Physical review. B./Physical review. B

Comment on “Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current”

Francisco Marcelo Fernández, Diego R. Alcoba, Alicia Torre, Luis Laín, Ofelia B. Oña, Elías Ríos

Published May 19, 2020• 0 citations

Abstract

In a recent study of the transport properties in the Aubry-Andr\'e-Harper model [Phys. Rev. B 100, 195143 (2019)], the authors point out the failure of the Hellmann-Feynman theorem (HFT) in the case of degenerate states. They try to support such a statement from earlier papers that prove exactly the opposite. It appears that the application of the HFT to degenerate states has not been well understood. For this reason, in this Comment we illustrate the correct application of the HFT to the model just mentioned.

DOI: 10.1103/physrevb.101.197101

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Physical review. B./Physical review. B

Comment on “Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current”

Francisco Marcelo Fernández, Diego R. Alcoba, Alicia Torre, Luis Laín, Ofelia B. Oña, Elías Ríos

Published May 19, 2020• 0 citations

Publisher

Abstract

In a recent study of the transport properties in the Aubry-Andr'e-Harper model [Phys. Rev. B 100, 195143 (2019)], the authors point out the failure of the Hellmann-Feynman theorem (HFT) in the case of degenerate states. They try to support such a statement from earlier papers that prove exactly the opposite. It appears that the application of the HFT to degenerate states has not been well understood. For this reason, in this Comment we illustrate the correct application of the HFT to the model just mentioned.

DOI: 10.1103/physrevb.101.197101

Related papers

Study of counterintuitive transport properties in the Aubry-André-Harper model via entanglement entropy and persistent current

Nilanjan Roy, Auditya Sharma

The single-particle eigenstates of the Aubry-Andr\'e-Harper model are known to show a delocalization-localization transition at a finite strength of the quasiperiodic disorder. In this work, we point out that an intimate relationship exists between the subband structure of the spectrum and transport properties of the model. To capture the transport properties, we have not only used a variety of single-particle measures like inverse participation ratio, and von Neumann entropy, but also many-particle measures such as persistent current and its variance, and many-body entanglement entropy. The many-particle measures are very sensitive to the subband structure of the spectrum. Even in the delocalized phase, surprisingly the entanglement entropy is substantially suppressed when the Fermi level is in the band gaps, whereas the persistent current is vanishingly small for the same locations of the Fermi level. The entanglement entropy seems to follow area law exclusively for these special locations of Fermi level or filling fractions of free fermions. A study of the standard deviation of persistent current offers further distinguishing features for the special fillings. In the delocalized phase, the standard deviation vs mean persistent current curves are discontinuous for the nonspecial values of filling fractions and continuous (closed) for the special values of filling fractions, whereas in the localized phase, these curves become straight lines for both types of filling fractions. We have also discussed how the results depend on the system size. Our results, especially on the persistent current, can potentially be tested experimentally using the present day setups based on ultracold atoms.The single-particle eigenstates of the Aubry-Andr\'e-Harper model are known to show a delocalization-localization transition at a finite strength of the quasiperiodic disorder. In this work, we point out that an intimate relationship exists between the subband structure of the spectrum and transport properties of the model. To capture the transport properties, we have not only used a variety of single-particle measures like inverse participation ratio, and von Neumann entropy, but also many-particle measures such as persistent current and its variance, and many-body entanglement entropy. The many-particle measures are very sensitive to the subband structure of the spectrum. Even in the delocalized phase, surprisingly the entanglement entropy is substantially suppressed when the Fermi level is in the band gaps, whereas the persistent current is vanishingly small for the same locations of the Fermi level. The entanglement entropy seems to follow area law exclusively for these special locations of Fermi level or filling fractions of free fermions. A study of the standard deviation of persistent current offers further distinguishing features for the special fillings. In the delocalized phase, the standard deviation vs mean persistent current curves are discontinuous for the nonspecial values of filling fractions and continuous (closed) for the special values of filling fractions, whereas in the localized phase, these curves become straight lines for both types of filling fractions. We have also discussed how the results depend on the system size. Our results, especially on the persistent current, can potentially be tested experimentally using the present day setups based on ultracold atoms.

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Gaurav Hajong, Ranjan Modak, Bhabani Prasad Mandal

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We revisit the celebrated Hellmann-Feynman theorem (HFT) in the parity-time

(\mathcal{PT})

invariant non-Hermitian quantum physics framework. We derive a modified version of HFT by changing the definition of inner product and explicitly show that it holds good for both

\mathcal{PT}

broken and unbroken phases and even at the exceptional point of the theory. The derivation is extremely general and works for even the

\mathcal{PT}

noninvariant Hamiltonian. We consider several examples of discrete and continuum variable systems to test our results. We find that, if the eigenvalue goes through a real-to-complex transition as a function of the Hermiticity breaking parameter, both sides of the modified HFT expression diverge at that point. If that point turns out to be an EP of the

\mathcal{PT}

-invariant quantum theory, then one also sees the divergence at EP. Moreover, we have also demonstrated that using the modified HFT can give rise to a potential numerical advantage for computing the expectation value of many-body operators for interacting many-body Hamiltonian. Finally, we also derive a generalized virial theorem for non-Hermitian systems using the modified HFT, which potentially can be tested in experiments.