Superconformal invariance in the Ashkin-Teller quantum chain with free boundary conditions

The finite-size limit of the lower part of the spectrum of the Ashkin-Teller chain with free boundary conditions is studied numerically and interpreted from the point of view of conformal invariance. Several irreducible representations of the Virasoro algebra with the central charge c=1 are identified. For two special values of the coupling constant, higher degeneracies occur and the whole spectrum can be understood in terms of a few irreducible representations of the N=2 superconformal algebra. Remarkably enough, although the spectrum is supersymmetric for free boundary conditions, it is not for periodic or twisted boundary conditions. (orig.)