Robust interpolation between weak- and strong-correlation regimes of quantum systems

摘要

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.