Continuum Limit of Spin-1 Chain (the only change is added references)

TL;DR

This paper investigates the continuum limit of the spin-1 chain using non-Abelian bosonization, revealing its connection to the supersymmetric sine-Gordon model and identifying non-local charges from quantum group generators.

Contribution

It demonstrates that the integrable spin-1 chain Hamiltonian converges to the supersymmetric sine-Gordon model in the continuum limit and links quantum group symmetries to non-local charges.

Findings

The Hamiltonian yields the supersymmetric sine-Gordon Lagrangian in the zero lattice spacing limit.

Quantum group generators correspond to non-local charges in the supersymmetric sine-Gordon theory.

The approach confirms the continuum limit relationship between spin-1 chains and supersymmetric field theories.

Abstract

We study the continuum limit of the spin-1 chain in the non-Abelian bosonization approach of Affleck and show that the Hamiltonian of integrable spin-1 chain yields the Lagrangian of supersymmetric sine-Gordon model in the zero lattice spacing limit. We also show that the quantum group generators of the spin-1 chain give non-local charges of the supersymmetric sine-Gordon theory.