Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model

TL;DR

This paper investigates the effects of long-range couplings in the spin-1/2 XXZ model, revealing how bound states influence dynamics and proposing an experimental realization with trapped ions.

Contribution

It provides explicit calculations of two-spin spectra in the long-range XXZ model and introduces a scheme for experimental simulation using trapped ions.

Findings

Bound states exist for fast decay of couplings but merge into the scattering region in deep long-range regime.

Two-spin bound states significantly affect the dynamics and stabilization of antiferromagnetic states.

A trapped-ion quantum simulator scheme is proposed for experimental study of the model.

Abstract

Experimental platforms based on trapped ions, cold molecules, and Rydberg atoms have made possible the investigation of highly-nonlocal spin-${1/2}$ Hamiltonians with long-range couplings. Here, we study the effects of such non-local couplings in the long-range spin-${1/2}$ XXZ Heisenberg Hamiltonian. We calculate explicitly the two-spin energy spectrum, which describes all possible energetic configurations of two spins pointing in a specific direction embedded in a background of spins with opposite orientation. For fast decay of the spin-spin couplings, we find that the two-spin energy spectrum is characterized by well-defined discrete values, corresponding to bound states, separated by a set of continuum states describing the scattering region. In the deep long-range regime instead, the bound states disappear as they get incorporated by the scattering region. The presence of two-spin bound states results to be crucial to determine both two- and many-spin dynamics. On one hand, radically different two-spin spreadings can be observed by tuning the decay of the spin couplings. On the other hand, two-spin bound states enable the dynamical stabilization of effective antiferromagnetic states in the presence of ferromagnetic couplings. Finally, we propose a novel scheme based on a trapped-ion quantum simulator to experimentally realize the long-range XXZ model and to study its out-of-equilibrium properties.