标题： 量子蒙特卡洛研究二维均匀电子液体的相图 显示英文标题

标题： Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid

摘要： 我们研究了自旋未极化和自旋极化的二维均匀电子液体，采用了变分蒙特卡洛（VMC）和扩散蒙特卡洛（DMC）方法，使用Slater-Jastrow-backflow试验波函数。在密度范围$1 \leq r_\text{s} \leq 40$内得到了基态VMC和DMC能量。通过规范系综扭转平均边界条件和扭转平均能量向无限系统大小的热力学极限外推，修正了单粒子和多体有限尺寸误差。讨论了由部分收敛的VMC能量最小化计算引起的Slater-Jastrow-backflow DMC能量的系统尺寸相关误差。我们发现，对于$1 \leq r_\text{s} \leq 5$，在每个扭转处优化backflow函数可以降低有限系统尺寸下的扭转平均DMC能量。然而，DMC能量中仍存在非系统性的系统尺寸相关效应，可以通过从多个有限系统尺寸外推到无限系统尺寸来部分消除。我们认为这些非系统性效应归因于低密度下不同系统尺寸时流体相和有缺陷晶体相之间的激烈竞争。利用热力学极限下的DMC能量，为非均匀电子系统参数化了局域自旋密度近似关联泛函。我们的零温相图显示，在$r_\text{s}=35(1)$处，从顺磁性流体到六角Wigner晶体发生单一转变，不存在亚铁磁性流体的稳定区域。 显示英文摘要

摘要： We present a study of spin-unpolarized and spin-polarized two-dimensional uniform electron liquids using variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions. Ground-state VMC and DMC energies are obtained in the density range $1 \leq r_\text{s} \leq 40$. Single-particle and many-body finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of twist-averaged energies to the thermodynamic limit of infinite system size. System-size-dependent errors in Slater-Jastrow-backflow DMC energies caused by partially converged VMC energy minimization calculations are discussed. We find that, for $1 \leq r_\text{s} \leq 5$, optimizing the backflow function at each twist lowers the twist-averaged DMC energy at finite system size. However, nonsystematic system-size-dependent effects remain in the DMC energies, which can be partially removed by extrapolation from multiple finite system sizes to infinite system size. We attribute these nonsystematic effects to the close competition between fluid and defected crystal phases at different system sizes at low density. The DMC energies in the thermodynamic limit are used to parameterize a local spin density approximation correlation functional for inhomogeneous electron systems. Our zero-temperature phase diagram shows a single transition from a paramagnetic fluid to a hexagonal Wigner crystal at $r_\text{s}=35(1)$, with no region of stability for a ferromagnetic fluid.