Phase diagrams of bosonic $AB_{n}$ chains

TL;DR

This paper explores the phase diagrams of bosonic $AB_{n}$ chains, revealing various insulator, superfluid, and charge density wave phases, with detailed analysis for specific chain lengths and densities.

Contribution

It provides the first detailed phase diagrams of bosonic $AB_{n}$ chains, including the effects of inhomogeneity and interactions for different densities and chain lengths.

Findings

Identified charge density wave, superfluid, and Mott insulator phases.

Constructed phase diagrams for $N=2$ and $3$ at the thermodynamic limit.

Found multiple insulator phases for integer and non-integer densities.

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 $\lambda$. 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 $\rho=\alpha/N$, with $\alpha$ 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 $\rho$, the system shows $\rho +1$ insulator phases, a Mott insulator phase, and $\rho$ CDW phases. For non-integer densities larger than one, several CDW phases appear.