We present a unified formulation to investigate solitons for all background densities in the Bose–Einstein condensate of a system of hard-core bosons with nearest-neighbour attractive interactions, using an extended Bose–Hubbard lattice model. We derive in detail the characteristics of the solitons supported in the continuum version, for the various cases possible. In general, two species of solitons appear: A nonpersistent (NP) type that fully delocalizes at its maximum speed and a persistent (P) type that survives even at its maximum speed. When the background condensate density is nonzero, both species coexist, the soliton is associated with a constant intrinsic frequency, and its maximum speed is the speed of sound. In contrast, when the background condensate density is zero, the system has neither a fixed frequency, nor a speed of sound. Here, the maximum soliton speed depends on the frequency, which can be tuned to lead to a cross-over between the NP-type and the P-type at a certain critical frequency, determined by the energy parameters of the system. We provide a single functional form for the soliton profile, from which diverse characteristics for various background densities can be obtained. Using mapping to spin systems enables us to characterize, in a unified fashion, the corresponding class of magnetic solitons in Heisenberg spin chains with different types of anisotropy.
Volume 96, 2022
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