Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit

TL;DR

This paper introduces a simplified and more efficient Diagrammatic Monte Carlo method that sums all connected Feynman diagrams simultaneously, reducing the sign problem and exponential complexity growth, demonstrated on the 2D Fermi-Hubbard model.

Contribution

A novel approach to sum all connected diagrams at once, improving performance and simplicity over traditional Diagrammatic Monte Carlo methods.

Findings

Enhanced efficiency in simulating fermionic models.

Reduced sign problem through diagram cancellations.

Complexity grows exponentially with order, not factorial.

Abstract

We present a simple trick that allows to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models. With our approach one achieves superior performance compared to Diagrammatic Monte Carlo, while rendering the algorithmic part dramatically simpler. As we consider the sum of all connected diagrams at once, we allow for cancellations between diagrams with different signs, alleviating the sign problem. Moreover, the complexity of the calculation grows exponentially with the order of the expansion, which should be constrasted with the factorial growth of the standard diagrammatic technique. We illustrate the efficiency of the technique for the two-dimensional Fermi-Hubbard model.