相互作用的Rice-Mele模型：体积和边界
The interacting Rice-Mele model: bulk and boundaries
摘要：
我们研究了相互作用的一维Rice-Mele模型，一个拓扑性质的原型费米模型。为了设置阶段，我们首先计算单粒子谱函数，局域密度和边界电荷在没有相互作用。边界电荷完全由指示体边界对应的体性质决定。在一个大参数的制度，它同意从有效的低能量理论（arXiv：2004.00463）。其次，我们研究了我们的结果对两粒子相互作用的鲁棒性。为了恢复小能隙的一系列主要理论，这些理论在相互作用中瓦解了普通微扰理论，我们使用了一种本质上分析的重整化群方法。它被控制为小的相互作用，可以直接应用到微观晶格模型。我们将结果与数值密度矩阵重整化群数据进行了比较。在散装的主要相互作用的影响是幂律重整化的间隙与相互作用相关的指数。边界电荷的重要特征是不变的，可以从重整化的体性质来理解，提升体边界对应的相互作用制度。这不仅需要一致地处理低能隙重整化，而且需要一致地处理高能带宽度重整化。与低能场论相反，我们的重整化群方法也提供了后者。我们发现，相互作用破坏了体属性和边缘状态的数量之间的关系，与观察到的Rice-Mele模型与有限的潜在调制没有揭示任何零能量边缘状态。
英文摘要：
We investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we firstly compute the single-particle spectral function, the local density, and the boundary charge in the absence of interactions. The boundary charge is fully determined by bulk properties indicating a bulk-boundary correspondence. In a large parameter regime it agrees with the one obtained from an effective low-energy theory (arXiv:2004.00463). Secondly, we investigate the robustness of our results towards two-particle interactions. To resum the series of leading logarithms for small gaps, which dismantle plain perturbation theory in the interaction, we use an essentially analytical renormalization group approach. It is controlled for small interactions and can directly be applied to the microscopic lattice model. We benchmark the results against numerical density matrix renormalization group data. The main interaction effect in the bulk is a power-law renormalization of the gap with an interaction dependent exponent. The important characteristics of the boundary charge are unaltered and can be understood from the renormalized bulk properties, elevating the bulk-boundary correspondence to the interacting regime. This requires a consistent treatment not only of the low-energy gap renormalization but also of the high-energy band width one. In contrast to low-energy field theories our renormalization group approach also provides the latter. We show that the interaction spoils the relation between the bulk properties and the number of edge states, consistent with the observation that the Rice-Mele model with finite potential modulation does not reveal any zero-energy edge states.
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