2014/11/05 by Sazi Li, Wei Li, Ziyu Chen · 1 citation
Mathematics · Physics and Astronomy · #Checkerboard #Condensed matter physics #Dimer #Geometry #Ising model #Kosterlitz–Thouless transition #Lattice (music) #Lattice model (finance) #Materials science #Mathematics #Monomer #Nuclear magnetic resonance #Opinion Dynamics and Social Influence #Phase (matter) #Phase diagram #Phase transition #Physics #Polymer #Quantum many-body systems #Quantum mechanics #Square lattice #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.90.052104
published as Physical Review E 90, 052104 (2014) · 8 pages, 15 figures
openalex publication_date 2014/11/05 · arxiv created 2015/04/07 · arxiv updated 2015/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using the tensor network approach, we investigate the monomer-dimer models on a checkerboard lattice, in which there are interactions (with strength v) 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 low-temperature symmetry breaking and the high-temperature critical phases; for the doped monomer-dimer case with finite chemical potential \ensuremathμ, 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 v\text\ensuremath-T and \ensuremathμ\text\ensuremath-T. Moreover, for the noninteracting monomer-dimer model (setting \ensuremathμ=\ensuremathν=0), we get an extraordinarily accurate determination of the free energy per site (negative of the monomer-dimer constant h2) as f=\ensuremath-0.662\phantom\rule0.16em0ex798\phantom\rule0.16em0ex972\phantom\rule0.16em0ex833\phantom\rule0.16em0ex746 with the dimer density n=0.638\phantom\rule0.16em0ex123\phantom\rule0.16em0ex109\phantom\rule0.16em0ex228\phantom\rule0.16em0ex547, both of 15 correct digits.