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arXiv:1610.03700 · Physical Review E

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

Octavio Castaños, Manuel Calixto, Francisco Pérez-Bernal, E. Romera

Published Nov 6, 2015• 19 citations
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Abstract

We propose a method to identify the order of a quantum phase transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the quantum cusp and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.
DOI
10.1103/physreve.92.052106

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This research demonstrates that entropy-based measures, calculated from marginals of the Husimi functions, effectively identify and characterize quantum phase transitions in the Lipkin-Meshkov-Glick model. The study reveals that changes in entropy, particularly Wehrl entropy, marginal entropies, and mutual information, act as sensitive indicators of criticality, distinguishing between different transition orders and highlighting the breakdown of separability near critical points. These findings establish entropy analysis as a powerful, complementary tool to traditional methods for understanding quantum criticality in many-body systems.
We present a phase-space study of first-, second- and third-order quantum phase transitions in the Lipkin–Meshkov–Glick model by means of the Husimi function. By analyzing the distribution of zeros of the ground state Husimi function we have characterized each phase and each type of quantum phase transition in this model. We show that Renyi–Wehrl entropies of the ground state Husimi function give a good description of quantum phase transitions. The study has been done using a numerical treatment and a variational approximation in terms of coherent states. Additionally, we have analyzed quantum phase transitions using the fidelity and fidelity susceptibility concepts.
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The fidelity, linear entropy and entanglement entropy, concepts of information theory, are used to determine the localization of quantum phase transitions of the Lipkin–Meshkov–Glick (LMG) and the Dicke models for a finite number of particles. Another concept, the so-called fidelity susceptibility, gives us information of the scaling behavior of the quantum phase transitions of the models. In particular universal curves are presented for the specific susceptibility. It is shown that the control parameters of both models have a similar dependence in the number of particles when the systems approach to the thermodynamic limit.
We propose a new method to characterize equilibrium quantum phase transitions in terms of the spectrum of multiple quantum coherence (MQC) intensities, a special type of out-of-time-order correlation. Using the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as illustrative examples, we show that an abrupt change in coherence and entanglement of the ground state across a quantum phase transition is clearly observable in the MQC spectrum. Furthermore, we develop a robust protocol to obtain the MQC intensities across the ground state phase diagram, which is accessible to a broad range of current experiments as it relies on standard quasi-adiabatic quenches without the requirement of time-reversing the dynamics.