Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains

TL;DR

This paper investigates how long-range interactions in a quantum spin chain cause confinement of quasiparticles, affecting dynamics and thermalization, with implications for experiments.

Contribution

It introduces a model for long-range interaction-induced confinement of quasiparticles and predicts their masses, linking theory with experimental observables.

Findings

Long-range interactions create a confining potential for quasiparticles.

Fourier spectra of order parameters reveal bound quasiparticle masses.

Confinement leads to slow thermalization in certain initial states.

Abstract

We study the quasiparticle excitation and quench dynamics of the one-dimensional transverse-field Ising model with power-law ($1/r^{\alpha}$) interactions. We find that long-range interactions give rise to a confining potential, which couples pairs of domain walls (kinks) into bound quasiparticles, analogous to mesonic bound states in high-energy physics. We show that these quasiparticles have signatures in the dynamics of order parameters following a global quench and the Fourier spectrum of these order parameters can be expolited as a direct probe of the masses of the confined quasiparticles. We introduce a two-kink model to qualitatively explain the phenomenon of long-range-interaction induced confinement, and to quantitatively predict the masses of the bound quasiparticles. Furthermore, we illustrate that these quasiparticle states can lead to slow thermalization of one-point observables for certain initial states. Our work is readily applicable to current trapped-ion experiments.