The Heisenberg-Ising spin ladder is one of the few short-range models showing confinement of elementary excitations without the need of an external field, neither transverse nor longitudinal. This feature makes the model suitable for an experimental realization with ultracold atoms. In this paper, we combine analytic and numerical techniques to precisely characterize its spectrum in the regime of Hamiltonian parameters showing confinement. We find two kinds of particles, which we dub intrachain and interchain mesons, that correspond to bound states of kinks within the same chain or between different ones, respectively. The ultimate physical reasons leading to the existence of two families of mesons is a residual double degeneracy of the ground state: the two types of mesons interpolate either between the same vacuum (intrachain) or between the two different ones (interchain). While the intrachain mesons can also be qualitatively assessed through an effective mean field description and were previously known, the interchain ones are new and they represent general features of spin ladders with confinement.

中文翻译：

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海森堡-伊辛自旋梯谱中的限制

海森堡-伊辛自旋阶梯是少数几个短程模型之一，它显示了基本激发的限制，不需要外部场，既不是横向也不是纵向。此功能使该模型适用于超冷原子的实验实现。在本文中，我们结合解析和数值技术来精确表征其在显示限制的哈密顿参数范围内的频谱。我们发现了两种粒子，我们称之为链内介子和链间介子，它们分别对应于同一链内或不同链之间的扭结束缚状态。导致两个介子族存在的最终物理原因是基态的残余双简并：这两种介子在同一真空（链内）或两个不同的真空（链间）之间进行插值。虽然链内介子也可以通过有效的平均场描述进行定性评估并且是以前已知的，但链间介子是新的，它们代表了带限制的自旋梯的一般特征。