Spin- S Kitaev-Heisenberg model on the honeycomb lattice: A high-order treatment via the many-body coupled cluster method

We study the spin-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>S</a:mi></a:math> Kitaev-Heisenberg model on the honeycomb lattice for <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>S</b:mi><b:mo>=</b:mo><b:mn>1</b:mn><b:mo>/</b:mo><b:mn>2</b:mn></b:mrow></b:math>, 1, and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>3</c:mn><c:mo>/</c:mo><c:mn>2</c:mn></c:mrow></c:math>, by using the coupled cluster method (CCM) of microscopic quantum many-body theory. This system is one of the earliest extensions of the Kitaev model and is believed to contain two extended spin liquid phases for any value of the spin quantum number <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>S</d:mi></d:math>. We show that the CCM delivers accurate estimates for the phase boundaries of these spin liquid phases, as well as other transition points in the phase diagram. Moreover, we find evidence of two unexpected narrow phases for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>S</e:mi><e:mo>=</e:mo><e:mn>1</e:mn><e:mo>/</e:mo><e:mn>2</e:mn></e:mrow></e:math>, one sandwiched between the zigzag and ferromagnetic phases and the other between the Néel and the stripy phases. The results establish the CCM as a versatile numerical technique that can capture the strong quantum-mechanical fluctuations that are inherently present in generalized Kitaev models with competing bond-dependent anisotropies. Published by the American Physical Society 2024