Spin Frustration and Spin Liquid on a Triangular Lattice

Searching for Spin liquid has been one of major subjects of strongly correlated systems in last two decades for both theoretician and experimentists. Spin frustrations are introduced to enhance quantum fluctuations for materials with triangular, kogome and pyrochlore structures. The progresses on the material synthesis were made in the last decade. In particular, a new triangular inorganics sample was made as YbMgGaO₄ which is nearly an ideal triangular lattice without Dyzaloshinskii-Moriya interaction. This is an effective spin-half triangular lattice with a strong spin-orbit coupling originating from the splitting the rare each element Yb the crystal field, which gives rise to extra competition imposed to the geometric frustration.
In this talk, I will give a simple introduction on this material and discuss some experimental results and present our theoretical results on the Hamiltonian proposed for this material, including the spin wave approaches and density matrix renormalization group computations. Although one highly considers the material to be a good candidate of a gapless spin liquid, our theoretical results cannot provide enough evidence on the presents of the spin liquid with the proposed Hamiltonian.