Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms

TL;DR

This paper uses the Drinfeld twist to derive explicit, symmetric, and polarization-free Bethe vectors for the open XYZ chain with non-diagonal boundary conditions, simplifying their structure.

Contribution

It introduces a new F-basis via the Drinfeld twist that yields symmetric and polarization-free Bethe vectors for the open XYZ chain with non-diagonal boundaries.

Findings

Explicit symmetric Bethe vectors obtained

F-basis simplifies Bethe state expressions

Enhanced understanding of boundary effects in XYZ chain

Abstract

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model.