Flat bands by latent symmetry
Flat bands by latent symmetry
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DOI：
10.1103/physrevb.104.035105
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发表时间：
2021-07-02
影响因子：
3.7
通讯作者：
Schmelcher, P.
中科院分区：
文献类型：
--
作者：
Morfonios, C., V;Roentgen, M.;Schmelcher, P.
模型晶格哈密顿量的平坦能带是设计无色散波激发的关键因素，已成为研究相互作用多体系统各方面的通用平台。它们的基本优点在于拥有紧凑的局域本征态，这些本征态源于晶格几何诱导的破坏性干涉，而这些干涉又往往基于对称原理。我们在这里表明，平带可以由晶格单胞的隐藏对称性产生，当晶胞在由有效二聚体哈密顿量控制的两个位置上约化时，显示为置换对称性。这种所谓的潜在对称性与粒子沿细胞位置的可能行走之间的对称性密切相关，这些对称始于和结束于每个有效的二聚体位置。在称为行走多重态的特殊位置子集上，在有效二聚体位置上具有奇宇称的任何本征态的总和幅度为零。我们利用这一点，通过步进多重态互连将一个潜在的对称单胞耦合到一个格子中来构造平带。我们证明了所得到的平带可以通过保持潜在对称性的晶格哈密顿矩阵元的不同参数来调节。所开发的框架为平带结构的分析和设计提供了丰富的视角。
Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing dispersionless wave excitations and have become a versatile platform to study various aspects of interacting many-body systems. Their essential merit lies in hosting compactly localized eigenstates which originate from destructive interference induced by the lattice geometry, in turn often based on symmetry principles. We here show that flat bands can be generated from a hidden symmetry of the lattice unit cell, revealed as a permutation symmetry upon reduction of the cell over two sites governed by an effective dimer Hamiltonian. This so-called latent symmetry is intimately connected to a symmetry between possible walks of a particle along the cell sites, starting and ending on each of the effective dimer sites. The summed amplitudes of any eigenstate with odd parity on the effective dimer sites vanish on special site subsets called walk multiplets. We exploit this to construct flat bands by using a latently symmetric unit cell coupled into a lattice via walk multiplet interconnections. We demonstrate that the resulting flat bands are tunable by different parametrizations of the lattice Hamiltonian matrix elements which preserve the latent symmetry. The developed framework may offer fruitful perspectives to analyze and design flat band structures.