Dynamical Correlation of Electrons in Two-Dimensions

The exchange-correlation kernel in the spin channel in an electron liquid has the structure ${f}_{xc,\ensuremath{-}}^{L,T}(q,\ensuremath{\omega})\stackrel{q\ensuremath{\rightarrow}0}{\ensuremath{\rightarrow}}A(\ensuremath{\omega})∕{q}^{2}+{B}^{L,T}(\ensuremath{\omega})$ in the limit of the long wavelength. Here $L$ denotes the longitudinal component and $T$ the transverse component relative to the direction of the wave vector $\mathbf{q}$ . A collection of exact results for $A(\ensuremath{\omega})$ and ${B}^{L,T}(\ensuremath{\omega})$ is obtained at limiting low and high frequency, respectively, in two dimensions. Based on these results, we further give approximate interpolations for $A(\ensuremath{\omega})$ and ${B}^{L,T}(\ensuremath{\omega})$ at all frequencies in the paramagnetic case.The exchange-correlation kernel in the spin channel in an electron liquid has the structure ${f}_{xc,\ensuremath{-}}^{L,T}(q,\ensuremath{\omega})\stackrel{q\ensuremath{\rightarrow}0}{\ensuremath{\rightarrow}}A(\ensuremath{\omega})∕{q}^{2}+{B}^{L,T}(\ensuremath{\omega})$ in the limit of the long wavelength. Here $L$ denotes the longitudinal component and $T$ the transverse component relative to the direction of the wave vector $\mathbf{q}$. A collection of exact results for $A(\ensuremath{\omega})$ and ${B}^{L,T}(\ensuremath{\omega})$ is obtained at limiting low and high frequency, respectively, in two dimensions. Based on these results, we further give approximate interpolations for $A(\ensuremath{\omega})$ and ${B}^{L,T}(\ensuremath{\omega})$ at all frequencies in the paramagnetic case.

Physical Review BAug 10, 20053 citations

L

denotes the longitudinal component and

T

the transverse component relative to the direction of the wave vector

\mathbf{q}

. A collection of exact results for $A(\ensuremath{\omega})$ and ${B}^{L,T}(\ensuremath{\omega})$ is obtained at limiting low and high frequency, respectively, in two dimensions. Based on these results, we further give approximate interpolations for $A(\ensuremath{\omega})$ and ${B}^{L,T}(\ensuremath{\omega})$ at all frequencies in the paramagnetic case.