Finding the Kitaev spin liquid in candidate materials involves understanding the entire phase diagram, including other allowed interactions. One of these interactions, called the Gamma (Γ) interaction, causes magnetic frustration and its interplay with the Kitaev (K) interaction is crucial to comprehend Kitaev materials. Due to the complexity of the combined KΓ model, quasi-one-dimensional models have been investigated. While several disordered phases are found in the 2-leg ladder, the nature of the phases are yet to be determined. Here we focus on the disordered phase near the antiferromagnetic Γ limit (denoted by AΓ phase) next to the ferromagnetic Kitaev phase. We report a distinct non-local string order parameter characterizing the AΓ phase, different from the string order parameter in the Kitaev phase. This string order parameter becomes evident only after two unitary transformation, referred to as a twice hidden string order parameter. The related entanglement spectrum, edge states, magnetic field responses, and the symmetry protecting the phase are presented, and its relevance to the two-dimensional Kitaev materials is discussed. Two newly identified disordered phases in the phase diagram of KΓ ladder is also reported.

在候选材料中寻找基塔耶夫自旋液体需要理解整个相图，包括其他允许的相互作用。其中一种相互作用被称为伽玛 (Γ) 相互作用，会引起磁挫败，其与基塔耶夫 ( K ) 相互作用的相互作用对于理解基塔耶夫材料至关重要。由于组合 KΓ 模型的复杂性，人们对准一维模型进行了研究。虽然在两腿梯子中发现了几个无序相，但这些相的性质尚未确定。在这里，我们重点关注铁磁 Kitaev 相旁边的反铁磁 Γ 极限附近的无序相（用 AΓ 相表示）。我们报告了一个独特的非局部弦序参数来表征 AΓ 相，与 Kitaev 相中的弦序参数不同。该字符串顺序参数仅在两次酉变换后才变得明显，称为两次隐藏字符串顺序参数。介绍了相关的纠缠谱、边缘态、磁场响应和保护相的对称性，并讨论了其与二维 Kitaev 材料的相关性。还报道了 KГ 梯形图相图中两个新发现的无序相。