一维库仑气体的精确基态性质
Exact ground state properties of the one-dimensional Coulomb gas
摘要：
研究了单组分一维库仑气体的基态性质。我们使用玻色-费米映射的基态波函数，它允许解决费米符号问题在以下方面（i）的节点表面是已知的，允许精确的计算（ii）评估的决定因素是避免的，减少了数值的复杂性的玻色子系统，从而允许模拟大量的费米子。由于这种映射，一维库仑系统中的能量和局域性质对于玻色-爱因斯坦和费米-狄拉克统计是完全相同的。用扩散蒙特卡罗方法计算了均匀和陷阱几何下的精确基态能量。我们表明，在低密度的维格纳晶体极限的基本低位激发是一个等离子体激元，这是与大密度的理想费米气体/Tonks-Girardeau限制，其中低位激发是声子。精确的密度分布面临的局部密度近似内计算的预测的变化，从一个半圆形的倒抛物线形状的密度分布的电荷的值增加。
英文摘要：
The ground state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground state wave function which permits to solve the Fermi sign problem in the following respects (i) the nodal surface is known, permitting exact calculations (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system, thus allowing simulation of a large number of fermions. Due to the mapping the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground state energy has been calculated in homogeneous and trapped geometries by using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the large-density ideal Fermi gas/Tonks-Girardeau limit, where low lying excitations are phonons. Exact density profiles are confronted to the ones calculated within the local density approximation which predicts a change from a semicircular to inverted parabolic shape of the density profile as the value of the charge is increased.
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