Solving the quantum dimer and six-vertex models one electric field line at a time
Solving the quantum dimer and six-vertex models one electric field line at a time
复制标题
一次求解一条电场线的量子二聚体和六顶点模型
DOI：
10.1103/physrevb.99.245108
复制
发表时间：
2019
影响因子：
3.7
通讯作者：
I. Sodemann
中科院分区：
文献类型：
--
作者：
Jonah Herzog;S. Mantilla;I. Sodemann
在量子二聚体模型中，将经典柱状相与Rokhsar和Kivelson点分开的共振斑块价键态的性质和存在与否仍未确定。在这里，我们通过利用电场线数目的整体守恒定律，对这个模型和密切相关的六顶点模型采取了不同的攻击路线。这使我们能够研究单个起伏的电场线，我们将其精确地映射到一维自旋链上。在六顶点模型的情况下，电场线映射到著名的自旋1/2 XXZ模型上，该模型可以精确求解。在量子二聚体模型中，电场线被映射到一个两腿自旋1/2阶梯上，我们用数值精确对角化来研究它。我们的发现与三个不同相的存在是一致的，其中包括Luttinger液相，这是二维斑块价键固体的一维前体。我们的准一维电场线问题与完整的二维问题有着惊人的相似之处，这表明后者的大部分行为可以通过将其视为紧密排列的场线阵列来理解，这些场线本身正在经历非平凡的相变。
The nature and the very existence of the resonant plaquette valence bond state that separates the classical columnar phase and the Rokhsar and Kivelson point in the quantum dimer model remains unsettled. Here we take a different line of attack on this model, and on the closely related six vertex model, by exploiting the global conservation law of the number of electric field lines. This allows us to study a single fluctuating electric field line which we show maps exactly onto a one dimensional spin chain. In the case of the six vertex model, the electric field line maps onto the celebrated spin 1/2 XXZ model which can be solved exactly. In the quantum dimer model, the electric field line is mapped onto a two-leg spin 1/2 ladder, which we study using numerical exact diagonalization. Our findings are consistent with the existence of three distinct phases including a Luttinger liquid phase, the one-dimensional precursor to the two-dimensional plaquette valence bond solid. The uncanny resemblance of our quasi-one-dimensional electric field line problem to the full two-dimensional problem suggests that much of the behavior of the latter might be understood by thinking of it as a closely packed array of field lines which themselves are undergoing non-trivial phase transitions.