Boson-Exchange Parquet Solver for dual fermions

TL;DR

This paper introduces a computationally efficient parquet approximation within the dual-fermion framework, utilizing partial bosonization and the truncated unity method to accurately capture long- and short-range correlations in the 2D Hubbard model.

Contribution

The paper develops a novel parquet solver based on dual fermions with partial bosonization, reducing computational cost and enabling accurate spectral calculations.

Findings

Method agrees quantitatively with stochastic diagram summation.

Efficient convergence with few Matsubara frequencies.

Captures both long-range and short-range correlations.

Abstract

We present and implement a parquet approximation within the dual-fermion formalism based on a partial bosonization of the dual vertex function which substantially reduces the computational cost of the calculation. The method relies on splitting the vertex exactly into single-boson exchange contributions and a residual four-fermion vertex, which physically embody respectively long-range and short-range spatial correlations. After recasting the parquet equations in terms of the residual vertex, these are solved using the truncated unity method of Eckhardt et al. [Phys. Rev. B 101, 155104 (2020)], which allows for a rapid convergence with the number of form factors in different regimes. While our numerical treatment of the parquet equations can be restricted to only a few Matsubara frequencies, reminiscent of Astretsov et al. [Phys. Rev. B 101, 075109 (2020)], the one- and two-particle spectral information is fully retained. In applications to the two-dimensional Hubbard model the method agrees quantitatively with a stochastic summation of diagrams over a wide range of parameters.