论文标题
边缘状态理论基于紧密结合的汉密尔顿操作员的墓穴
Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators
论文作者
论文摘要
我们基于哈密顿操作员的墓穴基础，开发出边缘状态的理论，用于在边界上定义的紧密结合模型。我们使用轮班操作员描述了哈密顿人，这些转移操作员是连续理论中的差异操作员。事实证明，这样的汉密尔顿运营商不一定是在边界上的晶格上的Hermitian，这是由于与部分的总和相关的边界条款。哈密顿操作员的墓穴导致了自然的边界条件，对于最近邻居（NN）跳的模型，有参考状态同时满足墓地和边界条件。基于此类参考状态，我们为半平面上NN模型的边缘状态开发了Bloch型理论。这使我们能够提取汉密尔顿人描述边缘的边缘，而边缘与批量贡献分开。因此，我们可以通过不同的哈密顿量在圆柱形几何体系中分别描述左右两端的边缘状态。我们展示了这种边缘状态汉密尔顿（ESH）的各种示例，包括霍夫史塔特模型，石墨烯模型和高阶拓扑绝缘子（HOTIS）。
We develop a theory of edge states based on the Hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which serve as differential operators in continuum theories. It turns out that such Hamiltonian operators are not necessarily Hermitian on lattices with boundaries, which is due to the boundary terms associated with the summation by parts. The Hermiticity of Hamiltonian operators leads to natural boundary conditions, and for models with nearest-neighbor (NN) hoppings only, there are reference states that satisfy the Hermiticity and boundary conditions simultaneously. Based on such reference states, we develop a Bloch-type theory for edge states of NN models on a half-plane. This enables us to extract Hamiltonians describing edge-states at one end, which are separated from the bulk contributions. It follows that we can describe edge states at the left and right ends separately by distinct Hamiltonians for systems of cylindrical geometry. We show various examples of such edge state Hamiltonians (ESHs), including Hofstadter model, graphene model, and higher-order topological insulators (HOTIs).
