Casimir effect for lattice fermions

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 $N\ge 3$, 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.

8 pages, 5 figures; published version

References in corpus (20)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume
• Finite-size effects on the phase structure of the Nambu-Jona-Lasinio model
• Anisotropic pressure induced by finite-size effects in SU(3) Yang-Mills theory
• Functional approach to the fermionic Casimir effect
• Volume dependence of baryon number cumulants and their ratios
• Finite-volume and magnetic effects on the phase structure of the three-flavor Nambu--Jona-Lasinio model
• The Casimir effect and deconfinement phase transition
• Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions
• Thermodynamics of the ideal overlap quarks on the lattice
• Finite-size effects on the Phase Structure of the Walecka Model
• Self-Consistent Large-$N$ Analytical Solutions of Inhomogneous Condensates in Quantum $\mathbb{C}{P}^{N-1}$ Model
• Interplay between superconductivity and chiral symmetry breaking in a (2+1)-dimensional model with compactified spatial coordinate
• Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory
• Critical behaviour of an effective relativistic mean field model in the presence of magnetic background and boundaries
• Thermodynamics of free Domain Wall fermions
• Four-Fermion Interaction Model on ${\mathcal{M}}^{D-1}\otimes S^1$
• Finite-sites corrections to the Casimir energy on a periodic lattice
• Casimir energy in the compact QED on the lattice