Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

TL;DR

This paper compares various advanced numerical algorithms to compute ground and excited state properties of the 2D Hubbard model, establishing benchmarks and highlighting uncertainties to improve future computational methods.

Contribution

It provides a comprehensive benchmark of multiple numerical algorithms for the 2D Hubbard model, assessing their accuracy and systematic errors in the thermodynamic limit.

Findings

Different methods show consistent results for certain properties.

Identification of uncertainties and systematic errors in numerical approaches.

Benchmark results useful for validating and improving computational techniques.

Abstract

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.