levels can decrease, and even tend to zero, resulting in an energy-level crossing. According to the von Neumann-Wigner no-crossing theorem, energy levels within a multiplet generically avoid crossing, provided only one of the parameters is varied in the Hamiltonian governing the system. In this paper, we investigate how effectively some of these entanglement indicators mimic the behaviour of $\xi_{\textsc{svne}}$ close to avoided crossings.

Energy-level crossings display other interesting features. Since they affect the level spacings and their probability distribution  [@BGSconj], they are also important from the point of view of non-integrability and quantum chaos (see, for instance, [@haake]). In addition, avoided crossings point to phase transitions which trigger a change in the quantum correlations in the system  [@cejnar; @heiss; @AClinkPT; @ent_change]. This aspect has been investigated extensively both theoretically and in experiments [@ACtheor1; @ACexpt1; @ACexpt2; @ACexpt3].

We examine two experimentally relevant bipartite CV systems: a Bose-Einstein condensate (BEC) in a double-well trap [@sanz], and a multilevel atom interacting with a radiation field [@agarwalpuri]. We also investigate a multipartite HQ system [@QuantMeta2; @QuantMeta] that is effectively described by the Tavis-Cummings model  [@tavis]. The rest of this paper is organized as follows: In the next section we introduce the entanglement indicators to 