Phase diagrams of bosonic ABn chains
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Abstract
The ABN−1 chain is a system that consists of repeating a unit cell with N sites where between
the A and B sites there is an energy difference of λ. We considered bosons in these special lattices and
took into account the kinetic energy, the local two-body interaction, and the inhomogenous local energy
in the Hamiltonian. We found the charge density wave (CDW) and superfluid and Mott insulator phases,
and constructed the phase diagram for N = 2 and 3 at the thermodynamic limit. The system exhibited
insulator phases for densities ρ = α/N, with α being an integer. We obtained that superfluid regions
separate the insulator phases for densities larger than one. For any N value, we found that for integer
densities ρ, the system exhibits ρ + 1 insulator phases, a Mott insulator phase, and ρ CDW phases. For
non-integer densities larger than one, several CDW phases appear.
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