Kosterlitz-Thouless transitions and phase diagrams of the interacting monomer-dimer model on a checkerboard lattice

Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength $\nu$) between the parallel dimers on half of the plaquettes. For the fully packed interacting dimer model, we observe a Kosterlitz-Thouless (KT) transition between the lowtemperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer casewith finite chemical potential $\mu$, we also find an order-disorder phase transition which is of second order instead. We use the boundary matrix product state approach to detect the KT and second-order phase transitions and obtain the phase diagrams $\nu -T$ and $\mu -T$ . Moreover, for the noninteracting monomer-dimer model (setting $\mu = \nu = 0$), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant $h_2$) as $f=-0.662, 798, 972, 833, 746$withthedimerdensity$n=0.638, 123, 109, 228, 547$, both of 15 correct digits.