Integrability and conformal data of the dimer model
Integrability and conformal data of the dimer model
复制标题
二聚体模型的可积性和保形数据
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
P. Ruelle
中科院分区：
文献类型：
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作者：
Alexi Morin;J. Rasmussen;P. Ruelle
方形晶格上二聚体模型的中心电荷仍在文献中争论。在本文中，我们提供了支持 c = − 2 ?> 描述一致性的证据。使用 Lieb 的转移矩阵及其在 β = 0 ?> 时的 Temperley-Lieb 代数 TL n ?> 的描述，我们根据倾斜晶格上的临界致密聚合物模型提供了二聚体模型的新解，并提供了对二聚体模型的晶格可积性的理解。在缩放极限下分析二聚体转移矩阵，并且L 0 − c 24 ?> 的结果以费米子的形式表示。更高的 Virasoro 模式同样被构造为 TL n ?> 元素的极限，并且被发现产生 Virasoro 代数的 c = − 2 ?> 实现，这在费米子 bc 鬼系统中很常见。在这种认识中，二聚体福克空间被证明可以分解为维拉索罗模，分解为 Feigin-Fuchs 模的直和，它们本身表现出可约但不可分解的结构。在标度极限下，运动晶格积分的特征值与 c = − 2 ?> 运动共形积分的特征值完全一致。与从转移矩阵得到的L 0 − c 24 ?> 的表达式一致，我们还构造了c = 1 的更高Virasoro 模式，并发现二聚体Fock 空间在它们的作用下是完全可约的。然而，我们发现传递矩阵并不是 c = 1 运动积分的生成函数。尽管这表明 Lieb 的转移矩阵描述与 c = 1 解释不兼容，但并不排除存在替代的、与 c = 1 兼容的二聚体模型转移矩阵描述。
The central charge of the dimer model on the square lattice is still being debated in the literature. In this paper, we provide evidence supporting the consistency of a c = − 2 ?> description. Using Lieb’s transfer matrix and its description in terms of the Temperley–Lieb algebra TL n ?> at β = 0 ?> , we provide a new solution of the dimer model in terms of the model of critical dense polymers on a tilted lattice and offer an understanding of the lattice integrability of the dimer model. The dimer transfer matrix is analyzed in the scaling limit, and the result for L 0 − c 24 ?> is expressed in terms of fermions. Higher Virasoro modes are likewise constructed as limits of elements of TL n ?> and are found to yield a c = − 2 ?> realization of the Virasoro algebra, familiar from fermionic bc ghost systems. In this realization, the dimer Fock spaces are shown to decompose, as Virasoro modules, into direct sums of Feigin–Fuchs modules, themselves exhibiting reducible yet indecomposable structures. In the scaling limit, the eigenvalues of the lattice integrals of motion are found to agree exactly with those of the c = − 2 ?> conformal integrals of motion. Consistent with the expression for L 0 − c 24 ?> obtained from the transfer matrix, we also construct higher Virasoro modes with c = 1 and find that the dimer Fock space is completely reducible under their action. However, the transfer matrix is found not to be a generating function for the c = 1 integrals of motion. Although this indicates that Lieb’s transfer matrix description is incompatible with the c = 1 interpretation, it does not rule out the existence of an alternative, c = 1 compatible, transfer matrix description of the dimer model.