Excited states in the twisted XXZ spin chain

We compute the finite-size spectrum for the spin-1/2 XXZ chain with twisted boundary conditions, for anisotropy in the regime 0 < y < pi/2, and arbitrary twist theta. The string hypothesis is employed for treating complex excitations. The Bethe ansatz equations are solved within a coupled nonlinear integral equation approach, with one equation for each type of string. The root-of-unity quantum group invariant periodic chain reduces to the XXZ(1/2) chain with a set of twist boundary conditions (pi/gamma epsilon Z, theta an integer multiple of gamma). For this model, the restricted Hilbert space corresponds to a unitary conformal field theory, and we recover all primary states in the Kac table in terms of states with specific twist and strings.