Critical dense polymers with Robin boundary conditions, half-integer Kac labels and Z4 fermions

Abstract

For general Temperley-Lieb loop models, including the logarithmic minimal models LM(p,p') with p, p' coprime integers, we construct an infinite family of Robin boundary conditions on the strip as linear combinations of Neumann and Dirichlet boundary conditions. These boundary conditions are Yang-Baxter integrable and allow loop segments to terminate on the boundary. Algebraically, the Robin boundary conditions are described by the one-boundary Temperley-Lieb algebra. Solvable critical dense polymers is the first member LM(1,2) of the family of logarithmic minimal models and has loop fugacity β=0 and central charge c=-2. Specialising to LM(1,2) with our Robin boundary conditions, we solve the..