Rossi Riccardo
Laboratoire de Physique Statistique de l'École Normale Supérieure, 75005 Paris, France.
Phys Rev Lett. 2017 Jul 28;119(4):045701. doi: 10.1103/PhysRevLett.119.045701. Epub 2017 Jul 25.
We present a simple trick that allows us to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models, such that the thermodynamic limit can be taken analytically. With our approach one can achieve superior performance compared to conventional diagrammatic Monte Carlo algorithm, while rendering the algorithmic part dramatically simpler. By considering the sum of all connected diagrams at once, we allow for massive cancellations between different diagrams, greatly reducing the sign problem. In the end, the computational effort increases only exponentially with the order of the expansion, which should be contrasted with the factorial growth of the standard diagrammatic technique. We illustrate the efficiency of the technique for the two-dimensional Fermi-Hubbard model.
我们提出了一种简单的技巧，它使我们能够在一般费米子模型中，在相互作用顶点的固定位置考虑所有连通费曼图的总和，从而可以解析地取热力学极限。与传统的图解蒙特卡罗算法相比，采用我们的方法可以实现更高的性能，同时使算法部分显著简化。通过一次性考虑所有连通图的总和，我们允许不同图之间大量抵消，极大地减少了符号问题。最后，计算量仅随展开阶数呈指数增长，这与标准图解技术的阶乘增长形成对比。我们展示了该技术在二维费米 - 哈伯德模型中的效率。
