species have uniform unit occupancy. For $U_{12} > U$ the MI lobes are replaced by DW as seen in Fig(d).[]{data-label="ebhm_v12_0"}](ebh_v12p0_ph.pdf){width="8.0cm"}

The ground state of the extended BHM Hamiltonian in Eq. (\[bhm\_ext\_ss\]), like in the previous case, is obtained using the Gutzwiller ansatz. The long range interactions in the extended BHM introduce two more phases, DW and SS, in the phase diagram. To analyse and highlight the effect of long range intra- and inter-species interactions, we first consider the case of $V_{12} = 0$. And, set the intra-species NN interaction strength $V_k = 0.05U$. Then, vary the inter species onsite interaction strength $U_{12}$, which can be achieved in experiments through Feshbach resonance. The choice of low value of $V_k$ is based on the parameters realized in dipolar BEC experiments [@baier_16]. In these experiments, $V/\hbar$ is in the range $\sim 10-100$ Hz, whereas $U/\hbar$ has typical values in kHz. In addition, this choice of parameters has the unique possibility to study the MI-DW quantum phase transition by changing $U_{12}$ keeping $V_k$ fixed. This is to be contrasted with the eBHM, where the NN interaction strength $V\ge0.25U$ [@iskin_11; @kuldeep_19] marks the critical point for such quantum phase transitions. Like in the BHM case, 