Explicit demonstration of the equivalence between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>DFT</mml:mi> <mml:mo>+</mml:mo> <mml:mi>U</mml:mi> </mml:mrow> </mml:math> and the Hartree-Fock limit of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="normal">DFT</mml:mi> <mml:mo>+</mml:mo> <mml:mi mathvariant="normal">DMFT</mml:mi> </mml:math>

Abstract

Several methods have been developed to improve the predictions of density functional theory (DFT) in the case of strongly correlated electron systems. Out of these approaches, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>DFT</a:mi> <a:mo>+</a:mo> <a:mi>U</a:mi> </a:mrow> </a:math> , which corresponds to a static treatment of the local interaction, and DFT combined with dynamical mean field theory ( <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi mathvariant="normal">DFT</b:mi> <b:mo>+</b:mo> <b:mi mathvariant="normal">DMFT</b:mi> </b:math> ), which considers local fluctuations, have both proven incredibly valuable in tackling the description of materials with strong local electron-electron interactions. While it is in principle known that the Hartree-Fock (HF) limit of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi mathvariant="normal">DFT</e:mi> <e:mo>+</e:mo> <e:mi mathvariant="normal">DMFT</e:mi> </e:math> approach should recover <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>DFT</h:mi> <h:mo>+</h:mo> <h:mi>U</h:mi> </h:mrow> </h:math> , demonstrating this equivalence in practice is challenging, due to the very different ways in which the two approaches are generally implemented. In this work, we introduce a way to perform <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>DFT</i:mi> <i:mo>+</i:mo> <i:mi>U</i:mi> </i:mrow> </i:math> calculations in using Wannier functions as calculated by , which allows us to use the same Hubbard projector functions both in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mi>DFT</j:mi> <j:mo>+</j:mo> <j:mi>U</j:mi> </j:mrow> </j:math> and in <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi mathvariant="normal">DFT</k:mi> <k:mo>+</k:mo> <k:mi mathvariant="normal">DMFT</k:mi> </k:math> . We benchmark these <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mi>DFT</n:mi> <n:mo>+</n:mo> <n:mi>U</n:mi> </n:mrow> </n:math> calculations against <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mi mathvariant="normal">DFT</o:mi> <o:mo>+</o:mo> <o:mi mathvariant="normal">DMFT</o:mi> </o:math> calculations where the DMFT impurity problem is solved within the HF approximation. Considering a number of prototypical materials including NiO, MnO, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:msub> <r:mi>LaMnO</r:mi> <r:mn>3</r:mn> </r:msub> </r:math> , and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:msub> <s:mi>LuNiO</s:mi> <s:mn>3</s:mn> </s:msub> </s:math> , we establish the sameness of the two approaches. Finally, we showcase the versatility of our approach by going beyond the commonly used atomic orbital-like projectors by performing <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mrow> <t:mi>DFT</t:mi> <t:mo>+</t:mo> <t:mi>U</t:mi> </t:mrow> </t:math> calculations for <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:msub> <u:mi>VO</u:mi> <u:mn>2</u:mn> </u:msub> </u:math> using a special set of bond-centered Wannier functions.

Topics & Concepts