Dynamics of the Spin Liquid Phase of Cs$_2$CuCl$_4$*

The dynamics of a spin-liquid phase of an antiferromagnet on the anisotropic triangular lattice and in a magnetic field are studied with a combination of Gutzwiller-projected wavefunctions and mean-field theory. Candidate ground states that support fermionic gapless spinon excitations include four different U(1) spin liquids\footnote{Y. Zhou, X. G. Wen, cond-mat/0210662 (2003).}. The lattice and the states interpolate between limiting cases of 1D decoupled chains ($J/J^{\prime} = 0$) and the isotropic 2D square lattice ($J/J^{\prime}= \infty$). Parameters of the mean field theory are chosen to minimize the ground state energy of the corresponding Gutzwiller-projected wavefunction. The spin-lattice relaxation rate $1/T_1$, calculated within the mean-field approximation, is compared to NMR measurements\footnote{M. A. Vachon, O. Ma, J. B. Marston, V. F. Mitrovi{\'c}, unpublished (2007).} in the spin liquid phase of Cs$_2$CuCl$_4$\footnote{Y. Tokiwa, T. Radu, R. Coldea, H. Wilhelm, Z. Tylczynski, F. Steglich, PRB 73, 134414 (2006).}.