Critical spin liquid at 1/3 magnetization in a spin-1/2 triangular antiferromagnet

Although magnetically ordered at low temperatures, the spin-1/2 triangular antiferromagnet Cs_2CuCl_4 exhibits remarkable spin dynamics that strongly suggest proximity to a spin liquid phase. Here we address the question of whether a proximate spin liquid may also occur in an applied magnetic field, leaving a similar imprint on the dynamical spin correlations of this material. Specifically, we explore a spatially anisotropic Heisenberg spin-1/2 triangular antiferromagnet at 1/3 magnetization from a dual vortex perspective, and indeed find a new critical'' spin liquid phase described by QED3 with an emergent SU(6) symmetry. A number of nontrivial predictions are given for the dynamical spin structure factor in this algebraic vortex liquid’’ phase, which can be tested experimentally via inelastic neutron scattering. We also discuss how the well-studied up-up-down'' magnetization plateaus can be captured within our approach, and further predict the existence of a stable gapless solid phase in a weakly ordered up-up-down state. Finally, we predict several anomalous roton’’ minima in the excitation spectrum in the regime of lattice anisotropy where the canted Neel state appears.