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

TL;DR

This paper explores the connection between finite-size corrections in one-dimensional spin systems and fermionic Casimir effects, revealing various phenomena and establishing a useful correspondence for experimental studies.

Contribution

It provides a detailed mapping between spin chain finite-size effects and fermionic Casimir phenomena, including multiple types of Casimir behaviors.

Findings

Finite-size corrections correspond to fermionic Casimir effects.

Identified various Casimir phenomena such as damping and oscillations.

Established a practical dictionary for experimental platforms.

Abstract

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.