order parameters are non-zero in the SS phase. For easy reference the properties of the different quantum phases are listed in Table. \[table\].

Phase diagram of TBHM {#sec_phdiag}
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![Phase diagram of TBEC by varying the inter-species interaction strength $U_{12}$. Blue solid lines represent numerically obtained phase boundaries for the mean field hamiltonian. Filled dots marks analytically obtained phase boundaries between compressible and incompressible phases, obtained analytically by perturbative analysis of the mean-field hamiltonian. The odd occupancy MI lobes appear for non zero $U_{12}$ and enlarges with increasing $U_{12}$.[]{data-label="tbec_ph"}](tbc_ph.pdf){width="8.0cm"}

To compute the ground state wavefunction and determine the phase, we initialize the SF order parameter $\phi$. This, then, defines the Hamiltonian in Eq. (\[ham\_ss\_tbec\]) and Hamiltonian matrix elements are computed using Gutzwiller wavefunction in Eq. (\[gw\_2s\]). By digonalizing the Hamiltonian matrix for each site we obtain the ground state wavefunction. From the results, the MI-SF phase boundary is identified based on the SF order parameter and the lattice occupancy. For the incompressible MI phase, at each lattice site, $\phi$ is zero and $\rho$ is integer commensurate. For the SF phase, $\phi$ is nonzero and $\rho$ is real commensurate. The phase diagrams of BH Hamiltonian of TBEC in Eq. (\[ham\_ss\_tbec\]) for 