论文标题
分离手性对称性和晶格哈密顿量方法的质量转移到Schwinger模型
Discrete Chiral Symmetry and Mass Shift in Lattice Hamiltonian Approach to Schwinger Model
论文作者
论文摘要
我们使用带交错的费米子的Kogut-susskind Hamiltonian方法来重新访问Schwinger模型的晶格公式。该模型由Banks等人介绍，包含质量项$ m _ {\ rm lat} \ sum_ {n}（-1）^{n}χ^\ dagger_nχ_n$，并且通常假定将其设置为零，以提供无数schwinger模型的晶格。相反，我们认为晶格和连续质量参数之间的关系应为$ m _ {\ rm lat} = m- \ frac 18 e^2 a $。 $ M = 0 $的模型显示出具有离散的手性对称性，该对称是由单元晶格翻译生成的，并伴随着$θ$ - 角（$π$）的偏移。尽管随着晶格间距的$ a $接近零，质量转移却消失了，但我们发现包括这种转变大大提高了收敛速度到连续限制。我们使用有限晶格系统的数值对角线以及晶格强耦合膨胀的外推，证明了更快的收敛性。
We revisit the lattice formulation of the Schwinger model using the Kogut-Susskind Hamiltonian approach with staggered fermions. This model, introduced by Banks et al., contains the mass term $m_{\rm lat} \sum_{n} (-1)^{n} χ^\dagger_n χ_n$, and setting it to zero is often assumed to provide the lattice regularization of the massless Schwinger model. We instead argue that the relation between the lattice and continuum mass parameters should be taken as $m_{\rm lat}=m- \frac 18 e^2 a$. The model with $m=0$ is shown to possess a discrete chiral symmetry that is generated by the unit lattice translation accompanied by the shift of the $θ$-angle by $π$. While the mass shift vanishes as the lattice spacing $a$ approaches zero, we find that including this shift greatly improves the rate of convergence to the continuum limit. We demonstrate the faster convergence using both numerical diagonalizations of finite lattice systems, as well as extrapolations of the lattice strong coupling expansions.
