Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1510.05244

Comment on "Comment on "Integrability of the Rabi Model""

Murray T. Batchelor, Zi-Min Li

Published Oct 18, 2015• 0 citations
arXivHTMLPDF

Abstract

In a recent Comment (arXiv:1510.00768) it was claimed that Braak's solution of the quantum Rabi model does not include the set of non-degenerate exceptional points and is thus not a complete solution. Braak's solution does contain these points however, as has been shown before, and which we demonstrate here by obtaining the same energy plots as in the Comment, directly from Braak's solution. Therefore the claim that Braak's solution is not complete is incorrect.

DOI
10.48550/arxiv.1510.05244

Related papers

Comment on "Integrability of the Rabi Model"

Wang Qing-wei, Yu-Liang Liu

Using Hill's determinant method we show that the set of Judd's solutions is only a subset of all the eigenvalues with the form $E_n=nω-g^2/ω$ in the spectrum of the Rabi model. Therefore Braak's solution of the quantum Rabi model is not complete.

arXiv:1510.00768•Oct 3, 2015•0 citations

Comment on "Integrability of the Rabi model"

Alexander Moroz

In his recent letter, Braak suggested that a regular spectrum of the Rabi model was given by the zeros of a transcendental function $G_\pm(x)$ (cf Eqs. (3)-(5) of Ref. [1]) and highlighted the role of the discrete $\mathbb{Z}_2$-symmetry, or parity, in determining $G_\pm(x)$. We show here to the contrary that one can define a transcendental function $F_0(x)$ and obtain the regular spectrum of the Rabi model as the zeros of $F_0(x)$ (see Fig. 1) without ever making use of the underlying $\mathbb{Z}_2$-symmetry of the model.

arXiv:1205.3139•May 14, 2012•2 citations

An Exact Solution of a Generalization of the Rabi Model

Fred Moolekamp

There has been renewed theoretical interest recently in the Rabi model due to Braak's analytical solution and introduction of a new criterion for integrability. We focus not on the integrability of the system but rather why it is solvable in the first place. We show that the Rabi model is the limiting case of a more general finite dimensional system by use of a contraction and suggest that this is the reason for it's solvability, which still applies in the case of non-integrable but solvable variations.

arXiv:1201.3843•Jan 18, 2012•2 citations

Comment on "Note on the Analytical Solution of the Rabi Model"

Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak

We make several comments on "Note on the Analytical Solution of the Rabi Model" (arXiv:1210.4946).

arXiv:1211.4639•Oct 29, 2012•2 citations

Comment on “Solvability of the two-photon Rabi Hamiltonian”

Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak

An implicit formula for the spectrum of the two-photon Rabi model was presented by Trav\ifmmode \check{e}\else \v{e}\fi{}nec in Phys. Rev. A 85, 043805 (2012), in analogy to the method of Braak [Phys. Rev. Lett. 107, 100401 (2011)]. The spectrum is given by common zeros of four functions ${G}_{c}(z,E)$ taken with a fixed value of $z\ensuremath{\in}\mathbb{C}$. We point out that all the ${G}_{c}(z,E)$ functions defined by Trav\ifmmode \check{e}\else \v{e}\fi{}nec are identically zero, thus the spectrum is not in fact given by their roots.

arXiv:1503.05636•Physical Review A•Mar 10, 2015•32 citations

Integrability and solvability of the simplified two-qubit Rabi model

Jie Peng, Zhongzhou Ren, Guangjie Guo +1 more

The simplified two-qubit Rabi model is proposed and its analytical solution is presented. There are no level crossings in the spectral graph of the model, which indicates that it is not integrable. The criterion of integrability for the Rabi model proposed by Braak (2011 Phys. Rev. Lett. 107 100401) is also used for the simplified two-qubit Rabi model and the same conclusion, consistent with what the spectral graph shows, can be drawn, which indicates that the criterion remains valid when applied to the two-qubit case. The simplified two-qubit Rabi model is another example of a non-integrable but exactly solvable system except for the generalized Rabi model.

Journal of Physics A Mathematical and Theoretical•Aug 22, 2012•23 citations
In a recent Comment (arXiv:1510.00768) it was claimed that Braak's solution of the quantum Rabi model does not include the set of non-degenerate exceptional points and is thus not a complete solution. Braak's solution does contain these points however, as has been shown before, and which we demonstrate here by obtaining the same energy plots as in the Comment, directly from Braak's solution. Therefore the claim that Braak's solution is not complete is incorrect.
Using Hill's determinant method we show that the set of Judd's solutions is only a subset of all the eigenvalues with the form En=nω−g2/ωE_n=nω-g^2/ωEn​=nω−g2/ω in the spectrum of the Rabi model. Therefore Braak's solution of the quantum Rabi model is not complete.
In his recent letter, Braak suggested that a regular spectrum of the Rabi model was given by the zeros of a transcendental function G±(x)G_\pm(x)G±​(x) (cf Eqs. (3)-(5) of Ref. [1]) and highlighted the role of the discrete Z2\mathbb{Z}_2Z2​-symmetry, or parity, in determining G±(x)G_\pm(x)G±​(x). We show here to the contrary that one can define a transcendental function F0(x)F_0(x)F0​(x) and obtain the regular spectrum of the Rabi model as the zeros of F0(x)F_0(x)F0​(x) (see Fig. 1) without ever making use of the underlying Z2\mathbb{Z}_2Z2​-symmetry of the model.
There has been renewed theoretical interest recently in the Rabi model due to Braak's analytical solution and introduction of a new criterion for integrability. We focus not on the integrability of the system but rather why it is solvable in the first place. We show that the Rabi model is the limiting case of a more general finite dimensional system by use of a contraction and suggest that this is the reason for it's solvability, which still applies in the case of non-integrable but solvable variations.
An implicit formula for the spectrum of the two-photon Rabi model was presented by Trav\ifmmode \check{e}\else \v{e}\fi{}nec in Phys. Rev. A 85, 043805 (2012), in analogy to the method of Braak [Phys. Rev. Lett. 107, 100401 (2011)]. The spectrum is given by common zeros of four functions Gc(z,E){G}_{c}(z,E)Gc​(z,E) taken with a fixed value of $z\ensuremath{\in}\mathbb{C}$. We point out that all the Gc(z,E){G}_{c}(z,E)Gc​(z,E) functions defined by Trav\ifmmode \check{e}\else \v{e}\fi{}nec are identically zero, thus the spectrum is not in fact given by their roots.
The simplified two-qubit Rabi model is proposed and its analytical solution is presented. There are no level crossings in the spectral graph of the model, which indicates that it is not integrable. The criterion of integrability for the Rabi model proposed by Braak (2011 Phys. Rev. Lett. 107 100401) is also used for the simplified two-qubit Rabi model and the same conclusion, consistent with what the spectral graph shows, can be drawn, which indicates that the criterion remains valid when applied to the two-qubit case. The simplified two-qubit Rabi model is another example of a non-integrable but exactly solvable system except for the generalized Rabi model.