Figure 3 | Scientific Reports

Figure 3

From: Methods for the construction of interacting many-body Hamiltonians with compact localized states in geometrically frustrated clusters

Figure 3

(a) Lieb lattice with two plaquettes. (b) One-particle localized state of a Lieb plaquette. This state result from the combination of two one-plaquette states with opposite momentum. (c) Compact localized states of the TB Hamiltonian for the lattice in (a), with one spin up and one spin down, in the network representation. The standing-waves associated to the CL states share some nodes (with finite particle wavefunction amplitude), evidencing the non-orthogonal nature of the CL states subspace basis. (d) Network associated to the TB Hamiltonian with Hubbard interacting terms projected onto the subspace of extended states, for the lattice in (a), with one spin up and one spin down. All sites with finite particle wavefunction amplitude (red sites) are connected to each other, meaning that hoppings of particles or pair of particles (or displaced pairs of particles) between plaquettes are allowed. Figure generated in Mathematica 8, https://www.wolfram.com/.

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