Compact localized states and flat bands from local symmetry partitioning
Compact localized states and flat bands from local symmetry partitioning
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DOI：
10.1103/physrevb.97.035161
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发表时间：
2017-09
影响因子：
3.7
通讯作者：
M. Röntgen;C. Morfonios;P. Schmelcher
中科院分区：
文献类型：
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作者：
M. Röntgen;C. Morfonios;P. Schmelcher
我们提出了一个关于离散哈密顿量的局部对称性与紧致局域态设计之间的联系的框架。这种紧凑的局域态被用来在能量连续体中创建可调的局域对称性诱导束缚态，并在一维和二维晶格中创建周期性重复的局域对称性的平坦能带。该框架是基于图论中最新的定理，这里使用这些定理来获得给定系统在局部位置置换下的对称性所诱导的哈密顿量的块划分。因此，哈密顿量的对角化简化为寻找较小矩阵的本征谱，特征向量自动划分为紧凑的局域态和扩展态。我们区分了与哈密顿量交换的局域对称操作和由于与周围位置的非对称耦合而不交换的局域对称操作。虽然对于具有局部对称结构的多功能离散系统来说，这种方法是一种有价值的计算工具，但它尤其提供了一种统一、直观和有效的方法来灵活地设计所需能量下的紧致局域态。
We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states in an energy continuum and flat energy bands for periodically repeated local symmetries in one- and two-dimensional lattices. The framework is based on very recent theorems in graph theory which are here employed to obtain a block partitioning of the Hamiltonian induced by the symmetry of a given system under local site permutations. The diagonalization of the Hamiltonian is thereby reduced to finding the eigenspectra of smaller matrices, with eigenvectors automatically divided into compact localized and extended states. We distinguish between local symmetry operations which commute with the Hamiltonian, and those which do not commute due to an asymmetric coupling to the surrounding sites. While valuable as a computational tool for versatile discrete systems with locally symmetric structures, the approach provides in particular a unified, intuitive, and efficient route to the flexible design of compact localized states at desired energies.