Solving the Parquet Equations for the Hubbard Model beyond Weak Coupling

TL;DR

This paper enhances the convergence of solving parquet equations for the Hubbard model by imposing crossing symmetry, enabling solutions at stronger interactions and lower temperatures, which advances computational methods for correlated electron systems.

Contribution

The authors introduce a modified algorithm that imposes crossing symmetry without extra computational cost, significantly extending the convergence range for the Hubbard model's parquet equations.

Findings

Imposing crossing symmetry improves convergence range.

Stable solutions achieved at stronger interactions and lower temperatures.

Latency hiding scheme enhances computational performance.

Abstract

We find that imposing the crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When the crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods are limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed time reversal and a subset of the point group symmetries, but they did not further improve the convergence. We elaborate the details of the latency hiding scheme which can significantly improve the performance in the computational implementation. With these modifications, stable solutions for the parquet equations can be obtained by iteration more quickly even for values of the interaction that are a significant fraction of the bandwidth and for temperatures that are much smaller than the bandwidth. This may represent a crucial step towards the solution of two-particle field theories for correlated electron models.