Physical review. B, Condensed matter

Fermionic structure of the magnon interaction vertex in quantum magnets

Avinash Singh

Published Oct 1, 1993• 0 citations

Abstract

Fermionic structure of the spin-wave interaction vertex within the Hubbard-model representation of a quantum magnet is presented in a scheme that systematically preserves the spin-rotational symmetry and hence the Goldstone mode. We evaluate the diagrams contributing to the interaction vertex for the case of a quantum antiferromagnet in the strong-coupling limit. The exact cancellation of the leading-order contributions (of order U), as required by spin-rotational symmetry, is demonstrated.

DOI: 10.1103/physrevb.48.10546

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Physical review. B, Condensed matter

Fermionic structure of the magnon interaction vertex in quantum magnets

Avinash Singh

Published Oct 1, 1993• 0 citations

Publisher

Abstract

DOI: 10.1103/physrevb.48.10546

Related papers

Ferromagnetism in the t−t′ Hubbard model: Interplay of lattice, band dispersion, and interaction effects studied within a Goldstone-mode preserving scheme

Sudhakar Pandey, Avinash Singh

Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy $(1∕\mathcal{N})$ expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the density of states (DOS) is sufficiently asymmetric and strongly peaked near the band edge, as for the fcc lattice with finite ${t}^{\ensuremath{'}}$. For short-wavelength modes, the behavior of a characteristic energy scale ${\ensuremath{\omega}}^{*}\ensuremath{\sim}{T}_{c}$ (magnon DOS peak energy) is in excellent agreement with the ${T}_{c}$ vs $n$ behavior within dynamical mean field theory, with respect to both the stable range of densities $(0.20<n<0.85)$ as well as the optimal density $n=0.65$ . However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy $(1∕\mathcal{N})$ expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the density of states (DOS) is sufficiently asymmetric and strongly peaked near the band edge, as for the fcc lattice with finite ${t}^{\ensuremath{'}}$. For short-wavelength modes, the behavior of a characteristic energy scale ${\ensuremath{\omega}}^{*}\ensuremath{\sim}{T}_{c}$ (magnon DOS peak energy) is in excellent agreement with the ${T}_{c}$ vs $n$ behavior within dynamical mean field theory, with respect to both the stable range of densities $(0.20<n<0.85)$ as well as the optimal density $n=0.65$. However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.

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We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using the self-consistent Hartree-Fock approximation combined with the Bethe-Salpeter equation in the random phase approximation, we map the U − t ′ phase diagram of the Lieb-kagome lattices and compute real-frequency transverse spin susceptibilities, i.e., the magnon spectra. Dynamical mean-field theory and exact diagonalization are used as complementary checks of static magnetic phases. In particular, besides gapless Goldstone magnons, the symmetry-broken ferrimagnetic and antiferromagnetic phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using the self-consistent Hartree-Fock approximation combined with the Bethe-Salpeter equation in the random phase approximation, we map the U − t ′ phase diagram of the Lieb-kagome lattices and compute real-frequency transverse spin susceptibilities, i.e., the magnon spectra. Dynamical mean-field theory and exact diagonalization are used as complementary checks of static magnetic phases. In particular, besides gapless Goldstone magnons, the symmetry-broken ferrimagnetic and antiferromagnetic phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.

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Electrons interacting with Goldstone modes and the rotating frame

Konstantinos Vasiliou, Yuchi He, Nick Bultinck

We consider electronic systems with a spontaneously broken continuous symmetry. The scattering vertex between electrons and Goldstone modes is calculated over the entire Brillouin zone using the random phase approximation. This calculation reveals two things: (1) electrons always couple to both ϕ and ∂tϕ , where ϕ is the Goldstone field, and (2) quasiparticles in a state with continuous symmetry breaking have to be defined in a rotating frame, which locally follows the fluctuations of the order parameter. The implications of these findings for electron spectral functions in both symmetry-broken and thermally disordered systems are discussed, and the examples of antiferromagnetism in the Hubbard model and spin spiral order in the three-band model are worked out in detail. Published by the American Physical Society 2024We consider electronic systems with a spontaneously broken continuous symmetry. The scattering vertex between electrons and Goldstone modes is calculated over the entire Brillouin zone using the random phase approximation. This calculation reveals two things: (1) electrons always couple to both ϕ and ∂tϕ , where ϕ is the Goldstone field, and (2) quasiparticles in a state with continuous symmetry breaking have to be defined in a rotating frame, which locally follows the fluctuations of the order parameter. The implications of these findings for electron spectral functions in both symmetry-broken and thermally disordered systems are discussed, and the examples of antiferromagnetism in the Hubbard model and spin spiral order in the three-band model are worked out in detail. Published by the American Physical Society 2024

arXiv:2307.05699Physical review. B./Physical review. BJan 31, 20245 citations

Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy

(1∕\mathcal{N})

expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the density of states (DOS) is sufficiently asymmetric and strongly peaked near the band edge, as for the fcc lattice with finite ${t}^{\ensuremath{'}}$. For short-wavelength modes, the behavior of a characteristic energy scale ${\ensuremath{\omega}}^{*}\ensuremath{\sim}{T}_{c}$ (magnon DOS peak energy) is in excellent agreement with the

{T}_{c}

n

behavior within dynamical mean field theory, with respect to both the stable range of densities

(0.20<n<0.85)

as well as the optimal density

n=0.65

. However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.

1/2

XY models using the Chern-Simons (CS) fermion representation of interacting spins. The interaction leads to Cooper instability and pairing of CS fermions, and to CS superconductivity which spontaneously violates the continuous

\mathrm{U}(1)

symmetry generating a linearly dispersing gapless Nambu-Goldstone mode due to phase fluctuations. We evaluate this mode and show that it is in high-precision agreement with magnons of the corresponding N\'eel antiferromagnet irrespective to the lattice symmetry. Using the fermion formulation of the system with frustration, we show that the competing interactions emerge in the form of long-range interaction vertices mediated by the CS gauge field, which are responsible for restoring the continuous symmetry at sufficiently strong frustration. We identify these new interaction vertices and discuss their implications for unconventional phase transitions. We also apply the proposed theory to a model of anyons that can be tuned continuously from fermions to bosons, and discuss the results.

\frac{1}{\mathcal{N}}

level in an inverse-degeneracy expansion, and the relevant two-magnon propagator is obtained by incorporating magnon interactions at a ladder-sum level. Evaluation of the magnon interaction vertex in the large-

U

limit yields a nearest-neighbor instantaneous interaction with interaction energy $\ensuremath{-}J$. Application of this approach to the intermediate-

U

regime, which is of relevance for cuprate antiferromagnets, is also discussed. Incorporating the zero-temperature magnon damping, which is estimated in terms of quantum spin fluctuations, the two-magnon Raman scattering intensity is evaluated and compared with experiments on

{\mathrm{La}}_{2}

{\mathrm{O}}_{4}

1/N

expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in

1/N

, which must be accounted for to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.