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

Abstract

We propose coherent (`Schrödinger 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 $L_{\mathrm{cat}}^{(N)}(\xi )\simeq 1-2/\sqrt{\pi N}$ [to be compared with $L_{max.}^{(N)}(\xi )=1-1/(N+1)$] and $S_{\mathrm{cat}}^{(N)}(\xi )\simeq \frac{1}{2}{\log }_2(N+1)$, 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.

8 pages, 7 figures

References in corpus (3)

• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• Husimi distribution and phase space analysis of Dicke model quantum phase transition
• Continuous unitary transformations in two-level boson systems

Cited by in corpus (11)

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• Identifying the order of a quantum phase transition by means of Wehrl entropy in phase-space
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• Anharmonicity-induced excited-state quantum phase transition in the symmetric phase of the two-dimensional limit of the vibron model
• Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules
• Information diagrams in the study of entanglement in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models
• Further results on the power-law decay of the fraction of the mixed eigenstates in kicked-top model with mixed-type classical phase space
• Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation
• Schmidt decomposition of parity adapted coherent states for symmetric multi-quDits
• Entanglement and U(D)-spin squeezing in symmetric multi-quDit systems and applications to quantum phase transitions in Lipkin-Meshkov-Glick D-level atom models