On the Bogoliubov transformation for quadratic boson observables

Maldonado, O.

doi:10.1063/1.530338

Cited by 14 publications

(21 citation statements)

References 7 publications

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“…First of all, the hermitian field parametrization of spin-wave theory developed in Sec. V B (see also Appendix B) is an efficient alternative to Colpa's algorithm [95][96][97]99] in the magnetically ordered phase of any spin-model with a complicated magnon spectrum consisting of several bands. Moreover, for the calculation of the magnon damping in multi-band magnon systems it is crucial to carefully keep track of all phase factors in the interaction vertices generated by Umklapp scattering processes.…”

Section: Discussionmentioning

confidence: 99%

Magnon damping in the zigzag phase of the Kitaev-Heisenberg- Γ model on a honeycomb lattice

et al. 2020

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We calculate magnon dispersions and damping in the Kitaev-Heisenberg model with an offdiagonal exchange Γ and isotropic third-nearest-neighbor interaction J3 on a honeycomb lattice. This model is relevant to a description of the magnetic properties of iridium oxides α-Li2IrO3 and Na2IrO3, and Ru-based materials such as α-RuCl3. We use an unconventional parametrization of the spin-wave expansion, in which each Holstein-Primakoff boson is represented by two conjugate hermitian operators. This approach gives us an advantage over the conventional one in identifying parameter regimes where calculations can be performed analytically. Focusing on the parameter regime with the zigzag spin pattern in the ground state that is consistent with experiments, we demonstrate that one such region is Γ = K > 0, where K is the Kitaev coupling. Within our approach we are able to obtain explicit analytical expressions for magnon energies and eigenstates and go beyond the standard linear spin-wave theory approximation by calculating magnon damping and demonstrating its role in the dynamical structure factor. We show that the magnon damping effects in both Born and self-consistent approximations are very significant, underscoring the importance of non-linear magnon coupling in interpreting broad features in the neutron-scattering spectra. arXiv:1911.12829v1 [cond-mat.str-el]

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Section: Discussionmentioning

confidence: 99%

Magnon damping in the zigzag phase of the Kitaev-Heisenberg- Γ model on a honeycomb lattice

et al. 2020

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“…Starting from the stationary point in the rotating frame as found above, the equation of motion for collective excitations can be cast in a matrix form [17] as M x @!x, with a vectorx ; 0 ; ÿ ; ; 0 ; ÿ T . j and j denote the deviations from the stationary point, and the associated matrix is…”

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confidence: 99%

Dynamical Instability and Domain Formation in a Spin-1 Bose-Einstein Condensate

et al. 2005

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We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.

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“…According to the Bogoliubov approximation, the time dependent equations of motion for the collective modes in a condensate can be cast in a matrix form as follows [31]:…”

Section: Spin Dynamics Of a Spin-1 Condensate Subjecting To Dynammentioning

confidence: 99%

“…However, the matrix M has paired eigenvalues with the same amplitude but different sign, due to its particular form [31]. The dynamical instability of a condensate is manifested as the existence of at least one pair of complex eigenvalues [3].…”

Section: Spin Dynamics Of a Spin-1 Condensate Subjecting To Dynammentioning

confidence: 99%

Enhancement of spin coherence in a spin-1 Bose-Einstein condensate by dynamical decoupling approaches

et al. 2011

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We study the enhancement of spin coherence with periodic, concatenated, or Uhrig dynamical decoupling N -pulse sequences in a spin-1 Bose condensate, where the intrinsic dynamical instability in such a ferromagnetically interacting condensate causes spin decoherence and eventually leads to a multiple spatial-domain structure or a spin texture. Our results show that all the three sequences successfully enhance the spin coherence by pushing the wave vector of the most unstable mode in the condensate to a larger value. Among the three sequences with the same number of pulses, the concatenated one shows the best performance in preserving the spin coherence. More interestingly, we find that all the three sequences exactly follow the same enhancement law, k−T 1/2 = c, with k− the wave vector of the most unstable mode, T the sequence period, and c a sequence-dependent constant. Such a law between k− and T is also derived analytically for an attractive scalar Bose condensate subjecting to a periodic dynamical decoupling sequence.

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On the Bogoliubov transformation for quadratic boson observables

Abstract: The diagonalization of Hermitian quadratic boson operators is studied in the equation of motion approach. The existence of a canonical transformation that diagonalizes such operators is discussed and an algorithm is sketched.

Cited by 14 publications

References 7 publications

Magnon damping in the zigzag phase of the Kitaev-Heisenberg- Γ model on a honeycomb lattice

Magnon damping in the zigzag phase of the Kitaev-Heisenberg- Γ model on a honeycomb lattice

Dynamical Instability and Domain Formation in a Spin-1 Bose-Einstein Condensate

Enhancement of spin coherence in a spin-1 Bose-Einstein condensate by dynamical decoupling approaches

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