Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
Amir Taheridehkordi, S. H. Curnoe, J. P. F. LeBlanc
Abstract
We present a general method to optimize the evaluation of Feynman diagrammatic expansions which uses an automated symbolic assignment of momentum/energy conserving variables to each diagram. With this symbolic representation, we utilize the pole structure of each diagram to sort the Feynman diagrams into groups that are likely to contain nearly equal or nearly canceling diagrams, and we show that for some model parameters this cancellation is exact. This allows for a potentially massive cancellation during the numerical integration of internal momenta variables, leading to an optimal suppression of the ``sign problem'' and hence reducing the computational cost. Although we define these groups using a frequency space representation, the equality or cancellation of diagrams within the group remains valid in other representations such as imaginary time used in standard diagrammatic Monte Carlo. As an application of the approach, we apply this method, combined with algorithmic Matsubara integration (AMI) [A. Taheridehkordi, S. H. Curnoe, and J. P. F. LeBlanc, Phys. Rev. B 99, 035120 (2019)] and Monte Carlo methods, to the Hubbard model self-energy expansion on a 2D square lattice, which we evaluate and compare with existing benchmarks.