Casimir forces on deformed fermionic chains

We characterize the Casimir forces for the Dirac vacuum on free-fermionic chains with smoothly varying hopping amplitudes, which correspond to (1 + 1)-dimensional [(1 + 1)D] curved spacetimes with a static metric in the continuum limit. The first-order energy potential for an obstacle on that lattice corresponds to the Newtonian potential associated with the metric, while the finite-size corrections are described by a curved extension of the conformal field theory predictions, including a suitable boundary term. We show that for weak deformations of the Minkowski metric, Casimir forces measured by a local observer at the boundary are universal. We provide numerical evidence for our results on a variety of (1 + 1)D deformations: Minkowski, Rindler, anti-de Sitter (the so-called rainbow system), and sinusoidal metrics. Moreover, we show that interactions do not preclude our conclusions, exemplifying this with the deformed Heisenberg chain.

Automated summary

This study characterizes the Casimir forces for the Dirac vacuum on free-fermionic chains with smoothly varying hopping amplitudes, revealing that Casimir forces measured by a local observer at the boundary are universal for weak deformations of the Minkowski metric. Numerical evidence is provided for various (1+1)D deformations, including Minkowski, Rindler, anti-de Sitter, and sinusoidal metrics, and interactions do not affect the conclusions, as exemplified by the deformed Heisenberg chain.