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

摘要

We propose coherent (`Schr\"odinger catlike') states adapted to the paritysymmetry providing a remarkable variational description of the ground and firstexcited states of vibron models for finite-($N$)-size molecules. Vibron modelsundergo a quantum shape phase transition (from linear to bent) at a criticalvalue $\xi_c$ of a control parameter. These trial cat states reveal a suddenincrease of vibration-rotation entanglement linear ($L$) and von Neumann ($S$)entropies from zero to $L^{(N)}_{\rm cat}(\xi)\simeq 1-{2}/{\sqrt{\pi N}}$ [tobe compared with $L^{(N)}_{\rm max.}(\xi)=1-{1}/{(N+1)}$] and $S^{(N)}_{\rmcat}(\xi)\simeq \frac{1}{2} \log_2(N+1)$, respectively, above the criticalpoint, $\xi>\xi_c$, in agreement with exact numerical calculations. We alsocompute inverse participation ratios, for which these cat states capture asudden delocalization of the ground state wave packet across the criticalpoint. Analytic expressions for entanglement entropies and inverseparticipation ratios of variational states, as functions of $N$ and $\xi$, aregiven in terms of hypergeometric functions.