Spectra of non-Hermitian quantum spin chains describing boundary induced phase transitions

The spectrum of the non-Hermitian asymmetric XXZ-chain with additional nondiagonal boundary terms is studied. The lowest-lying eigenvalues are determined numerically. For the ferromagnetic chain the temporal correlation length shows the same properties as the spatial correlation length. For the antiferromagnetic chain, we find a conformal invariant spectrum where the partition function corresponds to the one of a Coulomb gas with only magnetic charges. This is in contrast to the case of diagonal boundary terms where one finds only electric charges. Similar results are obtained in a toy model that can be diagonalized analytically in terms of free fermions.