Eight-color chiral spin liquid in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> bilinear-biquadratic model with Kitaev interactions

Abstract

Multipolar spin systems provide a rich ground for the emergence of unexpected states of matter due to their enlarged spin degree of freedom. In this study, with a specific emphasis on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>S</a:mi><a:mo>=</a:mo><a:mn>1</a:mn></a:mrow></a:math> magnets, we explore the interplay between spin nematic states and spin liquids. Based on the foundations laid in the prior work [R. Pohle , ], we investigate the <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:mrow></b:math> Kitaev model with bilinear-biquadratic interactions, which stabilizes, next to Kitaev spin liquid, spin nematic and triple-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>q</c:mi></c:math> phases, also an exotic chiral spin liquid. Through a systematic reduction of the spin degree of freedom—from <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msup><d:mi mathvariant="double-struck">CP</d:mi><d:mn>2</d:mn></d:msup></d:math> to <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msup><f:mi mathvariant="double-struck">CP</f:mi><f:mn>1</f:mn></f:msup></f:math> and ultimately to a discrete eight-color model—we provide an intuitive understanding of the nature and origin of this chiral spin liquid. We find that the chiral spin liquid is characterized by an extensive ground-state degeneracy, bound by a residual entropy, extremely short-ranged correlations, a nonzero scalar spin chirality marked by <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:msub><h:mi mathvariant="double-struck">Z</h:mi><h:mn>2</h:mn></h:msub></h:math> flux order, and a gapped continuum of excitations. Our work contributes not only to the specific exploration of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>S</j:mi><j:mo>=</j:mo><j:mn>1</j:mn></j:mrow></j:math> Kitaev magnets but also to the broader understanding of the importance of multipolar spin degree of freedom on the ground state and excitation properties in quantum magnets. Published by the American Physical Society 2024

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