Testing density-functional approximations on a lattice and the applicability of the related Hohenberg-Kohn-like theorem

Autor(es)

Franca, Vivian V. ^[1] ; Coe, Jeremy P. ^[2] ; D'Amico, Irene ^{[3, 4]}

Afiliação do(s) autor(es)

^[1] Sao Paulo State Univ, Inst Chem, BR-14800060 Araraquara, SP - Brazil

^[2] Heriot Watt Univ, Sch Engn & Phys Sci, Inst Chem Sci, Edinburgh EH14 4AS, Midlothian - Scotland

^[3] Univ Sao Paulo, Inst Fis Sao Carlos, BR-13560970 Sao Carlos, SP - Brazil

^[4] Univ York, Dept Phys, York YO10 5DD, N Yorkshire - England

• Tipo de documento: Artigo Científico
• Fonte: SCIENTIFIC REPORTS; v. 8, JAN 12 2018.
• Citações Web of Science: 5

Resumo

We present a metric-space approach to quantify the performance of approximations in lattice density-functional theory for interacting many-body systems and to explore the regimes where the Hohenberg-Kohn-type theorem on fermionic lattices is applicable. This theorem demonstrates the existence of one-to-one mappings between particle densities, wave functions and external potentials. We then focus on these quantities, and quantify how far apart in metric space the approximated and exact ones are. We apply our method to the one-dimensional Hubbard model for different types of external potentials, and assess the regimes where it is applicable to one of the most used approximations in density-functional theory, the local density approximation (LDA). We find that the potential distance may have a very different behaviour from the density and wave function distances, in some cases even providing the wrong assessments of the LDA performance trends. We attribute this to the systems reaching behaviours which are borderline for the applicability of the one-to-one correspondence between density and external potential. On the contrary the wave function and density distances behave similarly and are always sensitive to system variations. Our metric-based method correctly predicts the regimes where the LDA performs fairly well and the regimes where it fails. This suggests that our method could be a practical tool for testing the efficiency of density-functional approximations. (AU)

• Processo FAPESP: 13/15982-3 - Teoria do funcional da densidade e aplicações em sólidos e átomos frios
• Beneficiário: Vivian Vanessa França Henn
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores