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Density Functional Theory from Effective Actions

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Density Functional Theory from Effective Actions Density Functional Theory from Effective Actions Dick Furnstahl Department of Physics Ohio State University September, 2005 Collaborators: A. Bhattacharyya, S. Bogner, H.-W. Hammer, S. Puglia, S. Ramanan, A. Schwenk, B. Serot Outline Overview Action Topics Summary Outline Overview: Microscopic DFT Effective Actions and DFT Issues and Ideas and Open Problems Summary Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Outline Overview: Microscopic DFT Effective Actions and DFT Issues and Ideas and Open Problems Summary Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan DFT from Microscopic NN··· N Interactions What? Constructive density functional theory (DFT) for nuclei Why now? Progress in chiral EFT Application of RG (e.g., low-momentum interactions) Advances in computational tools and methods How? Use framework of effective actions with EFT principles EFT interactions and operators evolved to low-momentum Few-body input not enough (?) =⇒ input from many-body Merge with other energy functional developments Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Density Functional Theory (DFT) with Coulomb Dominant application: inhomogeneous Atomization Energies of Hydrocarbon Molecules electron gas 20 Interacting point electrons 0 in static potential of -20 atomic nuclei -40 “Ab initio” calculations of -60 Hartree-Fock DFT Local Spin Density Approximation atoms, molecules, crystals, DFT Generalized Gradient Approximation surfaces, . % deviation from experiment -80 -100 H C C H CH C H C H C H HF is good starting point, 2 2 2 2 4 2 4 2 6 6 6 molecule DFT/LSD is better, DFT/GGA is better still, . Dick Furnstahl DFT from Effective Actions Consequences: In Coulomb DFT, Hartree-Fock gives dominate contribution =⇒ correlations are small corrections =⇒ DFT works! cf. NN interactions =⇒ correlations HF =⇒ DFT fails?? However . the first two depend on the resolution =⇒ different cutoffs third one is affected by Pauli blocking Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Sources of Nonperturbative Physics for NN 1 Strong short-range repulsion (“hard core”) 2 Iterated tensor (S12) interaction 3 Near zero-energy bound states Dick Furnstahl DFT from Effective Actions However . the first two depend on the resolution =⇒ different cutoffs third one is affected by Pauli blocking Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Sources of Nonperturbative Physics for NN 1 Strong short-range repulsion (“hard core”) 2 Iterated tensor (S12) interaction 3 Near zero-energy bound states Consequences: In Coulomb DFT, Hartree-Fock gives dominate contribution =⇒ correlations are small corrections =⇒ DFT works! cf. NN interactions =⇒ correlations HF =⇒ DFT fails?? Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Sources of Nonperturbative Physics for NN 1 Strong short-range repulsion (“hard core”) 2 Iterated tensor (S12) interaction 3 Near zero-energy bound states Consequences: In Coulomb DFT, Hartree-Fock gives dominate contribution =⇒ correlations are small corrections =⇒ DFT works! cf. NN interactions =⇒ correlations HF =⇒ DFT fails?? However . the first two depend on the resolution =⇒ different cutoffs third one is affected by Pauli blocking Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Wavelength and Resolution Dick Furnstahl DFT from Effective Actions Low-momentum potential =⇒ much simpler wave function! Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan The Deuteron at Different Resolutions 0.5 10 3 3 S deuteron w.f. S1 deuteron w.f. 0.4 1 Argonne v ] 1 18 ] 3/2 0.3 Argonne v18 -3/2 (k)| [fm 0 (r) [fm 0.2 ψ 0.1 ψ | 0.1 0.01 0 0 1 2 3 4 5 0 2 4 6 8 10 -1 r [fm] k [fm ] Repulsive core =⇒ short-distance suppression =⇒ high-momentum components Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan The Deuteron at Different Resolutions 0.5 10 3 3 S deuteron w.f. S1 deuteron w.f. 0.4 1 -1 ] 1 Λ = 2 fm ] -1 -1 3/2 0.3 = 2.0 fm Λ = 3 fm -3/2 Λ -1 -1 Λ = 3.0 fm Λ = 4 fm -1 Argonne v18 Λ = 4.0 fm (k)| [fm 0 (r) [fm 0.2 Argonne v 18 ψ 0.1 ψ | 0.1 0.01 0 0 1 2 3 4 5 0 2 4 6 8 10 -1 r [fm] k [fm ] Repulsive core =⇒ short-distance suppression =⇒ high-momentum components Low-momentum potential =⇒ much simpler wave function! Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan The Deuteron at Different Resolutions more Integrand of −〈ψ | V |ψ 〉 for Λ =6.0 fm−1 d Λ d 6 5 10 4 3 5 2 0 1 0 0 2 2 0 k' (fm−1) 4 4 k (fm−1) −1 6 6 Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan The Deuteron at Different Resolutions more Integrand of −〈ψ | V |ψ 〉 for Λ =5.0 fm−1 d Λ d 6 5 10 4 3 5 2 0 1 0 0 2 2 0 k' (fm−1) 4 4 k (fm−1) −1 6 6 Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan The Deuteron at Different Resolutions more Integrand of −〈ψ | V |ψ 〉 for Λ =4.0 fm−1 d Λ d 6 5 10 4 3 5 2 0 1 0 0 2 2 0 −1 k' (fm ) 4 4 k (fm−1) −1 6 6 Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan The Deuteron at Different Resolutions more Integrand of −〈ψ | V |ψ 〉 for Λ =3.0 fm−1 d Λ d 6 5 10 4 3 5 2 0 1 0 0 2 2 0 k' (fm−1) 4 4 k (fm−1) −1 6 6 Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan The Deuteron at Different Resolutions more Integrand of −〈ψ | V |ψ 〉 for Λ =2.0 fm−1 d Λ d 6 5 10 4 3 5 2 0 1 0 0 2 2 0 −1 k' (fm ) 4 4 k (fm−1) −1 6 6 Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan In-Medium Wave Functions (NN Only) 1.6 1.6 1 -1 3 -1 1.4 S0 at kF = 1.35 fm 1.4 S1 at kF = 1.35 fm -1 -1 [P = 0, k = 0.1 fm , m*/m = 1] [P = 0, k = 0.1 fm , m*/m = 1] 1.2 1.2 1 1 (r) (r) k 0.8 k 0.8 Ψ Ψ 0.6 Fermi gas 0.6 Fermi gas v18 v18 3 3 0.4 N LO 0.4 N LO 0.2 0.2 0 0 0 1 2 3 4 5 0 1 2 3 4 5 r [fm] r [fm] Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan In-Medium Wave Functions (NN Only) 1.6 1.6 1 -1 3 -1 1.4 S0 at kF = 1.35 fm 1.4 S1 at kF = 1.35 fm -1 -1 [P = 0, k = 0.1 fm , m*/m = 1] [P = 0, k = 0.1 fm , m*/m = 1] 1.2 1.2 1 1 (r) (r) k 0.8 k 0.8 Ψ Ψ 0.6 Fermi gas 0.6 Fermi gas v18 v18 3 3 0.4 N LO 0.4 N LO -1 -1 Λ = 2.0 fm (v18) Λ = 2.0 fm (v18) -1 3 -1 3 0.2 Λ = 2.0 fm (N LO) 0.2 Λ = 2.0 fm (N LO) 0 0 0 1 2 3 4 5 0 1 2 3 4 5 r [fm] r [fm] Dick Furnstahl DFT from Effective Actions “Very soft potentials must be excluded because they do not give saturation; they give too much binding and too high density. In particular, a substantial tensor force is required.” Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Conventional Wisdom on Nuclear Many-Body Hans Bethe in review of nuclear matter (1971): “The theory must be such that it can deal with any nucleon-nucleon (NN) force, including hard or ‘soft’ core, tensor forces, and other complications. It ought not to be necessary to tailor the NN force for the sake of making the computation of nuclear matter (or finite nuclei) easier, but the force should be chosen on the basis of NN experiments (and possibly subsidiary experimental evidence, like the binding energy of H3).” Dick Furnstahl DFT from Effective Actions Outline Overview Action Topics Summary Intro Vlowk Philosophy ChPT NM Plan Conventional Wisdom on Nuclear Many-Body Hans Bethe in review of nuclear matter (1971): “The theory must be such that it can deal with any nucleon-nucleon (NN) force, including hard or ‘soft’ core, tensor forces, and other complications.
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