Applications of Renormalization Group Methods in Nuclear Physics 5 - PowerPoint PPT Presentation

Applications of Renormalization Group Methods in Nuclear Physics – 5 Dick Furnstahl Department of Physics Ohio State University HUGS 2014

Outline: Lecture 5 Lecture 5: New methods and IM-SRG in detail New methods with some applications In-Medium Similarity Renormalization Group

Outline: Lecture 5 Lecture 5: New methods and IM-SRG in detail New methods with some applications In-Medium Similarity Renormalization Group

dimension of the problem Interfaces provide crucial clues

SciDAC-2 NUCLEI Project NUclear Computational Low Energy Initiative Collaboration of physicists, applied mathematicians, and computer scientists = ⇒ builds on UNEDF project [unedf.org] US funding but many international collaborators See computingnuclei.org for highlights!

fusion ¡ Validated ¡Nuclear ¡ Interac/ons ¡ Op/miza/on ¡ Chiral ¡EFT ¡ Model ¡valida/on ¡ Ab-­‑ini/o ¡ Uncertainty ¡Quan/fica/on ¡ Neutron ¡drops ¡ Structure ¡and ¡Reac/ons: ¡ Structure ¡and ¡Reac/ons: ¡ ¡ Light ¡and ¡Medium ¡Nuclei ¡ Heavy ¡Nuclei ¡ EOS ¡ Correla/ons ¡ Stellar ¡burning ¡ DFT ¡ Load ¡balancing ¡ Ab-­‑ini/o ¡ Load ¡balancing ¡ TDDFT ¡ Op/miza/on ¡ RGM ¡ Eigensolvers ¡ Model ¡valida/on ¡ CI ¡ Nonlinear ¡solvers ¡ Uncertainty ¡Quan/fica/on ¡ Model ¡valida/on ¡ Eigensolvers ¡ Uncertainty ¡Quan/fica/on ¡ Nonlinear ¡solvers ¡ ¡ Mul/resolu/on ¡analysis ¡ ¡ ¡ Neutrinos ¡and ¡ Fundamental ¡Symmetries ¡ Neutron ¡Stars ¡ Fission ¡

Explosion of many-body methods using microscopic input Ab initio (new and enhanced methods; microscopic NN+3NF) Stochastic: GFMC/AFDMC (new: with local EFT); lattice EFT Diagonalization: IT-NCSM Coupled cluster (CCSD(T), CR-CC(2,3), Bogoliubov, . . . ) IM-SRG (In-medium similarity renormalization group) Self-consistent Green’s function Many-body perturbation theory Shell model (usual: empirical inputs) Effective interactions from coupled cluster, IM-SRG Density functional theory Microscopic input, e.g., through density matrix expansion

Do we really need all of these methods? Compare to lattice QCD: Are all the different lattice actions needed? clover quarks on anisotropic lattices (mass spectrum) domain wall quarks (chiral symmetry) highly improved staggered quarks (high-precision extrapolations) and more! Answer: yes! Complementary strengths A frame from an animation illustrating the typical four-dimensional structure of Cross-check results gluon-field configurations used in Identify theory error bars describing the vacuum properties of QCD.

Oxygen chain with 3 methods [from H. Hergert et al. (2013)] 0 0 0 0 0 0 A O A O A O A O A O A O ⇥ � ⇤ ⇥ NN + 3N-ind. NN + 3N-full (400) ⇤ ⇥ ⇥ � E 3 Max ⇥ 14 E 3 Max ⇥ 14 E 3 Max ⇥ 14 E 3 Max ⇥ 14 E 3 Max ⇥ 14 E 3 Max ⇥ 14 � 25 � 25 � 25 � 25 � 25 � 25 ⇤⇥ 1.9 fm � 1 ⇤⇥ 1.9 fm � 1 ⇤⇥ 1.9 fm � 1 ⇤⇥ 1.9 fm � 1 ⇤⇥ 1.9 fm � 1 ⇤⇥ 1.9 fm � 1 � ⇥ � � ⇥ Hergert&et&al.,&PRL& 110 ,&242501&(2013)&& � 50 � 50 � 50 � 50 � 50 � 50 � � � ⇥ ⇥ & � 75 � 75 � 75 � 75 � 75 � 75 E � MeV ⇥ E � MeV ⇥ E � MeV ⇥ E � MeV ⇥ E � MeV ⇥ E � MeV ⇥ ⇤ � � ⇥ ⇥ � ⇤ � � ⇥ ⇥ � � 100 � 100 � 100 � 100 � 100 � 100 exp. � ⇤ � ⇥ � ⇥ � 125 � 125 � 125 � 125 � 125 � 125 � � ⇥ ⇥ � � ⇤ � � ⇥ ⇥ � � IM � SRG IM � SRG IM � SRG IM � SRG IM � SRG IM � SRG � ⇥ ⇥ ⇥ ⇥ � ⇥ � ⇥ � � ⇥ ⇥ � ⇤ � � ⇥ � ⇥ IT � NCSM IT � NCSM IT � NCSM IT � NCSM � � � 150 � 150 � 150 � � � 150 � 150 � 150 � � ⇥ � ⇥ � � ⇤ ⇥ � ⇥ � � ⇥ ⇥ � � ⇤ � ⇤ CCSD ⇤ CCSD � ⇥ ⇥ � � � � ⇥ ⇥ � ⇤ ⇥ ⇥ � � 175 � 175 � 175 � 175 � 175 � 175 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 22 22 22 24 24 24 26 26 26 10 10 10 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 22 22 22 24 24 24 26 26 26 A A A A A A In-medium SRG, importance-truncated NCSM, coupled cluster Same Hamiltonian = ⇒ test for consistency between methods Impact of three-nucleon force (3NF) on dripline Need precision experiment and theory

