Two spin liquid phases in the spatially anisotropic triangular Heisenberg model

The quantum spin-$1∕2$ antiferromagnetic Heisenberg model on a two dimensional triangular lattice geometry with spatial anisotropy is relevant to describe materials such as ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_4$ and organic compounds such as $\kappa \text{−}{\left(\mathrm{ET}\right)}_2{\mathrm{Cu}}_2{\left(\mathrm{C}\mathrm{N}\right)}_3$. The strength of the spatial anisotropy can increase quantum fluctuations and can destabilize the magnetically ordered state leading to nonconventional spin liquid phases. In order to understand these intriguing phenomena, quantum Monte Carlo methods are used to study this model system as a function of the anisotropic strength, represented by the ratio $J^{\prime }∕J$ between the intrachain nearest neighbor coupling $J$ and the interchain one $J^{\prime }$. We have found evidence of two spin liquid regions. The first one is stable for small values of the coupling $J^{\prime }∕J\lesssim 0.65$, and appears gapless and fractionalized, whereas the second one is a more conventional spin liquid with a small spin gap and is energetically favored in the region $0.65\lesssim J^{\prime }∕J\lesssim 0.8$. We have also shown that in both spin liquid phases there is no evidence of broken translation symmetry with dimer or spin-Peirls order or any broken spatial reflection symmetry of the lattice. The various phases are in good agreement with the experimental findings, thus supporting the existence of spin liquid phases in two dimensional quantum spin-$1∕2$ systems.