Emergent Phases in an Extended Bose-Hubbard Model with Three-body On-site Interaction

We study the Extended Bose-Hubbard Model with a three-body onsite interaction. Using an exact diagonalization method and a variational Matrix Product States algorithm, \emph{Alps mps-optim}, we compute and analyse the energy charge gap and finite system correlation functions to obtain the phase boundaries and determine the phases and phase transitions of the model. For \mbox{$\frac{V}{U} = 0.6$} and \mbox{$\frac{W}{U} = 0$}, we observed the emergence of the Haldane insulator (HI) phase at the tip of the \mbox{$\rho = 1$} charge density wave (CDW) lobe and for \mbox{$\frac{V}{U} = 0.6$} and \mbox{$\frac{W}{U} = 1$}, we observed the emergence of the supersolid (SS) phase at the tip of the \mbox{$\rho = 1/2$} charge density wave (CDW) lobe. We also noticed that the effect of the inclusion of both the three-body onsite and nearest neighbor interactions on the phase diagram of the model for filling factor \mbox{$\rho = 2$} is to stabilize the Mott insulator (MI) phase such that the system remains in the MI phase for all values of $\frac{V}{U}$.