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arXiv 2005.10758hep-latcond-mat.mes-hallhep-th
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格点费米子的Casimir效应

Casimir effect for lattice fermions

Tsutomu Ishikawa, Katsumasa Nakayama, Kei Suzuki

备注：
8 pages, 5 figures; published version
发表信息：
Phys. Lett. B 809 (2020), 135713
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摘要：

提出了自由格点费米子的Casimir能量的定义。从这个定义出发，我们研究了$1+1$维时空中具有空间周期或反周期边界条件的无质量或有质量初始费米子、Wilson费米子和（Möbius）畴壁费米子的Casimir效应.对于纯费米子，我们发现Casimir能量的振荡行为，这是由奇数和偶数晶格尺寸之间的差异引起的。对于Wilson费米子，在小晶格尺寸的$N \geq 3$中，Casimir能与连续介质理论的Casimir能非常一致，这表明我们可以控制晶格模拟中测量的Casimir效应的离散伪影。我们还研究了莫比乌斯畴壁费米子的可调参数的依赖性。我们的研究结果将在凝聚态系统和小尺寸的晶格模拟中观察到。

英文摘要：

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.

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