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 multireference projected Hartree-Fock methods. 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.

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

Becca, Federico;Ferrero, Michel;Tocchio, Luca Fausto;
2015-01-01

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 multireference projected Hartree-Fock methods. 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.
2015
5
4
041041
Leblanc, Jpf; Antipov, Ae; Becca, Federico; Bulik, Iw; Chan, Gkl; Chung, Cm; Deng, Yj; Ferrero, Michel; Henderson, Tm; Jimenez Hoyos, Ca; Kozik, E; Liu, Xw; Millis, Aj; Prokof'Ev, Nv; Qin, Mp; Scuseria, Ge; Shi, H; Svistunov, Bv; Tocchio, Luca Fausto; Tupitsyn, Is; White, Sr; Zhang, Sw; Zheng, Bx; Zhu, Zy; Gull, E.
File in questo prodotto:
File Dimensione Formato  
PhysRevX.5.041041.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 1.29 MB
Formato Adobe PDF
1.29 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/33167
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 431
  • ???jsp.display-item.citation.isi??? 452
social impact