Proximate Tomonaga-Luttinger liquid 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. In this Letter, we study an extended spin-1/2 Kitaev-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi mathvariant="normal">Γ</a:mi></a:math> 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-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi mathvariant="normal">Γ</c:mi></c:math> chains, which is known to exhibit an emergent <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>S</e:mi><e:mi>U</e:mi><e:msub><e:mrow><e:mo>(</e:mo><e:mn>2</e:mn><e:mo>)</e:mo></e:mrow><e:mn>1</e:mn></e:msub></e:mrow></e:math> Tomonaga-Luttinger liquid phase [Yang , ], to the two-dimensional model. We report on an instance, in which properties of the Tomonaga-Luttinger liquid persist for finite interchain coupling forming a phase we call the proximate Tomonaga-Luttinger liquid (pTLL). This pTLL is strongly anisotropic in character analogous to , and features spinon-like excitations similar to those of the antiferromagnetic 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.