Scaling of von Neumann entropy in dissipative Liouvillian dynamics

The universal dynamical phenomenon of von Neumann entropy plays an important role in understanding the nature of open many-body systems, as it uncovers general collective properties driven by correlation and quantum dynamics. Here, we reveal a universal time evolution behavior of bipartite von Neumann entropy in open quantum systems with dissipation into the surrounding environments. The coupling with the environment leads to a rapid growth of the entropy, resulting in an exotic short-time evolution law, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>S</a:mi><a:mo>(</a:mo><a:mi>t</a:mi><a:mo>)</a:mo><a:mo>∼</a:mo><a:mo>−</a:mo><a:mspace width="0.16em"/><a:mi>t</a:mi><a:mo form="prefix">ln</a:mo><a:mi>t</a:mi></a:mrow></a:math>. Such a fast growth behavior is proved to be a general phenomenon for generic many-body systems in dissipative environments, as long as the systems exhibit well-defined fermionic quasiparticles. Interestingly, even for strongly interacting Luttinger liquids, which display vanishing fermionic but emergent bosonic quasiparticles, the same dynamical phenomenon is still found to persist. These results demonstrate a universal Liouvillian dynamical feature that has no counterpart in isolated Hamiltonian systems.