Spin-1 magnets — a u(3) formalism

Spin-1 magnets include dipolar and quadrupolar moments on a single site, which allow for novel properties as seen in spin nematic phases [1], Fe-based superconductors [2] and cold atom systems [3].

However, such unconventional phases can be found hard to probe experimentally, and therefore require new theoretical tools to describe and interpret their ground state and excitation properties.

In this talk, we extend the commonly used algebra for spin-1 moments from su(3) to u(3) [4], and derive equations of motions well suited for numerical implementation.

We benchmark our method by studying the ferroquadrupolar phase of the spin-1 bilinear-biquadratic (BBQ) model on the triangular lattice, and find a perfect match between our formalism and analytical flavour-wave theory complemented by low-temperature expansion.

Furthermore, we show the application of our method to dynamics of topological defects and spin liquids in spin-1 magnets.

 

[1] H. Tsunetsugu and M. Arikawa, J. Phys. Soc. Jpn 75, 083701 (2006)

[2] R. M. Fernandes, A. V. Chubukov, and J. Schmalian, Nature Physics 10, 97 EP (2014)

[3] E. Demler and F. Zhou, Phys. Rev. Lett. 88, 163001 (2002)

[4] N. Papanicolaou, Nuclear Physics B 305, 367 (1988)