Bound state dynamics in the long-range spin-1/2 XXZ model

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 nonlocal 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.

Automated summary

The study investigates the effects of nonlocal couplings in the long-range spin-1/2 XXZ Heisenberg Hamiltonian, particularly focusing on the calculation of the two-spin energy spectrum. The presence of bound states for two spins is crucial for determining both two- and many-spin dynamics, with implications on spin spreading and dynamical stabilization of effective antiferromagnetic states. The research also proposes a novel scheme using a trapped-ion quantum simulator to experimentally realize the long-range XXZ model and study its out-of-equilibrium properties.