Entanglement growth in diffusive systems

Recent works 1,2 argued that Rényi entropies Sα with indices α > 1 exhibit a sub-ballistic, / ffiffi t p , 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 works 1,2 argued that Rényi entropies Sα with indices α > 1 exhibit a sub-ballistic, / ffiffi t p , 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 ballis...     »