论文标题
二维强耦合QCD的Grassmann高阶张量重量化组方法
Grassmann higher-order tensor renormalization group approach for two-dimensional strong-coupling QCD
论文作者
论文摘要
我们提出了一种张量 - 网络的方法，用于二维强耦合QCD，并在非零化学势方面与交错的夸克。在无限耦合时集成了量规场后，可以将分区函数写成由量子网络的完整收缩，该张量网络由耦合的局部数字和Grassmann张量组成。为了评估分区函数并计算可观测值，我们开发了Grassmann高阶张量重新归一化组方法，该方法是专门针对该模型量身定制的。在粗化过程中，分析进行相邻的Grassmann张量的阻塞，并且在每个粗糙步骤中，张量网络中的Grassmann变量总数减少了两倍。使用高阶奇异值分解将粗位数数字张量截断。该方法通过比较分区函数，手性冷凝物和用张量方法计算的巴属密度和重量的小晶格的精确分析结果来验证该方法。对于较大的体积，我们为手性冷凝物作为质量和体积的函数提出了第一个张量结果，并观察到手性对称性在二维中不会动态破裂。我们还提出了数量密度与化学电位函数的张量结果，这暗示了一阶相变。
We present a tensor-network approach for two-dimensional strong-coupling QCD with staggered quarks at nonzero chemical potential. After integrating out the gauge fields at infinite coupling, the partition function can be written as a full contraction of a tensor network consisting of coupled local numeric and Grassmann tensors. To evaluate the partition function and to compute observables, we develop a Grassmann higher-order tensor renormalization group method, specifically tailored for this model. During the coarsening procedure, the blocking of adjacent Grassmann tensors is performed analytically, and the total number of Grassmann variables in the tensor network is reduced by a factor of two at each coarsening step. The coarse-site numeric tensors are truncated using higher-order singular value decompositions. The method is validated by comparing the partition function, the chiral condensate and the baryon density computed with the tensor method with exact analytical results on small lattices up to volumes of $4\times4$. For larger volumes, we present first tensor results for the chiral condensate as a function of the mass and volume, and observe that the chiral symmetry is not broken dynamically in two dimensions. We also present tensor results for the number density as a function of the chemical potential, which hint at a first-order phase transition.
