Lattice-fermionic Casimir effect and topological insulators

TL;DR

This paper investigates how lattice fermions modify the Casimir effect, revealing oscillatory behaviors due to ultraviolet modes, with implications for condensed matter systems like topological insulators and lattice simulations.

Contribution

It provides a detailed analysis of the lattice fermion Casimir effect across various formulations and dimensions, highlighting the role of ultraviolet modes and boundary conditions.

Findings

Oscillatory Casimir energy between odd and even lattice sizes.

Ultraviolet modes induce these oscillations in naive, Wilson, and overlap fermions.

Results applicable to topological insulators and lattice simulation measurements.

Abstract

The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the M\"obius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.