arXiv:cond-mat/9705049 · Physical Review Letters

Is the π Particle Responsible for the 41 meV Peak in YBa2Cu3O7 ?

Martin Greiter

Published Dec 15, 1997• 24 citations

Abstract

It is argued that there is no low-energy resonance associated with the $\ensuremath{\pi}$ operators introduced by Demler and Zhang. This implies that the Hubbard model does not possess an approximate SO(5) symmetry generated by these operators. Recent finite-size studies are reinterpreted accordingly.

DOI: 10.1103/physrevlett.79.4898

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Response to Greiter's Comment

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Greiter claimed erroneously that the pi-excitation of the Hubbard model has an energy of the order of U. This mistake originates from a inconsistent treatment of the two particle Hartree energy and the Hartee correction to the chemical potential. In any self-consistent calculations, these two contributions cancel exactly, as shown by Kohn, Luttinger and Ward. We also show that his interpretation of the finite-size studies is inconsistent.

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arXiv:cond-mat/9705049 · Physical Review Letters

Is the π Particle Responsible for the 41 meV Peak in YBa2Cu3O7 ?

Martin Greiter

Published Dec 15, 1997• 24 citations

arXiv HTML PDF

Abstract

It is argued that there is no low-energy resonance associated with the

\ensuremath{\pi}

operators introduced by Demler and Zhang. This implies that the Hubbard model does not possess an approximate SO(5) symmetry generated by these operators. Recent finite-size studies are reinterpreted accordingly.

DOI: 10.1103/physrevlett.79.4898

Related papers

Greiter replies to Demler, Zhang, Meixner, and Hanke

Martin Greiter

In a comment on my recent manuscript on the pi-particle [cond-mat/9705049], Demler et al. [cond-mat/9705191] argued that there is a correction to the chemical potential which enters the expression for the energy of the pi-particle given in [Demler and Zhang, Phys. Rev. Lett. 77, 4126 (1995)]. This is shown to be incorrect. I further offer an interpretation for the low-energy resonances observed by Meixner et al. [cond-mat/9701217] in the pi-pi correlation function in a finite-size Hubbard cluster at low electron densities.In a comment on my recent manuscript on the pi-particle [cond-mat/9705049], Demler et al. [cond-mat/9705191] argued that there is a correction to the chemical potential which enters the expression for the energy of the pi-particle given in [Demler and Zhang, Phys. Rev. Lett. 77, 4126 (1995)]. This is shown to be incorrect. I further offer an interpretation for the low-energy resonances observed by Meixner et al. [cond-mat/9701217] in the pi-pi correlation function in a finite-size Hubbard cluster at low electron densities.

arXiv:cond-mat/9705282May 28, 19970 citations

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Eugene Demler, Hiroshi Kohno, Shoucheng Zhang

In this paper, we present analytical and numerical calculations of the \ensuremath{\pi} resonance in the $t\ensuremath{-}J$ model. We show in detail how the $\ensuremath{\pi}$ resonance in the particle-particle channel couples to the dynamical spin correlation function in a superconducting state. The contribution of the \ensuremath{\pi} resonance to the spin excitation spectrum can be estimated from general model-independent sum rules, and it agrees with our detailed calculations. The results are in overall agreement with the exact diagonalization studies of the $t\ensuremath{-}J$ model. Earlier calculations predicted the correct doping dependence of the neutron resonance peak in the ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ superconductor, and in this paper detailed energy and momentum dependence of the spin correlation function is presented. The microscopic equations of motion obtained within current formalism agree with that of the SO(5) nonlinear \ensuremath{\sigma} model, where the \ensuremath{\pi} resonance is interpreted as a pseudo-Goldstone mode of the spontaneous SO(5) symmetry breaking.In this paper, we present analytical and numerical calculations of the \ensuremath{\pi} resonance in the $t\ensuremath{-}J$ model. We show in detail how the $\ensuremath{\pi}$ resonance in the particle-particle channel couples to the dynamical spin correlation function in a superconducting state. The contribution of the \ensuremath{\pi} resonance to the spin excitation spectrum can be estimated from general model-independent sum rules, and it agrees with our detailed calculations. The results are in overall agreement with the exact diagonalization studies of the $t\ensuremath{-}J$ model. Earlier calculations predicted the correct doping dependence of the neutron resonance peak in the ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}$ superconductor, and in this paper detailed energy and momentum dependence of the spin correlation function is presented. The microscopic equations of motion obtained within current formalism agree with that of the SO(5) nonlinear \ensuremath{\sigma} model, where the \ensuremath{\pi} resonance is interpreted as a pseudo-Goldstone mode of the spontaneous SO(5) symmetry breaking.

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Response to Greiter's Comment

Eugene Demler, Shoucheng Zhang, Stefan Meixner +1 more

arXiv:cond-mat/9705191May 20, 19970 citations

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N. Bulut, Douglas J. Scalapino, Steven R. White

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Bethe-Salpeter equations for the collective modes of the $t-U-V-J$ model with d-wave pairingBethe-Salpeter equations for the collective modes of the $t-U-V-J$ model with d-wave pairing

Zlatko G. Koinov, Patrick L. Nash

The Bethe-Salpeter equations for the collective modes of a $t$ - $U$ - $V$ - $J$ model are used to analyze the resonance peak observed at $\bf{Q}=(π,π)$ in neutron scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model ( $J=0$ ) vs the on-site repulsive interaction $U$ , as well as the $UJ$ lines in the interaction parameter space which are consistent with the ARPES data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.The Bethe-Salpeter equations for the collective modes of a $t$-$U$-$V$-$J$ model are used to analyze the resonance peak observed at $\bf{Q}=(π,π)$ in neutron scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model ($J=0$) vs the on-site repulsive interaction $U$, as well as the $UJ$ lines in the interaction parameter space which are consistent with the ARPES data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.

arXiv:1006.1388Jun 7, 20100 citations

It is argued that there is no low-energy resonance associated with the

\ensuremath{\pi}

{\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+x}

superconductor, and in this paper detailed energy and momentum dependence of the spin correlation function is presented. The microscopic equations of motion obtained within current formalism agree with that of the SO(5) nonlinear \ensuremath{\sigma} model, where the \ensuremath{\pi} resonance is interpreted as a pseudo-Goldstone mode of the spontaneous SO(5) symmetry breaking.

Zhang recently conjectured an approximate SO(5) symmetry relating antiferromagnetic and superconducting states in high-

{T}_{c}

cuprates. Here, an exact SO(5) symmetry is implemented in a generalized Hubbard model (with long-range interactions) on a lattice. The possible relation to a more realistic extended Hubbard Hamiltonian is discussed.

Bethe-Salpeter equations for the collective modes of the

t-U-V-J

model with d-wave pairing

The Bethe-Salpeter equations for the collective modes of a

t

U

V

J

model are used to analyze the resonance peak observed at

\bf{Q}=(π,π)

in neutron scattering experiments on the cuprates. We assume that the resonance emerges due to the mixing between the spin channel and 19 other channels. We have calculated the energy of the lowest mode of the extended Hubbard model (

J=0

) vs the on-site repulsive interaction

U

, as well as the

UJ

lines in the interaction parameter space which are consistent with the ARPES data and reproduces the resonance peak at 40 meV in Bi2212 compound. We find that the resonance is predominantly a spin exciton.