Entanglement growth in diffusive systems with large spin

Recent works1,2 argued that Rényi entropies Sα with indices α > 1 exhibit a sub-ballistic, , growth in systems with diffusive transport. A subsequent work by Žnidarič3 claims that such sub-ballistic growth occurs only in certain cases (in particular, d = 1 dimensional systems with q = 2 states per site) and is generically replaced by ballistic growth in the absence of further fine-tuning. Below, we try to make precise the conditions needed for diffusive (rather than ballistic) Rényi growth and argue that they apply to a much wider class of systems than what is suggested by Žnidarič3. In particular, the examples presented by Žnidarič that avoid diffusive growth do so because of the presence of additional non-conserved degrees of freedom, not merely their larger local Hilbert space.     «

Recent works1,2 argued that Rényi entropies Sα with indices α > 1 exhibit a sub-ballistic, , growth in systems with diffusive transport. A subsequent work by Žnidarič3 claims that such sub-ballistic growth occurs only in certain cases (in particular, d = 1 dimensional systems with q = 2 states per site) and is generically replaced by ballistic growth in the absence of further fine-tuning. Below, we try to make precise the conditions needed for diffusive (rather than ballistic) Rényi growth and a...     »