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

Abstract

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 $f=-0.662798972833746$ with the dimer density $n=0.638123109228547$, both of 15 correct digits.

8 pages, 15 figures

References in corpus (6)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• The iTEBD algorithm beyond unitary evolution
• Interacting classical dimers on the square lattice
• Classical dimers with aligning interactions on the square lattice
• Linearized Tensor Renormalization Group Algorithm for Thermodynamics of Quantum Lattice Models
• Approximating the monomer-dimer constants through matrix permanent

Cited by in corpus (2)

• CTMRG study of the critical behavior of an interacting-dimer model
• Topology-driven phase transitions in the classical monomer-dimer-loop model