Entanglement Negativity of Random Hamiltonian Dynamics*

The dynamics of quantum many-body entanglement gives an important way to understand thermalization. There has been rapid progresses in understanding quantum thermalization based on mixed-state entanglment. Several methods including many-body lcalized (MBL) Hamiltonian and random mixed state all indicate that the averaged bipartite entanglement entropy follows a change from area law to volume law when the ratio f of a subsystem to the total system approaches 0.5. 

In this paper, we use a new and novel way, random Hamiltonian dynamics to confirm the above result and find the early time to late time dynamics of  entanglement entropy. For this purpose, we consider a tripartite system with subregion A, B, C and study the Renyi negativity(n=3) between A and B. An important step is to translate Renyi negativity as an entanglement feature (EF) of quantum many-body states. Therefore, different subregion divisions correspond to different final states. Furthermore, we generate unitary evolution using GUE Hamiltonian such that the unitary gate entanglement property determined the evolution of the final state. So our main calculation lies in computing entanglement features of unitary gates corresponding to different subregion divisions. 

It turns out that Renyi negativity indeed changes from area law to volume law at f = 0.5 in the late time. We are still working on more data to give a complete explanation of early time dynamics. There are also some interesting phenomenon of Renyi nagativity goes below 0 when Hilbert space dimention is small that's needed to be analyzed further.