Refined conformal spectra in the dimer model

Abstract

Working with Lieb's transfer matrix for the dimer model, we point out that the full set of dimer configurations may be partitioned into disjoint subsets (sectors) closed under the action of the transfer matrix. These sectors are labelled by an integer or half-integer quantum number we call the variation index. In the continuum scaling limit, each sector gives rise to a representation of the Virasoro algebra. We determine the corresponding conformal partition functions and their finitizations, and observe an intriguing link to the Ramond and Neveu-Schwarz sectors of the critical dense polymer model as described by a conformal field theory with central charge c=-2.

44 pages

References in corpus (7)

• Classical dimers with aligning interactions on the square lattice
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Indecomposability parameters in chiral Logarithmic Conformal Field Theory
• Random trimer tilings
• The Jordan Structure of Two Dimensional Loop Models
• Wind on the boundary for the Abelian sandpile model
• Boundary monomers in the dimer model

Cited by in corpus (11)

• Logarithmic conformal invariance in the Abelian sandpile model
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Integrability and conformal data of the dimer model
• Dimer representations of the Temperley-Lieb algebra
• Topological sectors, dimer correlations and monomers from the transfer-matrix solution of the dimer model
• Yang-Baxter Solution of Dimers as a Free-Fermion Six-Vertex Model
• Exact finite-size corrections in the dimer model on a planar square lattice
• Finite Size Corrections for Dimers
• Yang-Baxter Integrable Dimers on a Strip
• Infinitely extended Kac table of solvable critical dense polymers
• Finite-size scaling of free energy in the dimer model on a hexagonal domain