The Baxter Q Operator of Critical Dense Polymers

TL;DR

This paper analyzes the Baxter Q operator for critical dense polymers, revealing its decomposition into lattice integrals of motion, and connects lattice operators with conformal field theory predictions, including spectral properties.

Contribution

It provides a novel lattice decomposition of the Baxter Q operator for critical dense polymers and links lattice charges with conformal field theory results.

Findings

Decomposition of the Baxter Q operator into lattice integrals of motion.

Identification of lattice operators matching CFT predictions.

Eigenvalues of Q reproduce the spectral determinant of the harmonic oscillator.

Abstract

We consider critical dense polymers ${\cal L}_{1,2}$, corresponding to a logarithmic conformal field theory with central charge $c=-2$. An elegant decomposition of the Baxter $Q$ operator is obtained in terms of a finite number of lattice integrals of motion. All local, non local and dual non local involutive charges are introduced directly on the lattice and their continuum limit is found to agree with the expressions predicted by conformal field theory. A highly non trivial operator $\Psi(\nu)$ is introduced on the lattice taking values in the Temperley Lieb Algebra. This $\Psi$ function provides a lattice discretization of the analogous function introduced by Bazhanov, Lukyanov and Zamolodchikov. It is also observed how the eigenvalues of the $Q$ operator reproduce the well known spectral determinant for the harmonic oscillator in the continuum scaling limit.