玻色-哈伯德模型中原子对的吸引束缚与反铁磁性
Attractively bound pairs of atoms in the Bose-Hubbard model and antiferromagnetism
摘要：
我们考虑一个周期性的晶格加载玻色子原子对紧密结合在一起，通过强大的吸引力的现场相互作用，超过了网站间的隧穿率。这样的晶格二聚体的系综准确地描述了一个有效的哈密顿的硬核玻色子与强最近邻排斥，这是等效的$XXZ$模型与Ising类各向异性。我们计算基态相图的一维系统，表现出不可压缩的阶段，对应于一个空的和一个完全填充的晶格（铁磁相）和半填充的交替密度晶体（反铁磁相），彼此分离的可压缩相。在有限晶格中，可压缩相在反铁磁密度分布和密度-密度相关性上显示出特征振荡调制。我们推导出一个扭结模型，提供了简单的定量解释这些功能。为了描述系统的长程相关性，我们采用Luttinger液体理论与相关的Luttinger参数$K$准确地获得使用Bethe Anesthesia解决方案。我们计算的密度密度以及一阶关联，并找到良好的协议与密度矩阵重整化群（DMRG）方法的数值结果。我们还提出了一个微扰处理系统在更高的维度。
英文摘要：
We consider a periodic lattice loaded with pairs of bosonic atoms tightly bound to each other via strong attractive on-site interaction that exceeds the inter-site tunneling rate. An ensemble of such lattice-dimers is accurately described by an effective Hamiltonian of hard core bosons with strong nearest-neighbor repulsion which is equivalent to the $XXZ$ model with Ising-like anisotropy. We calculate the ground-state phase diagram for a one-dimensional system which exhibits incompressible phases, corresponding to an empty and a fully filled lattice (ferromagnetic phases) and a half-filled alternating density crystal (anti-ferromagnetic phase), separated from each other by compressible phases. In a finite lattice the compressible phases show characteristic oscillatory modulations on top of the anti-ferromagnetic density profile and in density-density correlations. We derive a kink model which provides simple quantitative explanation of these features. To describe the long-range correlations of the system we employ the Luttinger liquid theory with the relevant Luttinger parameter $K$ obtained exactly using the Bethe Ansatz solution. We calculate the density-density as well as first-order correlations and find excellent agreement with numerical results obtained with density matrix renormalization group (DMRG) methods. We also present a perturbative treatment of the system in higher dimensions.
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