Jordan-Wigner mapping between quantum-spin and fermionic Casimir effects

The Jordan-Wigner transformation connects spin operators in one-dimensional spin systems and fermionic operators. In this work, we elucidate the relationship between the finite-size corrections in the spin representation and the fermionic Casimir effect in the corresponding fermion representation. In particular, we focus on the ground-state energy of one-dimensional transverse-field Ising and XY models, and show that all finite-size corrections can be interpreted as lattice fermionic Casimir effects. We further find several types of Casimir phenomena, such as the conventional Casimir energy from massless fields, damping behavior from massive fields, vanishing behavior from flat or nonrelativistic bands, and oscillating behavior from the finite-density effect. Our findings establish a dictionary between finite-size corrections in spin chains and fermionic Casimir effects, and provide experimentally relevant platforms for the fermionic Casimir phenomena.