New solutions to the Reflection Equation and the projecting method

TL;DR

This paper introduces new integrable boundary conditions for quantum systems by tuning scattering phases and projecting onto sub-spaces, demonstrated through specific impurity and spin models.

Contribution

It presents a novel method for constructing integrable boundary conditions via phase tuning and projection, applied to impurity and spin models.

Findings

Constructed new boundary conditions for quantum chains.

Demonstrated the method on impurity and spin models.

Showed integrability is preserved under these conditions.

Abstract

New integrable boundary conditions for integrable quantum systems can be constructed by tuning of scattering phases due to reflection at a boundary and an adjacent impurity and subsequent projection onto sub-spaces. We illustrate this mechanism by considering a gl(m<n)-impurity attached to an open gl(n)-invariant quantum chain and a Kondo spin S coupled to the supersymmetric t-J model.