Casimir forces on deformed fermionic chains

We characterize the Casimir forces for Dirac vacuum on free-fermionic chains with smoothly varying hopping amplitudes, which correspond to (1+1)D curved spacetimes a static metric in continuum limit. The first-order energy potential an obstacle that lattice corresponds Newtonian associated metric, while finite-size corrections are described by extension of conformal field theory predictions, including suitable boundary term. show that, weak deformations Minkowski measured local observer at metric-independent. provide numerical evidence our results variety deformations: Minkowski, Rindler, anti-de Sitter (the so-called rainbow system) and sinusoidal metrics.