Effect of classical bifurcations on the quantum entanglement of two coupled quartic oscillators

We study entanglement in a system comprising two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated periodic orbits whose bifurcation sequence affects a class of strongly scarred quantum eigenstates, called the channel localized states. For these states, the entanglement is a local minima in the vicinity of a pitchfork bifurcation but is a local maxima near an antipitchfork bifurcation. We place these results in the context of the close connections that may exist between entanglement measures and conventional measures of localization. We also point to an interesting near degeneracy that arises in the spectrum of reduced density matrices of certain states as an interplay between localization and symmetry.