论文标题
在几何沮丧的集群中建造与紧凑的局部状态相互作用的多体哈密顿量相互作用的方法
Methods for the construction of interacting many-body Hamiltonians with compact localized states in geometrically frustrated clusters
论文作者
论文摘要
在几何沮丧的晶格中增加相互作用的互动通常会导致局部状态的子空间减少。在本文中，我们展示了如何构建相互作用的多体汉密尔顿人，从无与伦比的紧密结合的汉密尔顿人开始，这些哈密顿人可以保留甚至扩大这些子空间。提出的方法涉及多体汉密尔顿人的一体网络表示，这些网络在这些哈密顿人中产生了新的相互作用术语。通过将相互作用的项投影到多体扩展状态的子空间，或者通过构造将折纸规则应用于网络的相互作用的子空间，可以保留许多粒子局部状态的子空间，以保存在相互作用的哈密顿量中。如果引入了将子空间与不同数量的粒子混合的相互作用项，则发现局部状态的扩展子空间。此外，我们提出了用于确定多体局部状态的数值方法，该方法允许人们解决更大的簇和颗粒数量较大的粒子，而不是通过完全对角线化的哈密顿相互作用。这些方法依赖于网络中紧凑型局部状态的概念的概括。最后，我们建议一种确定使用大量网络的局部状态的方法。
Adding interactions to many-body Hamiltonians of geometrically frustrated lattices often leads to diminished subspaces of localized states. In this paper, we show how to construct interacting many-body Hamiltonians, starting from the non-interacting tight-binding Hamiltonians, that preserve or even expand these subspaces. The methods presented involve modifications in the one-body network representation of the many-body Hamiltonians which generate new interacting terms in these Hamiltonians. The subspace of many-particle localized states can be preserved in the interacting Hamiltonian, by projecting the interacting terms onto the subspace of many-body extended states or by constructing the interacting Hamiltonian applying origami rules to the network. Expanded subspaces of localized states are found if interacting terms that mix subspaces with different number of particles are introduced. Furthermore, we present numerical methods for the determination of many-body localized states that allows one to address larger clusters and larger number of particles than those accessible by full diagonalization of the interacting Hamiltonian. These methods rely on the generalization of the concept of compact localized state in the network. Finally, we suggest a method to determine localized states that use a considerable fraction of the network.
