Phase diagram of the non-Hermitian asymmetric XXZ spin chain

The low-lying excitations of the asymmetric XXZ spin chain are derived explicitly in the antiferromagnetic regime through the Bethe ansatz. It is found that a massless and conformal invariant phase with central charge c = 1 is separated from a massive phase by a line on which the low-lying excitations surprisingly scale with the lattice length as Delta E similar to N--1/2. The mass gap vanishes with an exponent 1/2 as one approaches the massless phase. The connection with the asymmetric six-vertex model and some physical consequences are discussed.