Phase diagrams of bosonic $AB_{n}$ chains

Abstract

The $AB_{N-1}$ 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 shows $ρ+1$ insulator phases, a Mott insulator phase, and $ρ$ CDW phases. For non-integer densities larger than one, several CDW phases appear.

8 pages, 13 Figures. Published version