Theory of Charge and Spin Dynamics in Electron Liquids

该基金支持凝聚态物理学的理论研究。 电子系统中电荷密度激发的含时密度泛函理论（TDFT）现在是一个发展良好的工具，其预测通常与实验测量进行比较。 然而，该理论仍然是相对欠发达方面的能力，以描述（i）杂质效应和（ii）自旋和耦合自旋-电荷动力学在完全或部分自旋极化的电子液体。 本研究的主要目标是发展自旋动力学和杂质效应的TDFT的复杂程度相媲美的普通TDFT已经达到。 从本质上讲，这意味着在杂质散射存在的情况下，发展自旋和频率相关的交换相关（xc）场的精确近似。 为了正确地包括延迟和弛豫效应，有必要超越绝热局部自旋密度近似，并且这可以使用自旋电流密度作为基本变量来完成。 在这种方法中，一个关键的作用是由自旋极化的电子气与杂质的均匀分布的自旋相关的粘弹性光谱。 这些量将在Kubo-Mori形式主义的框架内计算。 在宏观极限的理论应产生广义流体力学（Navier-Stokes）方程的电荷和自旋电流。 这一理论是对最近提出的绝热自旋动力学的补充和推广，高磁场下二维电子液体（所有电子都处于最低朗道能级）粘弹性谱的计算是一个有趣的问题。 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弹性理论很好地描述。 这个理论需要在两个方向上扩展：第一，必须包括能量耗散，因为正确描述可压缩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，统一处理自旋和电荷密度激发的最低朗道水平。 该理论将被应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以及自旋边缘波的色散。最近的理论工作强调了在晶体绝缘体介电响应的密度泛函计算中需要超越局域密度近似（LDA）。 在这种情况下，将作出努力，以表达作为一个明确的功能的宏观极化的LDA的校正。 这种极化密度泛函理论，如果成功的话，将允许相对容易地进行介电性质的第一原理计算。该基金支持凝聚态物理学的理论研究。 这项研究将扩展相互作用电子的理论，包括杂质和电子自旋的影响。 特别是，相互作用的电子在非常高的磁场-量子霍尔态-的性质将被研究。 这项研究有助于对凝聚态物理学的基本理解 *。

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.***