倾斜螺旋：XXZ锯齿形梯子的精确基态
The Canted Spiral: An Exact Ground State of XXZ Zigzag Ladders
摘要：
我们导出了一维$S=1/2$ XXZ哈密顿量族在Z字形阶梯上的精确基态。这些态表现出真正的长程螺旋序，自发地打破了哈密顿量的U（1）不变性。除了破坏$d=1$中的连续对称性之外，这种螺旋排序还具有沿对称轴的铁磁分量，其可以取零和完全饱和之间的任何值。在这个意义上，我们的斜螺旋解是SU（2）海森堡铁磁体到横自旋分量的非零序波矢的推广。我们将这个结果推广到$d=2$各向异性三角晶格。
英文摘要：
We derive the exact ground states for a one dimensional family of $S=1/2$ XXZ Hamiltonians on the zigzag ladder. These states exhibit true long range spiral order that spontaneously breaks the U(1) invariance of the Hamiltonian. Besides breaking a continuous symmetry in $d=1$, this spiral ordering has a ferromagnetic component along the symmetry axis that can take any value between zero and full saturation. In this sense, our canted spiral solutions are a generalization of the SU(2) Heisenberg ferromagnet to non-zero ordering wave-vectors of the transverse spin components. We extend this result to the $d=2$ anisotropic triangular lattice.
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