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

TL;DR

This paper introduces parity-symmetry-adapted coherent states to effectively describe quantum phase transitions and entanglement in vibron models of finite molecules, revealing sharp entanglement increases at critical points.

Contribution

It develops a variational approach using cat states that incorporate parity symmetry, providing analytic expressions for entanglement and delocalization in vibron models.

Findings

Entanglement entropy sharply increases at the phase transition

Variational states accurately match numerical results

Analytic formulas for entanglement and participation ratios are derived

Abstract

We propose coherent (`Schr\"odinger catlike') 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 $\xi_c$ of a control parameter. These trial cat states reveal a sudden increase of vibration-rotation entanglement linear ($L$) and von Neumann ($S$) entropies from zero to $L^{(N)}_{\rm cat}(\xi)\simeq 1-{2}/{\sqrt{\pi N}}$ [to be compared with $L^{(N)}_{\rm max.}(\xi)=1-{1}/{(N+1)}$] and $S^{(N)}_{\rm cat}(\xi)\simeq \frac{1}{2} \log_2(N+1)$, respectively, above the critical point, $\xi>\xi_c$, 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 $\xi$, are given in terms of hypergeometric functions.