含时Hubbard链中Kohn-Sham势的绝热和局域近似
Adiabatic and local approximations for the Kohn-Sham potential in time-dependent Hubbard chains
摘要：
我们得到了一维Hubbard链在直流电驱动下含时密度泛函理论的精确Kohn-Sham势$V_{\mathrm{KS}}$.外场，使用随时间变化的电子密度和电流密度从精确的多体时间演化。将精确的$V_{\mathrm{xc}}$与绝热精确的$V_{\mathrm{xc}}^{\mathrm{ad}}$和“瞬时基态“$V_{\mathrm{xc}}^{\mathrm{igs}}$进行比较。后者被证明是有效的，在某些情况下，当前者失败。近似的交换相关电位$V_{\mathrm{xc}}$及其梯度，基于局部密度和局部电流密度，也被认为是和两个物理量被观察到远远超出任何可能的局部近似的范围。洞察基态和激发态的相关性在时间依赖的系统中，反映在潜在的各自的角色，提供了对关联函数。
英文摘要：
We obtain the exact Kohn-Sham potentials $V_{\mathrm{KS}}$ of time-dependent density-functional theory for 1D Hubbard chains, driven by a d.c.\ external field, using the time-dependent electron density and current density obtained from exact many-body time-evolution. The exact $V_{\mathrm{xc}}$ is compared to the adiabatically-exact $V_{\mathrm{xc}}^{\mathrm{ad}}$ and the "instantaneous ground state" $V_{\mathrm{xc}}^{\mathrm{igs}}$. The latter is shown to work effectively in some cases when the former fails. Approximations for the exchange-correlation potential $V_{\mathrm{xc}}$ and its gradient, based on the local density and on the local current density, are also considered and both physical quantities are observed to be far outside the reach of any possible local approximation. Insight into the respective roles of ground-state and excited-state correlation in the time-dependent system, as reflected in the potentials, is provided by the pair correlation function.
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