Abstract
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≥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.
Highlights
The Casimir effect [1] is known as negative energy and attractive force caused by a zero-point energy shift of photon fields between two parallel plates
The original Casimir effect is physics related to photon fields, which is perturbatively described in quantum electrodynamics (QED), but a similar concept can be applied to any field such as scalar fields, fermion fields, and other gauge fields
We investigated the properties of the Casimir energy for the massless/massive naive fermion, Wilson fermion, and overlap fermion with the Möbius domain-wall (MDW) kernel operator
Summary
The Casimir effect [1] is known as negative energy and attractive force caused by a zero-point energy shift of photon fields between two parallel plates. Ishikawa et al / Physics Letters B 809 (2020) 135713 tinuum theory In this sense, the comprehensive examination of the phase structure of a fermion action in finite (especially, small) volume will be important, which is similar to theoretical studies at finite temperature and/or density. The domain-wall fermions are well known as an analogy to zero-mode Dirac fermions realized on the surface of topological insulators [58,59] In this sense, this study is not limited to theoretical interests, and it can provide us motivations for future tabletop experiments in condensed matter. This study is not limited to theoretical interests, and it can provide us motivations for future tabletop experiments in condensed matter In such situations, we can experimentally observe Casimir effects for (Dirac-like) lattice fermions.
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