Spin dynamics of the bilinear-biquadratic $S=1$ Heisenberg model on the triangular lattice: a quantum Monte Carlo study

TL;DR

This study employs quantum Monte Carlo simulations to analyze the thermodynamic and dynamical properties of the spin-1 Heisenberg model with bilinear-biquadratic interactions on a triangular lattice, revealing Goldstone modes and phase behaviors.

Contribution

It introduces a sign-problem-free quantum Monte Carlo method to explore both ordered and symmetric phases of the model, providing new insights into low-energy excitations.

Findings

Identification of Goldstone soft-modes in structure factors

Comparison of excitations with thermodynamic data and flavor-wave theory

Characterization of phase boundaries and excitations in the model

Abstract

We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compared to the thermodynamic behavior observed at finite temperatures as well as to Schwinger-boson flavor-wave theory.