Yang-Baxter Integrable Dimers as a Free-Fermion Six-Vertex Model on a cylinder and a strip

by Dr Alessandra Vittorini Orgeas (University of Melbourne, Australia)

Wednesday 11 Sept 2019, 14:00 → 16:00 Europe/Rome

Aula Teorici (DIFA)

The dimer model is formulated as a Yang-Baxter integrable free-fermion six-vertex model. In a suitable gauge, the dimer model is described by the Temperley-Lieb algebra with zero loop fugacity. We establish and solve inversion identities for dimers with periodic boundary conditions on the cylinder and with simple Kac boundary conditions on the strip geometry. Through the combinatorial analysis of the pattern of the zeros of the transfer matrix eigenvalues, we obtain empirical selection rules and use them to classify the spectra of eigenvalues, including degeneracies, and construct finitized characters. The analysis of the finite-size corrections to the free energy yield the central charge and conformal characters. We argue that the dimer model gives rise to a logarithmic conformal field theory with central charge c = −2. This is confirmed by the appearance of nontrivial Jordan cells in the double row transfer matrices of dimers with vacuum boundary conditions and the associated quantum hamiltonians.