The half-infinite XXZ chain in Onsager's approach

Understand

The half-infinite XXZ open spin chain with general integrable boundary conditions is considered within the recently developed `Onsager's approach'.

• Inspired by the finite size case, for any type of integrable boundary conditions it is shown that the transfer matrix is simply expressed in terms of the elements of a new type of current algebra recently introduced.
• In the massive regime $-1<q<0$, level one infinite dimensional representation ($q-$vertex operators) of the new current algebra are constructed in order to diagonalize the transfer matrix.
• For diagonal boundary conditions, known results of Jimbo {\it et al.} are recovered.