论文标题
DMRG高电线schwinger模型及其't Hooft异常的研究
DMRG study of the higher-charge Schwinger model and its 't Hooft anomaly
论文作者
论文摘要
费用-Q $ schwinger型号是$（1+1）$ - 尺寸量子电动力学（QED），带有充电-Q $ DIRAC FERMION。它具有$ \ mathbb {z} _q $ $ 1 $ - 形式对称性，并且还享受$ \ mathbb {z} _q $手性对称性的对称性，并且这些对称性之间存在混合的shoft hooft异常。我们使用密度 - 矩阵重质化组（DMRG）在晶格哈密顿制剂中的数值研究中的电荷$ q $ schwinger模型。应用DMRG时，我们将Schwinger模型映射到通过Jordan-Wigner Transformation进行非局部相互作用的自旋链，我们采用开放的边界条件而不是周期性的边界条件，以使Hilbert Space有限二维。当计算能量密度或手性冷凝物时，我们发现与相应的广泛数量除以体积的计算相比，使用本地操作员会显着降低边界效应。为了讨论't Hooft异常的结果，我们仔细处理手性冷凝物的重新归一化，然后我们确认Wilson循环在连续性极限内会产生离散的手性转化。
The charge-$q$ Schwinger model is the $(1+1)$-dimensional quantum electrodynamics (QED) with a charge-$q$ Dirac fermion. It has the $\mathbb{Z}_q$ $1$-form symmetry and also enjoys the $\mathbb{Z}_q$ chiral symmetry in the chiral limit, and there is a mixed 't Hooft anomaly between those symmetries. We numerically study the charge-$q$ Schwinger model in the lattice Hamiltonian formulation using the density-matrix renormalization group (DMRG). When applying DMRG, we map the Schwinger model to a spin chain with nonlocal interaction via Jordan-Wigner transformation, and we take the open boundary condition instead of the periodic one to make the Hilbert space finite-dimensional. When computing the energy density or chiral condensate, we find that using local operators significantly reduces the boundary effect compared with the computation of corresponding extensive quantities divided by the volume. To discuss the consequence of the 't Hooft anomaly, we carefully treat the renormalization of the chiral condensates, and then we confirm that Wilson loops generate the discrete chiral transformations in the continuum limit.
