角连接海森堡正方形 plaquette 中由阻挫诱导的具有上-上-下-下有序性的简并自旋态
Frustration-induced degenerate spin state with up-up-down-down ordering in corner-connected Heisenberg square-plaquettes
AI总结：
本文结合Luttinger-Tisza分析与蒙特卡洛模拟，研究角连接海森堡正方形plaquette模型的阻挫磁性，发现低温下存在反铁磁相、铁磁相及具有uudd有序性的简并自旋态，并绘制了相关相图。
AI中文摘要：
我们研究了角连接正方形 plaquette 海森堡模型的阻挫磁性，该模型包含沿边的交换相互作用（$J_1$）、沿 plaquette 间连接的交换相互作用（$J_2$）以及沿正方形对角线的交换相互作用（$J_3$）。通过对傅里叶相互作用矩阵 $\boldsymbol{\textit{J}}(\boldsymbol{\textit{q}})$ 进行 Luttinger-Tisza（LT）最小化，并结合大规模蒙特卡洛（MC）模拟，我们在归一化平面（$J_1/|J_2|, J_3/|J_2|$）中得到了经典低温磁相图。两种方法发挥互补作用：LT分析提供零温候选有序波矢，而MC模拟则阐明了在低温有限温度下硬自旋约束下的有序倾向。低温下出现三个区域：反铁磁相（AF）、铁磁相（FM）以及具有上-上-下-下（uudd）有序性的简并自旋态（DS）。对于阻挫简并自旋态，LT在 $hk$ 平面的 $q_x=\boldsymbol{\textit{\textpm}} q_y$ 处呈现线状极小值，揭示了违反硬自旋约束的高度简并自旋构型。MC结果揭示了一种准二维有序态。DS区域本质上是多$\boldsymbol{\textit{q}}$的：有序结构由线上对称相关的模式自组装而成，形成“uudd”自旋排列，其中包含对角线上独特的强反铁磁关联、角连接上的铁磁关联以及边上高度抑制的关联。通过MC模拟确定的DS区域中一个代表性参数点的场-温度相图，产生了场诱导的负相关层和正相关层的不同区域，这两个区域由对应层间关联可忽略的曲线分隔开。
英文摘要：
We investigate frustrated magnetism of a corner-connected square plaquette Heisenberg model with exchange interactions along the edges $(J_1)$, along inter-plaquette links $(J_2)$, and along square diagonals $(J_3)$. Using Luttinger--Tisza (LT) minimization of the Fourier interaction matrix $\mathcal J(\mathbf q)$ together with large-scale Monte Carlo (MC) simulations, we obtain a classical low-temperature magnetic phase diagram in the normalized plane $(J_1/|J_2|, J_3/|J_2|)$. The two methods play complementary roles: the LT analysis provides the zero-temperature candidate ordering wave vectors, while the MC simulations elucidate the resulting ordering tendencies under the hard-spin constraint at low but finite temperatures. Three regimes emerge at low temperatures, an antiferromagnetic phase (AF), a ferromagnetic phase (FM) and a degenerate spin state with \textit{up-up-down-down (uudd)} ordering (DS). For the frustrated degenerate spinstate, LT exhibits line-like minima along $q_x=\pm q_y$ in the $hk$-plane, revealing a highly degenerate spin configuration which violates the hard-spin constraint. The MC results uncover a state with quasi-two-dimensional ordering. The DS regime is intrinsically multi-$\mathbf{q}$: the ordered texture assembles itself from symmetry-related modes on the lines, producing a ``\textit{uudd}'' spin arrangement comprising of distinctive strong antiferromagnetic correlations on diagonals, ferromagnetic correlations on corner links, and highly suppressed correlations on the edges. The field-temperature phase diagram for a representative parameter point in the DS regime, determined by MC simulations, yields field induced distinct regions of negatively and positively correlated layers. These two regions are separated by a curve corresponding to negligible inter-layer correlations.
