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International Journal of Modern Physics B

Charge dynamics in strongly-correlated electronic systems

Nguen Dan Tung, Nikolay M. Plakida

Published Nov 14, 2018• 1 citation
Publisher

Abstract

We consider the dynamic charge susceptibility and the charge density waves in strongly-correlated electronic systems within the two-dimensional t-J-V model. Using the equation of motion method for the relaxation functions in terms of the Hubbard operators, we calculate the static susceptibility and the spectrum of charge fluctuations as functions of doped hole concentrations and temperature. Charge density waves emerge for a sufficiently strong intersite Coulomb interaction. Calculation of the dynamic charge susceptibility reveals a strong damping of charge density waves for a small hole doping and propagating high-energy charge excitations at large doping.

DOI
10.1142/s0217979218503277

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We consider the dynamic charge susceptibility and the charge density waves in strongly-correlated electronic systems within the two-dimensional t-J-V model. Using the equation of motion method for the relaxation functions in terms of the Hubbard operators, we calculate the static susceptibility and the spectrum of charge fluctuations as functions of doped hole concentrations and temperature. Charge density waves emerge for a sufficiently strong intersite Coulomb interaction. Calculation of the dynamic charge susceptibility reveals a strong damping of charge density waves for a small hole doping and propagating high-energy charge excitations at large doping.
The dynamic charge susceptibility and the optical conductivity are calculated in the planar $t\ensuremath{-}J$ model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped soundlike mode for small wave vectors and a broad high energy peak $(\ensuremath{\sim}t)$ for large momenta. The study of the optical conductivity shows that electron scattering from spin fluctuations leads to the Drude-frequency dependent relaxation rate which exhibits a crossover from ${\ensuremath{\omega}}^{3/2}$ behavior at low frequencies $(\ensuremath{\omega}<2|\ensuremath{\mu}|),$ to a linear $\ensuremath{\omega}$ dependence for frequencies larger than $2|\ensuremath{\mu}|.$ Due to the spin-polaron nature of charge carriers, extra absorptions arise starting at a frequency $\ensuremath{\omega}\ensuremath{\gtrsim}J.$ The obtained results are in a good agreement with exact diagonalization studies.
Motivated by recent experiments, we append long ranged Coulomb interactions to dominant strong local correlations and study the resulting t-J-VC model for the 2-dimensional cuprate materials. This model includes the effect of short ranged Hubbard–Gutzwiller–Kanamori type correlations and long ranged Coulomb interactions on tight binding electrons. We calculate the {q→,ω} dependent charge density fluctuations in this model using the extremely correlated Fermi liquid theory characterized by quasiparticles with very small weight Z. We develop a novel set of formulae to represent the dynamical charge susceptibility and the dielectric function, using a version of the charge-current continuity equation for a band system, valid for arbitrary q→. Combining these ingredients, we present results for the irreducible dynamical charge susceptibility χ˜ρρ(q→,ω), (longitudinal) dielectric function ɛ(q→,ω), current susceptibility χ˜JJ(q→,ω), conductivity σ(q→,ω), and the plasma frequency for any q→. We also present calculations for the first moment of the structure function and discuss a characteristic energy scale Ωp(q→) which locates a peak in Imχ˜ρρ(q→,ω).
The ground state of the two-dimensional (2D) Hubbard model is investigated by adopting improved wave functions that take into account intersite electron correlation beyond the Gutzwiller ansatz. The ground-state energy is lowered considerably, giving the best estimate of the ground-state energy for the 2D Hubbard model. There is a crossover from weakly to strongly correlated regions as the on-site Coulomb interaction UUU increases. The antiferromagnetic correlation induced by UUU is reduced for hole doping when UUU is large, being greater than the bandwidth, thus increasing the kinetic energy gain. The spin and charge fluctuations are induced in the strongly correlated region. These antiferromagnetic and kinetic charge fluctuations induce electron pairings, which would result in high-temperature superconductivity.
We investigate the charge susceptibility in strongly correlated electron systems by using a Bethe-Salpeter equation in a generalized cumulant expansion for the p{d model, at varying values of the doping and temperature.We nd that for small values of the correlation Ud, the charge susceptibility decreases near the half{ lling as hole{doping approaches zero, this behavior suggesting the precursor of the Mott{Hubbard gap formation.Particular attention is paid to the role played by the Van Hove singularity near the Fermi level in the density of states, in connection with the unusual normal state properties of the hole{doped cuprates.
Abstract We investigate the spin dynamics in weakly doped high‐temperature superconductors. The system is described by the two‐dimensional t‐J model. Our focus is on the interaction between mobile holes and spin waves. The calculations are based on a recently introduced cumulant method for computing the ground state energy of correlated electronic systems. Contrary to previous works using dynamical quantities like correlation functions or spectral densities our approach contains a static view to the system. This new method treats spin and hole dynamics on the same basis and allows for the calculation of static and dynamical quantities. We present results for spin‐wave energies and transverse static susceptibilities for small hole concentrations and various values of t/J. We find a strong renor‐malization of the spin‐wave energies due to the spin‐hole interaction. In agreement with neutron scattering experiments the spin‐wave velocity vanishes at a critical hole density of a few percent which is equivalent to the instability of the antiferromagnetic order.