YangBaxter solution of dimers as a freefermion sixvertex model
Abstract
It is shown that Dimers is YangBaxter integrable as a sixvertex model at the freefermion point with crossing parameter \newcommand⪉λ λ=\fracπ{2} . A onetomany mapping of vertices onto dimer configurations allows the freefermion solutions to be applied to the anisotropic dimer model on a square lattice where the dimers are rotated by 45^{\circ} compared to their usual orientation. This dimer model is exactly solvable in geometries of arbitrary finite size. In this paper, we establish and solve inversion identities for Dimers with periodic boundary conditions on the cylinder. In the particle representation, the local face tile operators give a representation of the fermion algebra, and the fermion particle trajectories play the role of nonlocal (logarithmic) degrees of freedom. In a suitable gauge, the dimer model is described by the TemperleyLieb algebra with loop fugacity \newcommand⪉λ β=2\cosλ=0 . At the isotropic point, the exact solution allows for the explicit counting of 45^{\circ} rotated dimer configurations on a periodic M× N rectangular lattice. We show that the modular invariant partition function on the torus is the same as that of symplectic fermions and critical dense polymers. We also show that nontrivial Jordan cells appear for the dimer Hamiltonian on the strip with vacuum boundary conditions. We therefore argue that, in the continuum scaling limit, the dimer model gives rise to a logarithmic conformal field theory with central charge c=2 , minimal conformal weight \newcommand{\D}Δ Δ_{min}=1/8 and effective central charge c_{eff}=1 .
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2017
 DOI:
 10.1088/17518121/aa86bc
 arXiv:
 arXiv:1612.09477
 Bibcode:
 2017JPhA...50Q4001P
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 arXiv:1612.09477 [mathph] 30 Dec 2016