evidence of a quantum paramagnetic phase or intermediate partially-magnetic phases.

Abstract

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 degree 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 degree 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 $\theta = \pi/2$, and we show that, also contrary to the square lattice case, this phase is not present on the triangular lattice.