Dynamic correlations of the Coulomb Luttinger liquid

The dynamic density response function, form-factor, and spectral function of a Luttinger liquid with Coulomb electron-electron interaction are studied with the emphasis on the short-range electron correlations. The Coulomb interaction changes dramatically the density response function as compared to the case of the short-ranged interaction. The form of the density response function is smoothing with time, and the oscillatory structure appears. However, the spectral functions remain qualitatively the same. The dynamic form-factor contains the $\delta$-peak in the long-wave region, corresponding to one-boson excitations. Besides, the multi-boson-excitations band exists in the wave-number region near to $2k_F$. The dynamic form-factor diverges at the edges of this band, while the dielectric function goes to zero there, which indicates the appearance of a soft mode. We develop a method to analyze the asymptotics of the spectral functions near to the edges of the multi-boson-excitations band.Comment: 11 pages, 3 figures, submitted to PR

Correlation energy of a two-dimensional electron gas from static and dynamic exchange-correlation kernels

We calculate the correlation energy of a two-dimensional homogeneous electron gas using several available approximations for the exchange-correlation kernel $f_{\rm xc}(q,\omega)$ entering the linear dielectric response of the system. As in the previous work of Lein {\it et al.} [Phys. Rev. B {\bf 67}, 13431 (2000)] on the three-dimensional electron gas, we give attention to the relative roles of the wave number and frequency dependence of the kernel and analyze the correlation energy in terms of contributions from the $(q, i\omega)$ plane. We find that consistency of the kernel with the electron-pair distribution function is important and in this case the nonlocality of the kernel in time is of minor importance, as far as the correlation energy is concerned. We also show that, and explain why, the popular Adiabatic Local Density Approximation performs much better in the two-dimensional case than in the three-dimensional one.Comment: 9 Pages, 4 Figure

Spin-resolved correlations in the warm-dense homogeneous electron gas

We have studied spin-resolved correlations in the warm-dense homogeneous electron gas by determining the linear density and spin-density response functions, within the dynamical self-consistent mean-field theory of Singwi et al. The calculated spin-resolved pair-correlation function gσσ′(r) is compared with the recent restricted path-integral Monte Carlo (RPIMC) simulations due to Brown et al. [Phys. Rev. Lett. 110, 146405 (2013)], while interaction energy Eint and exchange-correlation free energy Fxc with the RPIMC and very recent ab initio quantum Monte Carlo (QMC) simulations by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. g↑↓(r) is found to be in good agreement with the RPIMC data, while a mismatch is seen in g↑↑(r) at small r where it becomes somewhat negative. As an interesting result, it is deduced that a non-monotonic T-dependence of g(0) is driven primarily by g↑↓(0). Our results of Eint and Fxc exhibit an excellent agreement with the QMC study due to Dornheim et al., which deals with the finite-size correction quite accurately. We observe, however, a visible deviation of Eint from the RPIMC data for high densities (~8% at rs = 1). Further, we have extended our study to the fully spin-polarized phase. Again, with the exception of high density region, we find a good agreement of Eint with the RPIMC data. This points to the need of settling the problem of finite-size correction in the spin-polarized phase also. Interestingly, we also find that the thermal effects tend to oppose spatial localization as well as spin polarization of electrons

Dynamic correlation effects on drag resistivity of a symmetric electron–electron bilayer

We have studied the effect of dynamic electron correlations on Coulomb drag in a low density symmetric electron–electron bilayer. The drag resistivity is calculated considering the contribution from direct e–e scattering processes using the semi-classical Boltzmann approach, with the effective inter-layer interaction W12(q, ω; T) determined within the Świerkowski, Szymanśki, and Gortel model, generalized to include the dynamics of electron correlations through the frequency-dependent intra- and inter-layer local-field correction (LFC) factors. In turn, the LFCs are obtained by extending the quantum Singwi, Tosi, Land, and Sjölander (qSTLS) approach to finite temperatures. At low temperatures (T ≲ 2 K), the calculated drag resistivity is found to agree nicely with the measurements by Kellogg et al., while it is somewhat overestimated at higher temperatures. The overestimation is seen to increase with decreasing density of electrons. However, there is found to be a marked improvement over the predictions of the conventional (i.e., static) STLS and random-phase approximation (RPA). It turns out that the inclusion of exchange-correlations in the RPA causes a red-shift in the bilayer plasmons which leads to an enhancement of drag resistivity. Our study demonstrates clearly the importance of including the dynamical nature of correlations to have a reasonable account of measured drag resistivity

Spin polarized electrons in a metallic quantum wire

We obtain explicit expressions for the spin-resolved density response functions of a spin polarized metallic quantum wire by including the first-order exchange and self-energy contributions to the random-phase approximation. These are used to calculate the spin-resolved static structure factors, pair-correlation functions, and correlation energy of the system for various values of the spin-polarization parameter ζ. The inclusion of first-order correction is found to bring the present approximate theory in overall very good agreement with the recent quantum Monte Carlo simulations by Shulenburger et al. [L. Shulenburger, M. Casula, G. Senatore, R.M. Martin, J. Phys. A 42, 214021 (2009)]. Particularly, we find excellently close results for the fully spin-polarized (i.e., ζ = 1) electrons for even larger coupling (rs ~ 4), implying a fairly good description of exchange correlations. Interestingly, there is no crossover found from para- to ferro-magnetic ground state. The static charge and spin susceptibilities, and spin sound are obtained analytically and found to be in good agreement with the available quantum Monte Carlo simulations. Furthermore, we present results for the wavevector dependent static charge density, spin density, and charge-spin density susceptibilities for some wire parameters. The dispersion of spin sound has also been obtained and found to be strongly dependent on wire width and density parameter

Collective density excitations in liquid sodium

Consiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome / CNR - Consiglio Nazionale delle RichercheSIGLEITItal