Spin-resolved Pair-correlation Research Articles

Spin-resolved pair-correlation functions of quasi one dimensional electron gas at finite temperature

In a recent paper [Phys. Status Solidi B 255, 1800174 (2018)], we found that the total contact pair-correlation function g(r = 0, T) of an unpolarized quasi one dimensional electron gas (Q1DEG) exhibits non-monotonous dependence on temperature T, initially decreasing with rise in T and then increasing beyond a critical T for a fixed electron number density. Here, we calculate the spin-resolved pair-correlation functions i.e., g↑↑(r, T) [= g↓↓(r, T)] and g↑↓(r, T) of the unpolarized Q1DEG for different values of T at a fixed wire width and electron number density. To this endeavor, we are using the celebrated theory given by Singwi, Tosi, Land and Sjölander developed for an interacting three-dimensional many-electron system. Our present study reveals that with rise in T, g↑↑(r, T) at small electron separation becomes stronger in complete contrast to g↑↓(r, T) and the non-monotonic T-dependence of g(r = 0, T) is governed by the cumulative behaviour of g↑↑(r, T) and g↑↓(r, T).

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 g σ σ′(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 E int and exchange-correlation free energy F xc 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 E int and F xc 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 E int from the RPIMC data for high densities (~8% at r s = 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 E int 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.

Spin-resolved correlations at arbitrary spin polarization and ground state of a quasi-one-dimensional electron gas

We study the spin-resolved correlations at arbitrary spin polarization ζ and the ground state of a quasi-one-dimensional electron gas by using the dynamical self-consistent mean-field theory of Singwi et al. Numerical results are presented for the spin-resolved pair-correlation functions, correlation energies, and ground-state energy at selected ζ and a range of electron density rs. Our results agree nicely with the recent lattice regularized diffusion Monte Carlo simulation data at small rs and ζ. With increasing rs and/or ζ, the spin-resolved correlations become less satisfactory, but the spin-summed quantities show a reasonable agreement, thus implying a cancellation among discrepancies in the components. Interestingly, theory predicts that the like-spin correlation energy becomes little positive for rs>1.5. A comparison between the ground-state energies of the unpolarized and fully polarized spin phases reveals that the exchange–correlations may induce a phase transition to the latter above a critical rs, rsc. Importantly, the transition is in agreement with recent experiments on low density electron quantum wires. However, the stability of partially spin-polarized states could not be ascertained due to difficulty in obtaining the self-consistent density response function beyond a certain rs, preceding rsc. Using the static mean-field theory, we find that the spin-polarization transition is abrupt (i.e., the partially spin-polarized states are energetically unstable) and it occurs at nearly the same rs as in the dynamical approach.

Artificial quantum-dot helium molecules: Electronic spectra, spin structures, and Heisenberg clusters

Energy spectra and spin configurations of a system of $N=4$ electrons in lateral double quantum dots (quantum dot helium molecules) are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field $(B)$, and strength of interelectron repulsion. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin and the ensuing spin degeneracies for four electrons. The energies of the six states appear to cross at a single value of the magnetic field, and with increasing Coulomb repulsion they tend to become degenerate, with a well-defined energy gap separating them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangle. Using spin-resolved pair-correlation distributions, a method for mapping the complicated EXD many-body wave functions onto simpler spin functions associated with a system of four localized spins is introduced. Detailed interpretation of the EXD spin functions and EXD spectra associated with the low-energy band via a four-site Heisenberg cluster (with $B$-dependent exchange integrals) is demonstrated. Aspects of spin entanglement, referring to the well-known $N$-qubit Dicke states, are also discussed.

Spin-resolved correlations and ground state of a three-dimensional electron gas: Spin-polarization effects

We have studied the spin-resolved correlations in a three-dimensional electron gas having arbitrary spin polarization $\ensuremath{\zeta}$ by using the static and dynamical versions of the self-consistent mean-field approximation of Singwi, Tosi, Land, and Sj\olander, the so-called STLS and qSTLS approaches, respectively. The spin-resolved pair-correlation functions and corresponding correlation energies, static density and spin susceptibilities, and ground-state energy are calculated over a wide range of electron number density and selected $\ensuremath{\zeta}$. Wherever available, our results are compared directly with the recent quantum Monte Carlo studies of Ortiz et al. and Zong et al. The qSTLS approach is found to be in better agreement with the simulation data. As an interesting result, it is found that both the qSTLS and STLS methods underestimate the parallel spin-correlation energy while the antiparallel spin contribution is overestimated to the extent that the total correlation energy is in excellent agreement with the simulation data. Furthermore, a direct comparison among the results of ground-state energy at different $\ensuremath{\zeta}$ reveals, in qualitative agreement with the simulation studies, the existence of a continuous spin-polarization transition on decreasing electron density.

A spin-polarized scheme for obtaining quasi-particle energies within the density functional theory

We discuss an efficient scheme for obtaining spin-polarized quasi-particle excitation energies within the general framework of the density functional theory (DFT). Our approach is to correct the DFT eigenvalues via the electrostatic energy of a majority or minority spin electron resulting from its interaction with the associated exchange and correlation holes by using appropriate spin-resolved pair correlation functions. A version of the method for treating systems with localized orbitals, including the case of partially filled metallic bands, is considered. Illustrative results on Cu are presented.

Analysis of Response Functions of a Spin-Polarized Electron Gas

We present a spin analysis of local-field corrections and various susceptibility functions of a spin-polarized electron gas (SPEG). With a use of spin-resolved pair correlation functions of the SPEG, including the carrier correlations, we evaluate the local-field correction within a generalized random-phase approximation (RPA) and examine spin-polarization dependences of various susceptibility functions generalized in terms of spin-dependent local-field corrections. A pronounced maximum in spin-resolved local-field correction is observed and the location of the peaks are found to depend strongly on the values of spin polarization. For a system with vanishing spin polarization, the charge–spin mixed susceptibilities vanish. However, in the SPEG of finite spin polarization, the mixed susceptibilities become finite and are as important as the usual charge–charge, and spin–spin susceptibilities.

Correlation energy, pair-distribution functions and static structure factors of jellium

We discuss and clarify a simple and accurate interpolation scheme for the spin-resolved electron static structure factor (and corresponding pair correlation function) of the 3D unpolarized homogeneous electron gas which, along with some analytic properties of the spin-resolved pair-correlation functions, we have just published (Phys. Rev. B, in press). We compare our results with the very recent spin-resolved scheme by Schmidt et al. (Phys. Rev. B 46 (1992) 12 497; 56 (1997) 7018; submitted for publication) and focus our attention on the spin-resolved correlation energies and the high-density limit of the correlation functions.

Analytic static structure factors and pair-correlation functions for the unpolarized homogeneous electron gas

We propose a simple and accurate model for the electron static structure factors (and corresponding pair-correlation functions) of the 3D unpolarized homogeneous electron gas. Our spin-resolved pair-correlation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts (i) fulfills more known integral and differential properties of the exact pair-correlation function, (ii) is analytic both in real and in reciprocal space, and (iii) accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.