Equations of motions for spin-1 magnets — a u(3) formalism, suitable to investigate dynamical and thermodynamical properties*

Spin-1 magnets include dipolar and quadrupolar moments on a single site, which allow for novel, unconventional phases, such as spin nematics [Blume69].

However, those phases are invisible to conventional probing and require special theoretical tools, in order to interpret and understand their ground state and excitation properties. [Andreev84, Barzykin91]

In this talk, we extend the commonly used su(3) algebra for spin-1 moments to the u(3) Algebra [Papanicolaou88], treating dipolar and quadrupolar degrees of freedom on an equal footing, and derive equations of motion, which take a simple form and are well suited for numerical implementation.

Illustrating our new method to the ferro-quadrupolar phase of the spin-1 bilinear-biquadratic Hamiltonian on the triangular lattice [Lauchli06], we successfully match zero-temperature flavor-wave theory to classical low-temperature expansion results, enabling us to accurately describe the implementation of our method to classical Monte Carlo and Molecular Dynamics simulations. Moreover, through simulations, we discovered the existence of a vortex bound state pair phase at finite temperature, allowing us to study topological defects in spin nematics.