Timeline for How exact is DFT, really?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Nov 19, 2020 at 9:59 | comment | added | Phil Hasnip | @wouter Yes exactly, all ground state properties are encoded in the density and a property-dependent universal functional. There is no fundamental assumption of Born-Oppenheimer or instantaneous Coulomb interaction, though they are ubiquitous in practice. | |
| Nov 19, 2020 at 4:49 | comment | added | Wouter | @PhilHasnip Ok, I get that DFT does not address the excited states. But nevertheless, if 'properties' are synonym for 'all possible expectation values' , this means that it should give the ground state. Btw, I think of two specific approximations that are assumed for DFT at the moment to solve the many-body problem: Born-Oppenheimer approximation (i.e. no nucleus-electron entanglement), and the instantaneous transmission of coulomb interaction. But probably these are often well justified | |
| Nov 13, 2020 at 11:40 | comment | added | Phil Hasnip | All information about the ground state is in the ground state electron density, assuming that the external potential is local. This does not get you the many-body wavefunction, what it says is that it is not necessary to get the many-body wavefunction in order to describe all properties of the ground state. (For excited states, you need to invoke the Runge-Gross theorem and TD-DFT.) | |
| Oct 16, 2020 at 14:18 | comment | added | Susi Lehtola | The difference is that the Gross-Pitaevskii equation (GPE) comes from a mean-field wave function theory where all particles are placed on the lowest-lying orbital (it's the bosonic equivalent of Hartree-Fock). GPE disregards all correlation effects, which are included in density-functional theory with the exact functional (which we do not know). | |
| Oct 16, 2020 at 2:21 | comment | added | Wouter | @SusiLehtola so essentially, DFT problems can be recast as a classical field theory. Then it's really striking that it is considered exact, while a GPE is only semiclassical. | |
| Oct 15, 2020 at 23:47 | comment | added | Susi Lehtola | ""All information is in the electron density". This means the single-particle reduced density matrix." Actually, it means the diagonal of the single-particle reduced density matrix - a much weaker property! | |
| Oct 12, 2020 at 12:34 | comment | added | Wouter | @user14717 basically, HK tells us that the electron field is in a Fock state at every point, compared with for example a Gross-Pitaevskii equation which assumes a coherent state at every point? | |
| Oct 12, 2020 at 12:27 | comment | added | user14717 | @Wouter: Definitely not useless for fundamental research, but not the correct way to think about many problems in solid state. | |
| Oct 10, 2020 at 20:33 | history | edited | Nike Dattani - No Free Time | CC BY-SA 4.0 |
added 1 character in body
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| Oct 10, 2020 at 15:18 | vote | accept | Wouter | ||
| Oct 10, 2020 at 13:14 | comment | added | Greg | So what is wrong with the HK theorem? | |
| Oct 10, 2020 at 4:20 | comment | added | Wouter | @user14717 thanks, very interesting. Your point is that DFT is virtually exact for the questions that it tries to answer; while useless for more fundamental research in quantum physics? | |
| Oct 10, 2020 at 0:55 | history | became hot network question | |||
| Oct 9, 2020 at 23:40 | answer | added | wcw | timeline score: 12 | |
| Oct 9, 2020 at 17:57 | comment | added | user14717 | P.W. Anderson's paper "More is different" seems appropriate: science.sciencemag.org/content/177/4047/393 | |
| Oct 9, 2020 at 15:17 | comment | added | Wouter | @TristanMaxson thanks, will take a look | |
| Oct 9, 2020 at 14:28 | comment | added | Tristan Maxson | This might be a partial duplicate. Not voting to close since i do see some differences. See this answer though. mattermodeling.stackexchange.com/a/533/697 | |
| Oct 9, 2020 at 14:11 | review | First posts | |||
| Oct 9, 2020 at 20:16 | |||||
| Oct 9, 2020 at 14:07 | history | asked | Wouter | CC BY-SA 4.0 |