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

14 pages, 4+1 figures, 2 appendices

References in corpus (27)

• Thermalization and its mechanism for generic isolated quantum systems
• Real time evolution using the density matrix renormalization group
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Cold atoms in cavity-generated dynamical optical potentials
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Repulsively bound atom pairs in an optical lattice
• Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
• Quantum simulation and computing with Rydberg-interacting qubits
• Dynamical crystallization in a low-dimensional Rydberg gas
• Generalized Portrait Quality Assessment
• Entanglement entropy for the long range Ising chain
• Kitaev chains with long-range pairing
• Observation of a prethermal discrete time crystal
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Time-step targetting methods for real-time dynamics using DMRG
• Observation of Stark many-body localization without disorder
• Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
• Transverse spin dynamics in the anisotropic Heisenberg model realized with ultracold atoms
• Scattering of mesons in quantum simulators
• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Nonequivalence of ensembles for long-range quantum spin systems in optical lattices
• Confinement and Mott transitions of dynamical charges in 1D lattice gauge theories
• Modulational instabilities in lattices with power-law hoppings and interactions
• XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling
• Experimental realization of fragmented models in tilted Fermi-Hubbard chains

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