We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with ``true'' spin-orbit coupling, involving spin-changing hoppings.We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with ``true'' spin-orbit coupling, involving spin-changing hoppings.

arXiv:1408.0769Physical Review BNov 17, 201424 citations

A transformation of lattice spin operators

H. J. Hilhorst

Physics Letters AMay 1, 19741 citation

Emergent SU(3) symmetry in a four-leg spin tube

E. Orignac

We consider an antiferromagnetic four-leg spin-1/2 tube using Abelian and non-Abelian bosonization. We show that in the limit of weak interchain coupling, the most relevant interaction gives rise to an emergent $\mathrm{SU}(3)$ symmetry, broken only by marginal interactions that can be canceled by diagonal interchain couplings. We discuss the low-energy spectrum in the semiclassical limit and using a mapping to a trimerized $\mathrm{SU}(3)$ spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.We consider an antiferromagnetic four-leg spin-1/2 tube using Abelian and non-Abelian bosonization. We show that in the limit of weak interchain coupling, the most relevant interaction gives rise to an emergent $\mathrm{SU}(3)$ symmetry, broken only by marginal interactions that can be canceled by diagonal interchain couplings. We discuss the low-energy spectrum in the semiclassical limit and using a mapping to a trimerized $\mathrm{SU}(3)$ spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.

arXiv:2402.11927Physical review. B./Physical review. BMay 16, 20240 citations

The most general representation of spin operators via boson operators

Vladimir Chernyak

Physics Letters AMar 1, 19925 citations

Quantum Spin Systems and Their Operator Algebras

Pedro de M. Rios, Eldar Straume

Springer eBooksJan 1, 20140 citations

\mathrm{SU}(3)

symmetry, broken only by marginal interactions that can be canceled by diagonal interchain couplings. We discuss the low-energy spectrum in the semiclassical limit and using a mapping to a trimerized

\mathrm{SU}(3)

spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.