Yang--Baxter symmetry in integrable models: new light from the Bethe Ansatz solution

TL;DR

This paper demonstrates that integrable 2D quantum field theories possess infinitely many non-abelian conserved charges with Yang--Baxter symmetry, and explicitly computes transfer matrix eigenvalues using algebraic Bethe ansatz, revealing deep algebraic structures.

Contribution

It generalizes the bootstrap construction of quantum monodromy operators to the sine-Gordon model and explicitly connects transfer matrix eigenvalues to conserved charges via Bethe ansatz.

Findings

Eigenvalues of the transfer matrix are computed explicitly.

The transfer matrix is a two-valued periodic function in the thermodynamic limit.

Bootstrap results match the ratio of the two transfer matrix determinations.

Abstract

We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a representation of $q-$deformed affine Lie algebras. We review and generalize the work of de Vega, Eichenherr and Maillet on the bootstrap construction of the quantum monodromy operators to the sine--Gordon (or massive Thirring) model, where such operators do not possess a classical analogue. Within the light--cone approach to the mT model, we explicitly compute the eigenvalues of the six--vertex alternating transfer matrix $\tau(\l)$ on a generic physical state, through algebraic Bethe ansatz. In the thermodynamic limit $\tau(\l)$ turns out to be a two--valued periodic function. One determination generates the local abelian charges, including energy and momentum, while the other yields the abelian subalgebra of the (non--local) YB algebra. In particular, the bootstrap results coincide with the ratio between the two determinations of the lattice transfer matrix.