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 ξc 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)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.

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space

“…Indeed, as conjectured by Wehrl [32] and proved by Lieb [31], any Glauber coherent state |ψ = |β has a minimum Wehrl entropy of W ψ = 1. It has also been shown [16,[28][29][30] that parity adapted coherent (Schrödinger cat) states, |ψ ∝ |β + | − β , increase the minimum entropy by approximately ln(2) (for negligible overlap −β|β ). With this information, we infer that the ground state |ψ is approximately a coherent state in the phase u > 0 and a catlike state in the phase u < 0.…”

“…Note that W ψ is a function of the control parameters and the system size N . We discuss typical (minimum) values of W ψ for each model, which are attained when the ground state ψ is coherent itself, and Wehrl entropy values of parity-adapted (Schrödinger cat) coherent states [72,73], which usually appear in second-order QPTs [16,17,28,30,44,45].…”

“…Alternative characterizations are based in the connection between geometric Berry phases and QPTs in the case of the XY Ising model [6,7] and in the overlap between two ground state wave functions for different values of the control parameter (fidelity susceptibility concept) [8][9][10]. In addition, many efforts have been devoted to characterize QPTs in terms of information theoretic measures of delocalization (see [11][12][13][14] and references therein) and quantum information tools, e.g., using entanglement entropy measures (see, e.g., [15] for the Dicke model and [16,17] for the vibron model).…”

Entanglement in shape phase transitions of coupled molecular benders

“…In this respect, the entanglement properties of a single-mode Dicke model [1,2], a two-mode Bose-Einstein condensate [3], and the vibrationrotation entanglement in the two-dimensional limit of the vibron model [4] can be found in the literature.…”

Complexity measure and quantum shape-phase transitions in the two-dimensional limit of the vibron model

“…These systems display remarkable properties when the so called LMC complexity [22,23] is computed on them [16,24]. Recently, it has been shown that Shannon and Rényi entropies [25][26][27] Wehrl entropies [28,29], entanglement entropies [30] and Rényi-Fisher products [31] detect QPTs in several atomic and chemical quantum models. In this article we show that the generalized complexity mesures [32] are also excellent descriptors of QPT in the vibron model for molecules.…”