论文标题
相互作用引起的双龙和嵌入式拓扑子空间在完整的平流系统中
Interaction induced doublons and embedded topological subspace in a complete flat-band system
论文作者
论文摘要
在这项工作中，我们研究了弱相互作用对玻色粒完全扁平频段系统的影响。通过采用带投射方法，具有弱相互作用的平坦频次汉密尔顿人被映射到有效的哈密顿量。有效的汉密尔顿（Hamiltonian）表明，双龙的行为和明确定义的准颗粒，通过相互作用引起的跳跃获得了行程。当我们专注于有效的哈密顿量的两粒子系统时，仅出现了一个有效的子空间。有效的子空间引起了单个doublon的扩散，我们发现了一个有趣的属性：单个doublon的动力学使短距离密度密度相关性与常规的两粒子扩散形成鲜明对比。此外，在引入调制的弱相互作用时，我们发现相互作用引起的拓扑子空间嵌入了整个希尔伯特空间中。我们通过观察单个doublon的动力学来阐明嵌入式拓扑子空间，并表明嵌入式拓扑子空间具有庞大的拓扑不变。我们进一步期望，对于具有开放边界的系统，嵌入式拓扑子空间具有Doublon所描述的相互作用引起的拓扑边缘模式。即使是嵌入式拓扑子空间，大量 - 边缘 - 对应也是如此。
In this work, we investigate effects of weak interactions on a bosonic complete flat-band system. By employing a band projection method, the flat-band Hamiltonian with weak interactions is mapped to an effective Hamiltonian. The effective Hamiltonian indicates that doublons behave as well-defined quasi-particles, which acquire itinerancy through the hopping induced by interactions. When we focus on a two-particle system, from the effective Hamiltonian, an effective subspace spanned only by doublon bases emerges. The effective subspace induces spreading of a single doublon and we find an interesting property: The dynamics of a single doublon keeps short-range density-density correlation in sharp contrast to a conventional two-particle spreading. Furthermore, when introducing a modulated weak interaction, we find an interaction induced topological subspace embedded in the full Hilbert space. We elucidate the embedded topological subspace by observing the dynamics of a single doublon, and show that the embedded topological subspace possesses a bulk topological invariant. We further expect that for the system with open boundary the embedded topological subspace has an interaction induced topological edge mode described by the doublon. The bulk--edge--correspondence holds even for the embedded topological subspace.
