动态平均场论在图解蒙特卡罗中的应用
Incorporating Dynamic Mean-Field Theory into Diagrammatic Monte Carlo
摘要：
大胆的图解蒙特卡罗（BDMC）方法使用骨架图对费曼图解系列进行无偏采样。对于格点模型，通过将动态平均场论（DMFT）解引入重整化传播子，可以显著提高BDMC的效率。从DMFT的角度来看，将其与BDCM相结合，可以得到一种具有明确精度的无偏方法。我们说明了这种方法的力量，通过计算单粒子传播子（从而状态密度）在非微扰制度的安德森局域化问题，在那里的顺序的$10^4$的增益实现相对于传统的BDMC在收敛到确切的答案。
英文摘要：
The bold diagrammatic Monte Carlo (BDMC) method performs an unbiased sampling of Feynman's diagrammatic series using skeleton diagrams. For lattice models the efficiency of BDMC can be dramatically improved by incorporating dynamic mean-field theory (DMFT) solutions into renormalized propagators. From the DMFT perspective, combining it with BDCM leads to an unbiased method with well-defined accuracy. We illustrate the power of this approach by computing the single-particle propagator (and thus the density of states) in the non-perturbative regime of the Anderson localization problem, where a gain of the order of $10^4$ is achieved with respect to conventional BDMC in terms of convergence to the exact answer.
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