The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-$1/2$ chains with uniform local couplings to a Markovian environment using the time-dependent density matrix renormalization group. For the open $XXZ$ model, we discover that the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. This is due to a vanishing gap in the spectrum of the corresponding Liouville superoperator and can be explained on the basis of a perturbative treatment. In contrast, decoherence in the open transverse-field Ising model is found to be always exponential. In this case, the internal interactions can both facilitate and impede the environment-induced decoherence.

• Received 25 April 2013

DOI:https://doi.org/10.1103/PhysRevLett.111.150403