Algebraic versus Exponential Decoherence in Dissipative Many-Particle Systems

Ultimately, every quantum system of interest is coupled to some form of environment which leads to decoherence. Until our recent study, it was assumed that, as long as the environment is memory-less (i.e. Markovian), the temporal coherence decay is always exponential-- to such a degree that this behavior was synonymously associated with decoherence. However, the situation can change if the system itself is a many-body system. In this case, the interplay between dissipation and internal interactions gives rise to a wealth of novel phenomena. In particular, we have discovered recently that the coherence decay can change to a power law. After recapitulating the mathematical framework and basic notions of decoherence, I will discuss an open XXZ chain for which the decoherence time diverges in the thermodynamic limit. The coherence decay is then algebraic instead of exponential. 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. The results are based on quasi-exact simulations using a matrix product representation of the density operator (time-dependent density matrix renormalization group) and explained on the basis of perturbative treatments. Reference: Z. Cai and T. Barthel, PRL 111, 150403 (2013)