Extended Quantum Spin Liquid with Spinon-like Excitations in an Anisotropic Kitaev-Gamma Model

The characterization of quantum spin liquid phases in Kitaev materials has been a subject of intensive studies over the recent years, both theoretically and experimentally. Most theoretical studies have focused on an isotropically interacting model with its coupling strength being equivalent on each bond in an attempt to simplify the problem. Here, we study an extended spin-1/2 Kitaev-$\Gamma$ model on a honeycomb lattice with an additional tuning parameter that controls the coupling strength on one of the bonds: we connect the limit of isolated Kitaev-$\Gamma$ chains, which is known to exhibit an emergent $SU(2)_1$ Tomonaga-Luttinger liquid phase [Yang et al. Phys. Rev. Lett. {\bf 124}, 147205 (2020)], to the two-dimensional model. We report on an instance, in which the Tomonaga-Luttinger liquid persists for finite inter-chain coupling. A quantum spin liquid phase develops in analogy to \emph{sliding Luttinger liquids} that differs from the Kitaev spin liquid. This quantum spin liquid phase features spinon-like excitations similar to those of the antiferromatnetic Heisenberg chain. We use numerical Exact Diagonalization and Density Matrix Renormalization Group on various cluster geometries in a complementary way to overcome finite-size limitations.