Theory of Charge and Spin Dynamics in Electron Liquids

这笔拨款支持凝聚态物理的理论研究。电子系统中电荷密度激发的含时密度泛函理论(TDFT)是一种成熟的工具，其预测通常与实验测量结果相比较。然而，在描述(I)杂质效应和(Ii)完全或部分自旋极化的电子液体中的自旋和自旋-电荷耦合动力学的能力方面，该理论仍然相对不发达。这项研究的主要目标是将自旋动力学和杂质效应的TDFT发展到可与普通TDFT相媲美的复杂水平。本质上，这意味着在存在杂质散射的情况下，建立与自旋和频率相关的交换相关(XC)场的精确近似。为了适当地包含延迟和驰豫效应，有必要超越绝热局域自旋密度近似，这可以用自旋流密度作为基本变量来实现。在这种方法中，杂质均匀分布的自旋极化电子气的自旋相关粘弹性谱起到了关键作用。这些量将在久保-森形式主义的框架内计算。在宏观极限下，该理论应给出电荷流和自旋流的广义流体动力学方程(Navier-Stokes)。这一理论应该是对最近提出的绝热自旋动力学的补充和推广。强磁场下二维电子液体的粘弹性谱的计算(使得所有电子都处于最低朗道能级)是一个有趣的问题。最近的研究表明，不可压缩分数量子霍尔态的电荷动力学可以用有效的弹性理论很好地描述。这一理论需要向两个方向扩展：第一，必须包括能量耗散，因为正确描述可压缩状态的电荷动力学是必不可少的；第二，必须考虑电子的自旋。我们的目标是发展一个有效的粘弹性理论来统一处理自旋和电荷密度激发在最低朗道能级的处理。该理论将被用于计算量子霍尔铁磁体在分数填充因子下的集体激发、拓扑自旋织构的动力学和自旋边缘波的色散。最近的理论工作强调了在计算晶体绝缘体的介电响应时超越局域密度近似(LDA)的必要性。在这种情况下，将努力将对LDA的校正表示为宏观极化的显式泛函。这一极化密度泛函理论，如果成功，将允许介电性质的第一性原理计算相对容易地进行。%这笔赠款支持凝聚态物理的理论研究。这项研究将扩展电子相互作用理论，以包括杂质和电子自旋的影响。特别是，将研究极高磁场中相互作用电子的性质-量子霍尔态。这项研究有助于对凝聚态物理的基本理解。

This grant supports theoretical research in condensed matter physics. The time-dependent density functional theory (TDFT) of charge-density excitations in electronic systems is by now a well developed tool, whose predictions are routinely compared to experimental measurements. However, the theory is still relatively underdeveloped with regard to its ability to describe (i) impurity effects and (ii) spin and coupled spin-charge dynamics in fully or partly spin-polarized electron liquids. The primary goal of this research is to develop the TDFT of spin dynamics and impurity effects to a level of sophistication comparable to what has been reached by ordinary TDFT. In essence, this means developing accurate approximations for the spin- and frequency-dependent exchange-correlation (xc) fields in the presence of impurity scattering. In order to properly include retardation and relaxation effects it is necessary to go beyond the adiabatic local spin-density approximation, and this can be done using the spin-current density as the basic variable. A key role in this approach is played by the spin-dependent visco-elastic spectra of the spin-polarized electron gas with a uniform distribution of impurities. These quantities will be calculated within the framework of the Kubo-Mori formalism. In the macroscopic limit the theory should yield generalized hydrodynamics (Navier-Stokes) equations for charge and spin currents. This theory should complement and extend the recently proposed adiabatic spin dynamics.The calculation of the visco-elastic spectra of a two-dimensional electron liquid at high magnetic field (such that all the electrons are in the lowest Landau level) poses a fascinating problem. It has been recently shown that the charge dynamics of incompressible fractional quantum Hall states are well described by an effective elasticity theory. This theory needs to be extended in two directions: first, energy dissipation must be included, since it is essential to correctly describe the charge dynamics of compressible states; second, the spin of the electron must be taken into account. The objective is to develop an effective visco-elastic theory to unify the treatment of spin and charge density excitations in the lowest Landau level. The theory will be applied to the calculation of the collective excitations of quantum Hall ferromagnets at fractional filling factors, the dynamics of topological spin textures, and the dispersion of spin edge waves.Recent theoretical work has highlighted the need to go beyond the local density approximation (LDA) in density-functional calculations of the dielectric response of crystalline insulators. In this context an effort will be made to express the correction to LDA as an explicit functional of the macroscopic polarization. This polarization density functional theory, if successful, will allow first-principles calculations of dielectric properties to be carried out with relative ease.%%% This grant supports theoretical research in condensed matter physics. The research will extend the theory of interacting electrons to include the effects of impurities and electron spin. In particular, the properties of interacting electrons in very high magnetic fields - the quantum Hall state - will be studied. The research contributes to fundamental understanding in condensed matter physics.***