Spin-1 magnets — a u(3) formalism

Systems based on spin-1 moments exhibit many fascinating properties, as demonstrated by spin nematics [1,2], Fe-based superconductors [3], and cold atom systems [4]. However, because spin-1 moments support quadrupoles, they cannot be described using O(3) vectors, even in the classical limit.



In this talk, we explore a new approach which correctly describes the (semi-)classical physics of spin-1 moments [5]. This approach, based on the algebra u(3) [6], provides a convenient starting point for Monte Carlo and molecular dynamics simulations, as well as for analytic theory. We benchmark our method by applying it to the ferroquadrupolar phase of the spin-1 bilinear-biquadratic model on the triangular lattice [5], reproducing and extending known results [1,2].



These results open the prospect of exploring dynamical properties of spin-1 magnets which lie outside the spin-wave paradigm, including spin-liquid phases, and the dynamics of topological excitations.



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

[2] A. Laeuchli et al, Phys. Rev. Lett. 97, 087205 (2006)

[3] R. M. Fernandes et al., Nature Physics 10, 97 EP (2014)

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

[5] K. Remund et al., Phys. Rev. Research 4 033106 (2022)

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