We investigate the response of an electron system which exhibits ideal nesting features. Using the standard Matsubara formalism we derive analytic expressions for the imaginary and real parts of the bare particle–hole susceptibility. The imaginary part has sharp peaks whose maxima at the nesting momenta approximately scale with (ω/T). The peak lineshapes resemble neutron scattering data on chromium and some copper oxide superconductors. The real part of the bare susceptibility at the nesting vectors diverges logarithmically at low temperatures. Analytic formulas for the first vertex correction to the susceptibility are derived for a Hubbard interaction and its momentum and temperature variations are calculated numerically. This term detracts substantially from the ordinary RPA terms for intermediate values of the Coulomb repulsion. Exact cancellation of a certain class of diagrams at half filling is shown to result from particle–hole symmetry. We discuss the consequences of these results for spin fluctuation theories of high temperature superconductors and spin density wave instabilities.
We investigate the response of an electron system which exhibits ideal nesting features. Using the standard Matsubara formalism we derive analytic expressions for the imaginary and real parts of the bare particle–hole susceptibility. The imaginary part has sharp peaks whose maxima at the nesting momenta approximately scale with (ω/T). The peak lineshapes resemble neutron scattering data on chromium and some copper oxide superconductors. The real part of the bare susceptibility at the nesting vectors diverges logarithmically at low temperatures. Analytic formulas for the first vertex correction to the susceptibility are derived for a Hubbard interaction and its momentum and temperature variations are calculated numerically. This term detracts substantially from the ordinary RPA terms for intermediate values of the Coulomb repulsion. Exact cancellation of a certain class of diagrams at half filling is shown to result from particle–hole symmetry. We discuss the consequences of these results for spin fluctuation theories of high temperature superconductors and spin density wave instabilities.
We investigate the response of an electron system which exhibits ideal nesting features. Using the standard Matsubara formalism we derive analytic expressions for the imaginary and real parts of the bare particle–hole susceptibility. The imaginary part has sharp peaks whose maxima at the nesting momenta approximately scale with (ω/T). The peak lineshapes resemble neutron scattering data on chromium and some copper oxide superconductors. The real part of the bare susceptibility at the nesting vectors diverges logarithmically at low temperatures. Analytic formulas for the first vertex correction to the susceptibility are derived for a Hubbard interaction and its momentum and temperature variations are calculated numerically. This term detracts substantially from the ordinary RPA terms for intermediate values of the Coulomb repulsion. Exact cancellation of a certain class of diagrams at half filling is shown to result from particle–hole symmetry. We discuss the consequences of these results for spin fluctuation theories of high temperature superconductors and spin density wave instabilities.
We investigate the response of an electron system which exhibits ideal nesting features. Using the standard Matsubara formalism we derive analytic expressions for the imaginary and real parts of the bare particle-hole susceptibility. The imaginary part has sharp peaks whose maxima at the nesting momenta approximately scale with frequency divided by temperature. The peak lineshapes resemble neutron scattering data on chromium and some copper oxide superconductors. The real part of the bare susceptibility at the nesting vectors diverges logarithmically at low temperatures. Analytic formulas for the first vertex correction to the susceptibility are derived for a Hubbard interaction, and its momentum and temperature variations are calculated numerically. This term detracts substantially from the ordinary RPA terms for intermediate values of the Coulomb repulsion. Exact cancellation of a certain class of diagrams at half filling is shown to result from particle-hole symmetry. We discuss the consequences of these results for spin fluctuation theories of high temperature superconductors and spin density wave instabilities.
An unusual scaling of the spin susceptibility, as a function of frequency/temperature, was discovered for noninteracting electrons on a nested Fermi surface. This scaling has been confirmed by neutron-scattering experiments on high-temperature superconductors, and it can explain the anomalous quasiparticle damping in cuprates if electron collisions are dominant. The present work proves that self-energy and vertex corrections preserve the scaling features of the susceptibility to leading order in the Hubbard on-site Coulomb repulsion U. Analytic results for the static susceptibility show how self-energy and vertex terms modify the traditional random-phase approximation results for a spin-density-wave instability and suppress the charge susceptibility. These results are relevant to d-wave superconductors, organic metals, and chromium.
We carry out a systematic study of collective spin and charge excitations for the canonical single-band Hubbard, t–J–U, and t–J models of high-temperature copper-oxide superconductors, both on electron- and hole-doped side of the phase diagram. A~recently developed variational wave function approach, combined with the expansion in the inverse number of fermionic flavors, is employed. All three models exhibit a substantial electron–hole asymmetry of magnetic excitations, with a robust paramagnon emerging for hole-doping, in agreement with available resonant inelastic X-ray scattering data for the cuprates. The t–J model yields additional high-energy peak in the magnetic spectrum that is not unambiguously identified in spectroscopy. For all considered Hamiltonians, the dynamical charge susceptibility contains a coherent mode for both hole- and electron doping, with overall bandwidth renormalization controlled by the on-site Coulomb repulsion. Away from the strong-coupling limit, the antiferromagnetic ordering tendency is more pronounced on the electron-doped side of the phase diagram.
Many correlated materials display a quantum-critical point between a paramagnetic and a spin-density wave (SDW) state. The SDW wave vector connects points, so-called hot spots, on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here, we consider the case where pairs of hot spots coalesce, and the wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility, and the self-energy at the hot spots are found using the two-particle self-consistent theory and specific numerical examples worked out for band and interaction parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudonesting conditions lead to drastic modifications of the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length $\ensuremath{\xi}$ scales like 1/T, namely, z=1 instead of the naive z=2, the $(\ensuremath{\pi},\ensuremath{\pi})$ static spin susceptibility $\ensuremath{\chi}$ like 1/T, and the imaginary part of the self-energy at the hot spots like T3/2. The correction ${T}_{1}^{\ensuremath{-}1}\ensuremath{\sim}{T}^{3/2}$ to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless collective bosonic modes (SDW fluctuations) interacting with fermions. The imaginary part of the retarded fermionic self-energy close to the hot spots scales as $\ensuremath{-}{\ensuremath{\omega}}^{3/2}\mathrm{ln}\ensuremath{\omega}$. This is less singular than earlier predictions of the form $\ensuremath{-}\ensuremath{\omega}\mathrm{ln}\ensuremath{\omega}$. The difference arises from the effects of umklapp terms that were not included in previous studies.
We have calculated within the fluctuation exchange approximation the full momentum and real-frequency dependence of the quasiparticle self-energy, the gap function, and the dynamic spin susceptibility for the two-dimensional Hubbard model near half filling. The spin-density-wave (SDW) instability is reached only asymptotically in the limit of infinite U or zero temperature. Near the SDW instability we find approximately marginal Fermi-liquid behavior, a pseudogap in the density of states, and a singlet dx2-y2 pairing instability. Below Tc, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The spectral density of the dynamic spin susceptibility agrees qualitatively with the neutron-scattering data on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$SrxCuO4. The quasiparticle scattering rate and spin-lattice relaxation rate ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$ decrease rapidly below Tc. The photoemission intensities along the antinode and node of the gap are in good agreement with the angle-resolved photoemission spectroscopy data on Bi 2212. Including next-nearest-neighbor hopping we obtain for sufficiently large coupling (U/t\ensuremath{\gtrsim}7) a broad commensurate neutron-scattering peak like the observed one in YBa2Cu3O6+x.