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Physical review. B, Condensed matter

Variational approach to linear dielectric response

Lauri J. Lantto, Pekka Pietiläinen, A. Kallio

Published Nov 15, 1982• 25 citations
Publisher

Abstract

The dielectric response of strongly correlated electron gas is studied by using a Jastrow variational many-body wave function to describe the electron-electron correlations in the fluid as well as its static response to a weak external perturbation. The Fermi hypernetted-chain method is employed to obtain an approximation to the local-field correction at a range of metallic densities. Results agree well with those obtained through recent developments of more conventional dielectric formulation.

DOI
10.1103/physrevb.26.5568

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•Aug 1, 1979•0 citations
The dielectric response of strongly correlated electron gas is studied by using a Jastrow variational many-body wave function to describe the electron-electron correlations in the fluid as well as its static response to a weak external perturbation. The Fermi hypernetted-chain method is employed to obtain an approximation to the local-field correction at a range of metallic densities. Results agree well with those obtained through recent developments of more conventional dielectric formulation.
The dielectric function of a charged Bose gas is determined from the response to an imposed static sinusoidal electric field. Variational and diffusion quantum Monte Carlo simulations are used to calculate the ground-state properties of the system with trial wave functions containing a parameter dependent on the amplitude and wavelength of the perturbation. The induced charge is most efficiently extracted from the difference in ground-state energies at different magnitudes of the external field, rather than directly from the expectation value of the density fluctuation operator. Results are compared to the random-phase approximation for the weakly coupled fluid and to classical lattice values at low densities where the system forms a Wigner crystal. The dielectric function is also calculated at intermediate fluid densities and the transition from positive to negative response is found to occur in the metallic regime.
We present a theoretical study on the response properties to an external electric field of strongly correlated one-dimensional metals. Our investigation is based on the recently developed Bethe ansatz local-density approximation (BALDA) to the density functional theory formulation of the Hubbard model. This is capable of describing both Luttinger liquid and Mott-insulator correlations. The BALDA calculated values for the static linear polarizability are compared with those obtained by numerically accurate methods, such as exact (Lanczos) diagonalization and the density-matrix renormalization group, over a broad range of parameters. In general BALDA linear polarizabilities are in good agreement with the exact results. The response of the exact exchange and correlation potential is found to point in the same direction of the perturbing potential. This is well reproduced by the BALDA approach, although the fine details depend on the specific parameterization for the local approximation. Finally we provide a numerical proof for the nonlocality of the exact exchange and correlation functional.
The static-linear-response function $\ensuremath{\chi}(k)$ is derived for the quantum Bose fluid with the use of the hypernetted-chain approximation in the Jastrow theory. The pair-correlation function of the uniform system required as an input function is optimized within the same theory. The compressibility sum rule as well as the sequential and screening conditions are exactly fulfilled by construction. It is shown analytically that in the small-wavelength limit the leading correction in ${\ensuremath{\chi}}^{\ensuremath{-}1}(k)$ to the freeparticle kinetic energy is a constant 23TJFN\frac{2}{3}\frac{{T}_{\mathrm{JF}}}{N}32​NTJF​​, where TJF{T}_{\mathrm{JF}}TJF​ is the Jackson-Feenberg kinetic energy. We have also developed a reliable numerical method which is used in the calculation of the linear-response function of the charged-boson gas at metallic densities.
We report a theoretical analysis of variational wave functions for the BCS pairing problem. Starting with a Jastrow-Feenberg (or, in a more recent language "fixed-node") wave function for the superfluid state, we develop the full optimized Fermi-Hypernetted Chain (FHNC-EL) equations which sum a local approximation of the parquet-diagrams. Close examination of the procedure reveals that it is essential to go beyond the usual Jastrow-Feenberg approximation to guarantee the correct stability range.
"A theory is developed to allow the systematic calculation of the properties of quantum fluids given the microscopic two-body potential. Physical arguments are used to construct a correlation operator that approximately transforms the states of a non-interacting system into the corresponding states of the interacting-system. The theory can be regarded as a microscopic realization of Landau's assumption of a one-to-one correspondence between the non-interacting and interacting states. It is variational since the correlation operator is determined by minimizing E(p) the expectation value of the ground-state energy. We first give a survey of various other many-body theories including the simpler Jastrow variational method. Differential equations are derived to calculate the correlation operator and the related Jastrow correlation"" function. A comparison of results in several Bose systems with various methods is given. The Fermi hypernetted chain integral equations are generalized to allow the calculation of E(p) in Fermi systems, using the correlation operator wave function. The method is applied to liquid 3He and the v2-model of nuclear matter. In 3He the correlation operator gives results in much closer agreement with experiment than that with the Jastrow wave function. A new set of hypernetted chain equations are then derived to allow the calculation of the excited st;ate energies in Bose systems. The theory is then applied to the calculation of the single quasi-particle excitation spectrum of liquid 4He. The spectrum is found to be a stringent test on the form of the correlation operator, deficiencies in the correlation operator giving corresponding errors in the spectrum. Good results are obtained for the density dependence of the roton energy. A variational principle for the free energy is used to generalize the correlation operator technique to finite temperatures. Results are given for the finite temperature properties of the v8-model of nuclear matter."