Phase diagram of a bilinear-biquadratic spin-1 model on the triangular lattice from density matrix renormalization group simulations

TL;DR

This study uses DMRG simulations to map the phase diagram of a frustrated spin-1 model on a triangular lattice, revealing multiple magnetic and nematic phases and potential phase transitions.

Contribution

First comprehensive DMRG analysis of the phase diagram of a frustrated bilinear-biquadratic spin-1 model on the triangular lattice, identifying various ordered and nematic phases.

Findings

Identified three magnetically ordered phases: 120° spiral, stripe, and tetrahedral.

Discovered two spin nematic phases: ferroquadrupolar and antiferroquadrupolar.

Suggested a likely direct continuous transition between 120° spiral and antiferroquadrupolar phases.

Abstract

We investigate a highly frustrated spin-1 model on the triangular lattice, with nearest- and next-nearest-neighbor antiferromagnetic $S\cdot S$ interactions and nearest-neighbor $(S\cdot S)^2$ interactions. Using the density matrix renormalization group (DMRG) technique, we find three magnetically ordered phases, namely 120$^\circ$ spiral order, stripe order, and tetrahedral order, as well as two spin nematic phases: ferroquadrupolar and antiferroquadrupolar. While our data could be consistent with a spin liquid phase between the 120$^\circ$ spiral and antiferroquadrupolar orders, the more likely scenario is a direct continuous transition between these two orders.