Entanglement in shape phase transitions of coupled molecular benders

Abstract

We study the entanglement properties of the shape phase transitions between different geometric limits of two coupled equivalent molecular benders modeled with the two-dimensional limit of the vibron model. This system has four possible geometric configurations: linear, cis-bent, trans-bent, and nonplanar. We show how the entanglement, accessed through the calculation of the linear entropy, between benders and between rotational and vibrational degrees of freedom changes sensitively in the critical regions of this two-fluid bosonic model. The numeric calculation is complemented with a variational approach to the ground-state wave function in terms of symmetry-adapted coherent states.

Hilbert space and ground-state structure of bilayer quantum Hall systems at ν=2/λ

“…Parity adapted coherent states like (29) have also been successfully used to better reproduce the exact quantum results at finite-size from the mean-field approximation in other interesting models undergoing a second order QPT like for example the Dicke model of atom-field interactions [32][33][34], the vibron model of molecules [35][36][37][38] and the Lipkin-Meshkov-Glick model [39].…”

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

“…In this case, we have conjectured [16] that minimum entropy W ψ = N(3+2N) (N+1)(N+2) is attained for U(3) coherent states. In the bent phase, the ground state |ψ is a cat [16,17,71] and therefore W ψ N(3+2N) (N+1)(N+2) + ln(2).…”

“…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].…”

“…Moreover, the zeros of this phase-space quasiprobability distribution have been used as an indicator of the regular or chaotic behavior in quantum maps for a variety of quantum problems: molecular [19] and atomic [20] systems, the kicked top [21], quantum billiards [22], or condensed matter systems [23] (see also [24,25] and references therein). They have also been considered as an indicator of metal insulator [26] and topological-band insulator [27] phase transitions, as well as of QPTs in Bose-Einstein condensates [10] and in the Dicke [28,29], vibron [17], and Lipkin-Meshkov-Glick (LMG) models [30].…”

“…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).…”