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Figure 1

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

Figure 1

(a) One-body CL state in a Lieb cluster. This state can be interpreted as a standing wave with normalized wavefunction amplitudes (+1, 0, −1, 0, +1, ...) in a small region of the lattice (and zero in the rest of the lattice). (b) Network associated with the tight-binding Hamiltonian for a Lieb lattice with four plaquettes with two holes as particles (in a ferromagnetic background). The set of amplitudes given (red(blue) nodes have finite(zero) particle wavefunction amplitude) corresponds to a many-body localized state. This state is compact in the network and can still be interpreted as a standing wave. In (c), the same state is shown but the blue nodes that have no connections to red nodes were dropped. We designate this structure as a bubble. The compact many-boy localized state corresponds to the interlocking of one-body standing waves in the network. Figure generated in Mathematica 8, https://www.wolfram.com/.

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