发表机构
University of Maryland（马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过四阶微扰级数分析Frohlich极化子，发现弱耦合级数在alpha约8.5处存在幂律奇异性，标志着向强耦合的交叉，且Pade近似与量子蒙特卡洛结果高度吻合。
AI 中文摘要
我们计算了三维Frohlich极化子基态能量和有效质量的Rayleigh-Schrodinger微扰级数，直至耦合常数alpha的四阶。有效质量的三阶和四阶系数是新的。由于Frohlich相互作用是固定总动量下孤立非简并基态的形式有界扰动，该级数具有非零收敛半径，我们采用适用于收敛级数的比值法和Pade方法对其进行分析。这些系数异常规整，可由alpha约8.5处指数约1.4的简单幂律奇异性描述。逆质量逐次截断消失时的耦合值（第一个是教科书中的失效值alpha=6）是对该半径的缓慢收敛估计。仅由弱耦合系数构建的Pade近似与图解蒙特卡洛结果在alpha高达5时质量吻合度优于百分之一。关于基态解析性和强耦合渐近性的精确结果意味着系数不可能保持恒定符号，尽管所有已知系数确实如此，因此表观奇异性必须是靠近正实轴的复共轭对。它标志着向强耦合的交叉：弱耦合级数能准确定位这一交叉，但无法通过它继续延拓。
英文摘要
We calculate the Rayleigh-Schrodinger perturbation series for the ground-state energy and the effective mass of the three-dimensional Frohlich polaron through fourth order in the coupling constant alpha. The third- and fourth-order coefficients of the effective mass are new. Because the Frohlich interaction is a form-bounded perturbation of an isolated nondegenerate ground state at fixed total momentum, the series has a nonzero radius of convergence, and we analyze it with the ratio and Pade methods appropriate to convergent series. The coefficients are strikingly regular and are described by a simple power-law singularity at alpha near 8.5 with an exponent near 1.4. The couplings at which successive truncations of the inverse mass vanish, the first of which is the textbook breakdown value alpha = 6, are slowly converging estimates of this radius. Pade approximants built from the weak-coupling coefficients alone agree with diagrammatic Monte Carlo results for the mass to better than one percent for alpha up to 5. Exact results on the analyticity of the ground state and on the strong-coupling asymptotics imply that the coefficients cannot keep a constant sign, although all known coefficients do, so that the apparent singularity must be a complex-conjugate pair close to the positive real axis. It marks the crossover to strong coupling: the weak-coupling series locates this crossover accurately but cannot be continued through it.
Comments15 pages, 5 figures, 10 tables
