U. Bilstein et B. Wehefritz, SPECTRA OF NON-HERMITIAN QUANTUM SPIN CHAINS DESCRIBING BOUNDARY INDUCED PHASE-TRANSITIONS, Journal of physics. A, mathematical and general, 30(14), 1997, pp. 4925-4938
The spectrum of the non-Hermitian asymmetric XXZ-chain with additional
nondiagonal boundary terms is studied. The lowest-lying eigenvalues a
re determined numerically. For the ferromagnetic chain the temporal co
rrelation 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 Cou
lomb gas with only magnetic charges. This is in contrast to the case o
f diagonal boundary terms where one finds only electric charges. Simil
ar results are obtained in a toy model that can be diagonalized analyt
ically in terms of free fermions.