� Hoyle state from lattice chiral EFT [E. Epelbaum et al.] Triple- α resonance in 12 C n Low-resolution (coarse) lattice L ∼ 10 . . . 20 fm p Suited to adjust to clusters Order-by-order improvement: ⇒ N 2 LO LO = ⇒ NLO = [Also high-precision GFMC!] a ∼ 1 . . . 2 fm 0 + 1 0 + 2 2 + 1 , J z = 0 2 + 1 , J z = 2 LO [ O ( Q 0 )] NLO [ O ( Q 2 )] IB + EM [ O ( Q 2 )] NNLO [ O ( Q 3 )] Experiment -110 -100 -90 -80 -70 E (MeV)

� � Hoyle state from lattice chiral EFT [E. Epelbaum et al.] Triple- α resonance in 12 C n Low-resolution (coarse) lattice L ∼ 10 . . . 20 fm p Suited to adjust to clusters Order-by-order improvement: ⇒ N 2 LO LO = ⇒ NLO = [Also high-precision GFMC!] a ∼ 1 . . . 2 fm “Survi -50 -50 drup LO [A] LO [C] LO [B] LO [D] -60 -60 Probing α cluster LO [ ! ] LO [ " ] structure of 0 + states -70 -70 E ( t ) (MeV) How does the triple- α -80 -80 reaction rate depend -90 on the quark mass? -90 Much more! -100 -100 -100 Most recent: -110 -110 -110 0 0.02 0.04 0.06 0.08 0.1 0.12 0.12 0 0.02 0.04 0.06 0.08 0.1 0.12 16 O structure t (MeV -1 ) t (MeV -1 )

Spectral functions from self-consistent Green’s function [figures from C. Barbieri] � ectral!func.on) : ab ( ! ) = 1 S h π Im g ab ( ! ) 56 Ni � E � A+1 � sca5ering � neutron+ neutron+ removal � addi2on � � rth:Jensen,!Pys.!Rev.!C 79 ,!064313!(2009);!CB,!Phys.!Rev.!LeI.! 103 ,!202502!(2009)]! One-body Greens function (or propagator) � g ab ( ω ) describes the motion of quasi-particles and quasi-holes E F � Contains all the structure information probed by nucleon transfer A:1 � Imaginary (absorptive) part of g ab ( ω ) is the spectral function

Confronting theory and experiment to both driplines 0 Precision mass measurements test N=8 -2 Ground-State Energy (MeV) impact of chiral 3NF -4 Proton rich [Holt et al. (2012)] -6 Neutron rich [Gallant et al. (2012)] -8 Many new tests possible! NN NN+3N -10 NN+3N (sdf 7/2 p 3/2 ) AME2011 confirmed in precision Penning trap exp. -12 IMME 16 17 18 19 20 21 22 23 24 AME Mass Number A AN collaboration + Holt, Menendez, Schwenk, submitted. Shell model description using chiral potential evolved to V low k plus 3NF fit to A = 3 , 4 Excitations outside valence space included in 3rd order MBPT

Confronting theory and experiment to both driplines 0 Precision mass measurements test N=20 Ground-State Energy (MeV) -2 impact of chiral 3NF Proton rich [Holt et al. (2012)] -4 Neutron rich [Gallant et al. (2012)] -6 Many new tests possible! NN -8 NN+3N NN+3N (pfg 9/2 ) -10 Exp and AME2011 extrapolation confirmed in precision Penning trap exp. IMME -12 40 41 42 43 44 45 46 47 48 AME Mass Number A AN collaboration + Holt, Menendez, Schwenk, submitted. Shell model description using chiral potential evolved to V low k plus 3NF fit to A = 3 , 4 Excitations outside valence space included in 3rd order MBPT

Non-empirical shell model [from J. Holt] Solving the Nuclear Many-Body Problem Nuclei understood as many-body system starting from closed shell, add nucleons Interaction and energies of valence space orbitals from original V low k This alone does not reproduce experimental data 0h,1f,2p 0g,1d,2s 0f,1p - “sd”-valence space Active nucleons occupy valence space 0p 0s Assume filled core

Non-empirical shell model [from J. Holt] Solving the Nuclear Many-Body Problem Nuclei understood as many-body system starting from closed shell, add nucleons Interaction and energies of valence space orbitals from original V low k This alone does not reproduce experimental data – allow explicit breaking of core Hjorth-Jensen, Kuo, Osnes (1995) 0h,1f,2p 0g,1d,2s Strong interactions with core generate effective interaction 0f,1p between valence nucleons - “sd”-valence space Active nucleons occupy valence space 0p 0s Assume filled core

Non-empirical shell model [from J. Holt] Solving the Nuclear Many-Body Problem Nuclei understood as many-body system starting from closed shell, add nucleons Interaction and energies of valence space orbitals from original V low k This alone does not reproduce experimental data – allow explicit breaking of core Effective two-body matrix elements Single-particle energies (SPEs) Hjorth-Jensen, Kuo, Osnes (1995) 0h,1f,2p 0g,1d,2s Strong interactions with core generate effective interaction 0f,1p between valence nucleons - “sd”-valence space Active nucleons occupy valence space 0p 0s Assume filled core

Chiral 3NFs meet the shell model [from J. Holt] 3N Forces for Valence-Shell Theories Normal-ordered 3N : contribution to valence neutron interactions Effective two-body Effective one-body 16 16 O core O core a V 3 N ,eff a ' = 1 # ab V 3 N ,eff a ' b ' = " ab V 3 N " a ' b ' $ "# a V 3 N "# a ' 2 " = core "# = core Combine with microscopic NN: eliminate empirical adjustments