论文标题
Casimir效应晶格费米子
Casimir effect for lattice fermions
论文作者
论文摘要
我们提出了自由晶格费米斯的卡西米尔能量的定义。从这个定义来看，我们研究了Casimir的无质量或巨大幼稚费物，威尔逊费米恩和（Möbius）域壁费米恩的效果，其$ 1+1 $尺寸的时空，并具有空间周期性或反膜状边界条件。对于天真的费米，我们发现卡西米尔能量的振荡行为是由奇数甚至晶格大小之间的差异引起的。对于Wilson Fermion来说，在$ n \ geq 3 $的小晶格大小中，Casimir Energy与连续理论的能源非常吻合，这表明我们可以控制在Lattice Simulations中测得的Casimir效应的离散化工件。我们还研究了对Möbius域壁费米子中可调节参数的依赖性。我们的发现将在凝结物质系统和尺寸较小的晶格模拟中观察到。
We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Möbius) domain-wall fermion in $1+1$ dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of $N \geq 3$, the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Möbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.
