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The finite size spectrum of the critical $\mathbb{Z}_2$-staggered spin-$1/2$XXZ model with quantum group invariant boundary conditions is studied. For aparticular (self-dual) choice of the staggering the spectrum of conformalweights of this model has been recently been shown to have a continuouscomponent, similar as in the model with periodic boundary conditions whosecontinuum limit has been found to be described in terms of the non-compact$SU(2,\mathbb{R})/U(1)$ Euclidean black hole conformal field theory (CFT). Herewe show that the same is true for a range of the staggering parameter. Inaddition we find that levels from the discrete part of the spectrum of this CFTemerge as the anisotropy is varied. The finite size amplitudes of both thecontinuous and the discrete levels are related to the corresponding eigenvaluesof a quasi-momentum operator which commutes with the Hamiltonian and thetransfer matrix of the model.

Finite size spectrum of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$-invariant boundary conditions