误导收敛的骨架图解技术：当正确的解决方案可以找到
Misleading convergence of the skeleton diagrammatic technique: when the correct solution can be found
摘要：
自洽骨架图解技术（SDT）的收敛-其中完整的格林函数是通过对费曼图本身求和来确定的-错误的答案与Luttinger-Ward泛函的非微扰分支的存在有关。虽然有可能在不知道确切结果的情况下发现误导性趋同，但特殊和差别待遇在发生这种情况的制度中仍然不适用。我们表明，误导收敛并不总是排除恢复的精确解。除了既定的机制，SDT收敛到错误的答案可以源于发散的固有的图解系列，这使我们能够恢复精确的解决方案，通过修改SDT协议的基础上控制解析延续。我们说明了这种方法，它的应用程序解析可解的（0+0）d哈伯德模型，哈伯德原子，和2D哈伯德模型在一个具有挑战性的强耦合制度，SDT解决了控制精度的图解蒙特卡罗（DiagMC）技术。
英文摘要：
Convergence of the self-consistent skeleton diagrammatic technique (SDT) -- in which the full Green's function is determined through summation of Feynman diagrams in terms of itself -- to the wrong answer has been associated with the existence of non-perturbative branches of the Luttinger-Ward functional. Although it has been possible to detect misleading convergence without the knowledge of the exact result, the SDT has remained inapplicable in the regimes where this happens. We show that misleading convergence does not always preclude recovering the exact solution. In addition to the established mechanism, convergence of the SDT to the wrong answer can stem from divergence of the inherent diagrammatic series, which allows us to recover the exact solution by a modified SDT protocol based on controlled analytic continuation. We illustrate this approach by its application to the analytically solvable (0+0)d Hubbard model, the Hubbard atom, and the 2d Hubbard model in a challenging strong-coupling regime, for which the SDT is solved with controlled accuracy by the diagrammatic Monte Carlo (DiagMC) technique.
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