Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland.
J Chem Phys. 2012 Jan 28;136(4):044109. doi: 10.1063/1.3679657.
A robust interpolation between the weak- and strong-correlation regimes of quantum systems is presented. It affords approximants to the function E(ω) describing the dependence of the total energy (or other observable) on the coupling parameter ω that measures the correlation strength. The approximants conform to truncations of the asymptotic expansions of E(ω) at the ω → 0 and ω → ∞ limits with arbitrary (but given) numbers of terms. In addition, depending on the number of fitted parameters, they either reproduce or optimally (in the least-square or maximum-error sense) approximate the exact E(ω) at any given number of values of the coupling strength. Numerical tests demonstrate the high accuracy of even the low-order approximate expression for E(ω). The approximants, which do not suffer from spurious poles, possess a wide range of applicability that stems from their capability of accurately reproducing not only E(ω) but also its derivatives with respect to ω. They are equally useful for interpolation between the low- and high-temperature limits of energy and other quantities associated with various models of statistical thermodynamics. The new interpolation scheme is not applicable to the cases where the weak- and strong-correlation asymptotics involve non-analytic functions of ω or expressions dependent on logarithm of the coupling strength. Excluded are also the cases where the weak- and strong-correlation asymptotics pertain to de facto different states, e.g., the ground state of a homogeneous electron gas in three dimensions.
提出了一种量子系统弱关联和强关联区域之间的稳健插值方法。它提供了描述总能量（或其他可观测量）与耦合参数ω之间关系的函数 E(ω)的逼近值，ω 用于衡量关联强度。逼近值符合 E(ω)在 ω→0 和 ω→∞ 极限下的渐近展开的截断，具有任意（但给定）数量的项。此外，根据拟合参数的数量，它们可以在任意数量的耦合强度值处再现或最优（最小二乘或最大误差意义上）逼近精确的 E(ω)。数值测试证明了即使是低阶近似表达式 E(ω)也具有很高的精度。逼近值不会出现虚假极点，具有广泛的适用性，这源于它们不仅能够准确再现 E(ω)，还能够准确再现其对 ω 的导数。它们在统计热力学各种模型的能量和其他与能量相关的量的低温和高温极限之间的插值中同样有用。新的插值方案不适用于弱关联和强关联渐近涉及 ω 的非解析函数或依赖于耦合强度对数的表达式的情况。也排除了弱关联和强关联渐近适用于实际上不同状态的情况，例如，三维各向同性电子气的基态。
