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Physical Review E

Reply to “Comment on ‘Exploring chaos in the Dicke model using ground-state fidelity and Loschmidt echo’ ”

Utso Bhattacharya, Sayak Dasgupta, Amit Dutta

Published Mar 10, 2015• 1 citation
Publisher

Abstract

Although we agree with the fact reported in García-Mata et al. [Phys. Rev. E 91, 036901 (2015)] that a computational error resulted in misinterpretation of the behavior of the ground-state fidelity only, we emphasize below that this does not alter the main conclusion of our paper. That is the main claim that we had made about the use of quantum information measures to study chaos in the Dicke model still holds true.

DOI
10.1103/physreve.91.036902

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Although we agree with the fact reported in García-Mata et al. [Phys. Rev. E 91, 036901 (2015)] that a computational error resulted in misinterpretation of the behavior of the ground-state fidelity only, we emphasize below that this does not alter the main conclusion of our paper. That is the main claim that we had made about the use of quantum information measures to study chaos in the Dicke model still holds true.
We study the quantum critical behavior of the Dicke Hamiltonian with finite number of atoms and explore the signature of quantum chaos using measures like the ground-state fidelity and the Loschmidt echo and the time-averaged Loschmidt echo. We show that these quantities clearly point to the classically chaotic nature of the system in the superradiant (SR) phase. While the ground-state fidelity shows aperiodic oscillations as a function of the coupling strength, the echo shows aperiodic oscillations in time and decays rapidly when the system is in the SR phase. We clearly demonstrate how the time-averaged value of the echo already incorporates the information about the ground-state fidelity and stays much less than unity, indicating the classically chaotic nature of the model in the SR phase.
We reply to the preceding Comment that attempts to clarify the connection between chaos and entanglement exposed in our previous paper [Phys. Rev. E 83, 016207 (2011)PRESCM1539-375510.1103/PhysRevE.83.016207]. We present additional computations that show the argument exposed in the Comment to explain the entangling power of some regular states is not important in the present case. More fundamentally we argue that the example chosen in the Comment is not the most significant in order to understand why specific regular dynamics can entangle as efficiently as when the corresponding classical dynamics is chaotic.
In the work of Das and Sharma [Phys. Rev. A 105, 033716 (2022)] the phase transitions of the Dicke model are studied. Its main result is that, besides the well-known quantum phase transition, excited-state quantum phase transition, and thermal phase transition exhibited by the model, there exists an upper bound energy E∗{E}_{*}E∗​ beyond which the model ceases to exhibit quantum chaotic behavior and the structure of the eigenfunctions changes. Based on this finding, a number of well-established results about the Dicke model are called into question. We argue that this result and all its consequences are spurious numerical effects resulting from an improper truncation of the infinite-dimensional Hilbert space necessary for numerical diagonalization.