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.
Bound state dynamics in the long-range spin- ½ XXZ model / Macri, T.; Lepori, L.; Pagano, G.; Lewenstein, M.; Barbiero, L.. - In: PHYSICAL REVIEW. B. - ISSN 2469-9950. - ELETTRONICO. - 104:21(2021). [10.1103/PhysRevB.104.214309]
|Titolo:||Bound state dynamics in the long-range spin- ½ XXZ model|
|Data di pubblicazione:||2021|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1103/PhysRevB.104.214309|
|Appare nelle tipologie:||1.1 Articolo in rivista|