Parity-symmetry-adapted coherent states and entanglement in quantum phase transitions of vibron models

We propose coherent ('Schrödinger cat-like') states adapted to the parity symmetry providing a remarkable variational description of the ground and first excited states of vibron models for finite (N)-size molecules. Vibron models undergo a quantum shape phase transition (from linear to bent) at a critical value ξc of a control parameter. These trial cat states reveal a sudden increase in vibration–rotation entanglement linear (L) and von Neumann (S) entropies from zero to L(N)cat(ξ)≅1-2/√(πN) (to be compared with L(N)max(ξ) = 1 − 1/(N + 1)) and S(N)cat(ξ)≅ 1/2 log 2(N+1), respectively, above the critical point, ξ > ξc, in agreement with exact numerical calculations. We also compute inverse participation ratios, for which these cat states capture a sudden delocalization of the ground-state wave packet across the critical point. Analytic expressions for entanglement entropies and inverse participation ratios of variational states, as functions of N and ξ, are given in terms of hypergeometric functions. (paper)