论文标题
揭示债券替代旋转的相图-U \ frac12 $ $ k $ - $γ$链
Unveiling the phase diagram of a bond-alternating spin-$\frac12$ $K$-$Γ$ chain
论文作者
论文摘要
在各种基塔夫材料中观察到的有趣现象的关键在于了解Kitaev（$ K $）相互作用的相互作用和对称的非对角线$γ$相互作用。为了洞悉具有挑战性的问题，我们研究了债券偏置旋转的量子相图 - $ 1/2 $ $ $ g_x $ - $ g_y $ $ $ $ k $ - $ k $ - $γ$通过密度 - 矩阵重rentrix renormatiation grout方法，其中$ g_x $ and $ g_x $和$ g_y $是奇数和奇数的债券强度，甚至是奇数和甚至债券的债券。相图由均匀的haldane（$ g_x> g_y $）和奇数（$ g_x <g_y $）阶段主导，其中前者在拓扑上是微不足道的，而后者则是对称性保护的拓扑阶段。在反铁磁性Kitaev限制附近，有两个间隙$ a_x $和$ a_y $阶段，其特征是不同的非局部弦乐相关器。相比之下，各向同性铁磁（FM）Kitaev点是两个拓扑相变相遇的多政治点。相图的其余部分包含三个对称性磁相。一个是一个六倍退化的fm $ _ {u_6} $阶段，其中所有旋转与$ \ pm \ hat {x} $，$ \ pm \ hat {y} $和$ \ hat {y pm \ pm \ hat {z} $在六个站点旋转的基础上均与其他三个复杂的旋转结构相关的轴，而在所有复杂的三个旋转的基础上，$ \ hat {x} $，$ \ pm \ pm \ hat {y}。还讨论了后者中排名2的自旋序列的存在。
The key to unraveling intriguing phenomena observed in various Kitaev materials lies in understanding the interplay of Kitaev ($K$) interaction and a symmetric off-diagonal $Γ$ interaction. To provide insight into the challenging problems, we study the quantum phase diagram of a bond-alternating spin-$1/2$ $g_x$-$g_y$ $K$-$Γ$ chain by density-matrix renormalization group method where $g_x$ and $g_y$ are the bond strengths of the odd and even bonds, respectively. The phase diagram is dominated by even-Haldane ($g_x > g_y$) and odd-Haldane ($g_x < g_y$) phases where the former is topologically trivial while the latter is a symmetry-protected topological phase. Near the antiferromagnetic Kitaev limit, there are two gapped $A_x$ and $A_y$ phases characterized by distinct nonlocal string correlators. In contrast, the isotropic ferromagnetic (FM) Kitaev point serves as a multicritical point where two topological phase transitions meet. The remaining part of the phase diagram contains three symmetry-breaking magnetic phases. One is a six-fold degenerate FM$_{U_6}$ phase where all the spins are parallel to one of the $\pm \hat{x}$, $\pm \hat{y}$, and $\pm \hat{z}$ axes in a six-site spin rotated basis, while the other two have more complex spin structures with all the three spin components being finite. Existence of a rank-2 spin-nematic ordering in the latter is also discussed.
