Truncated-Determinant Diagrammatic Monte Carlo for Fermions with Contact Interaction

TL;DR

This paper introduces a truncated-determinant Monte Carlo method that reduces computational effort in simulating interacting fermions, making the process more efficient by focusing on local matrices.

Contribution

The authors propose a novel truncated-determinant approach that approximates ratios of large fermionic determinants using local matrices, improving efficiency in Monte Carlo simulations.

Findings

Efficient computation of determinant ratios using truncated matrices.

Application to the attractive Hubbard model demonstrating practical utility.

Potential for broader use in sign-free determinant Monte Carlo schemes.

Abstract

For some models of interacting fermions the known solution to the notorious sign-problem in Monte Carlo (MC) simulations is to work with macroscopic fermionic determinants; the price, however, is a macroscopic scaling of the numerical effort spent on elementary local updates. We find that the {\it ratio} of two macroscopic determinants can be found with any desired accuracy by considering truncated (local in space and time) matices. In this respect, MC for interacting fermionic systems becomes similar to that for the sign-problem-free bosonic systems with system-size independent update cost. We demonstrate the utility of the truncated-determinant method by simulating the attractive Hubbard model within the MC scheme based on partially summed Feynman diagrams. We conjecture that similar approach may be useful in other implementations of the sign-free determinant schemes.