Abstract
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.
Highlights
Flat-band systems have been heavily studied in the past two decades[1,2,3,4,5,6,7,8,9]
A many-body interacting Hamiltonian can be interpreted as a one-body Hamiltonian with possibly long range hoppings and local potentials in the many-body Wannier base, where the single particle moves in the network defined by the finite Hamiltonian matrix elements between the many-body Wannier states [see[17] for details]
We show how to construct interacting many-body Hamiltonians that allow the existence of compact localized (CL) states and expand some of the ideas that were introduced in reference[17]
Summary
Flat-band systems have been heavily studied in the past two decades[1,2,3,4,5,6,7,8,9]. This implies that the set of one-particle maximally CL states generates a non-orthogonal basis of the flat band subspace, but they are still linearly independent, and the number of one-hole localized states is equal to the number of plaquettes, Nplaq.
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