On the parafermionic scattering of an integrable Heisenberg model with impurity

TL;DR

This paper investigates the effects of an impurity in an integrable spin chain using parafermionic scattering theory, revealing how impurities influence finite size properties and ground state degeneracy, with implications for boundary conformal invariance.

Contribution

It introduces a computable parafermionic impurity scattering amplitude and analyzes its impact on the finite size properties and ground state degeneracy of the model.

Findings

Impurity scattering amplitude is explicitly computed.

Impurity affects the finite size free energy.

Ground state degeneracy is non-integer and characterized.

Abstract

We have studied the massive parafermionic sector of an integrable spin-$s$ chain with an impurity of spin-$s^{'}$ in presence of a magnetic field. The effect of the impurity is encoded in a computable parafermionic impurity scattering amplitude and its contribution to the finite size properties of the free energy is discussed. As an example we compute the non-integer degeneracy of the ground state. For the simplest model of $s=1$ and $s^{'}=1/2$, its interpretation in terms of conformally invariant boundary conditions is presented.