Spinon excitation in spatially anisotropic frustrated Heisenberg models

We investigate the elementary excitations of spin-1/2 antiferromagnetic Heisenberg models with spatially anisotropic frustrated couplings. By projecting the Hamiltonian into a subspace of exact spinon eigenstates of the one-dimensional chains, we obtain and solve an effective Schr\"odinger equation. We argue this weak interchain-coupling approach has a broad regime of validity for frustrated models. As a general feature, we find a bound state of spinons and incoherent excitations depending on the momentum. Various experimental features observed in Cs$_{2}$CuCl$_{4}$ such as asymmetry of the dispersion relation and large tail at $k_x$=$\pi$\footnote{R. Coldea, D. A. Tennant, and Z. Tylczynski, Phys. Rev. B 68, 134424 (2003).} are consistently explained within the framework of the present approach with few adjustable parameters. Our results suggest that the spectral features in Cs$_{2}$CuCl$_{4}$ should be interpreted as descendents of one-dimensional spinons, which persist more strongly at some momenta in spatially anisotropic frustrated systems even with finite interchain couplings.