Lectures on ab-initio applications of Self-Consistent Green's Function

148 Pages·2015·53.06 MB·English

by  Carlo Barbieri

Mee#ng&with&HAL&QCD&collabora#on&
RIKEN&–&2>6&February&2015!
Self-consistent Green’s function
applications in ab-initio nuclear physics
Carlo Barbieri — University of Surrey
-1-1V]V] 24O:! dd55//22 ss11//22 pp33//22 pp11//22,, ff77//22 0111...824 01111....8246
MeMe 11..55 pp33//22 pp11//22 dd33//22 00..46 00..46
ωω(n)(n)-3-3S(r,) S(r,) [fm[fm2424OO 00 ..1155--3300 --2255 --2200 --1155 --1100 EE--55FF 00 55 1100 1155 66 44rr [[ffmm]] 22 00 S [MeV] 2n00.234560000 AKCSTciar 00.2
20
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18 20 22 24 26 28 30 32
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Outline!
!
Day 1 (formalism):!
!- definition of propagator!
!- how we can deal with short range physics!
!- FRPA/ADC(3) self-energy, Gorkov, and 3NFs diagrams!
!
Day 2 (results):!
!- studies of chiral interactions in mid mass nuclei!
!- impact of 3NFs!
!- some words on applications to infinite matter!
Current Status of low-energy nuclear physics
Composite&system&of&interac#ng&fermions& Experimental&
Binding&and&limits&of&stability& programs&
Coexistence&of&individual&and&collec6ve&behaviors&
RIKEN,&FAIR,&FRIB&
Self:organiza6on&and&emerging&phenomena&
EOS&of&neutron&star&ma?er&
r#process!path…!
(
s
n
o
t
o
r
p
Unstable&nuclei&
neutrons(
•  ~3,200!known!isotopes!
•  !~7,000!predicted!to!exist!
•  Correla;on!characterised!
in!full!for!~283!stable(!
Nature!473,!25!!(2011);!486,!509!(2012)!
Current Status of low-energy nuclear physics
Composite&system&of&interac#ng&fermions& Experimental&
Binding&and&limits&of&stability& programs&
Coexistence&of&individual&and&collec6ve&behaviors&
RIKEN,&FAIR,&FRIB&
Self:organiza6on&and&emerging&phenomena&
EOS&of&neutron&star&ma?er&
r#process!path…!
II)&Nuclear&correla#ons&
(
s
n
o Fully&known&for&stable&isotopes&
t
o
r [C.&Barbieri&and&W.&H.&Dickhoff,&Prog.&Part.&Nucl.&Phys&52,&377&(2004)]&
p
&
UnstaNbeluet&rnonu:crilceh&in&uclei;&Shell&evolu6on&(far&from&stability)&
neutrons(
•  ~3,200!known!isotopes!
III)&Interdisciplinary&character&
•  !~7,000!predicted!to!exist!
I)&Understanding&the&nuclear&force& Astrophysics&
•  Correla;on!characterised!
QCD:derived;&3:nucleon&forces&(3NFs)& Tests&of&the&standard&model&
in!full!for!~283!stable(!
First&principle&(ab:ini6o)&predic6ons& Other&fermionic&systems:&
Nature!473,!25!!(2011);!486,!509!(2012)!
&&&ultracold&gasses;&molecules;&
Nuclear forces in exotic nuclei
22 K.Muranoetal./PhysicsLettersB735(2014)19–24
Murano!et!al.!(HAL!QCD!coll.)!
Nucleon interactions are very Phys.!LeQ.!B!(2014)!
complex and difficult to handle
Change of regime from
stable to dripline isotopes !&
Fig.1.Central (S 0and 1), tensor and spin–orbit potentials in parity-odd sector obtained by lattice QCD (left), and their enlargements (right). (For interpretation of the
Neurefetrernceos to ncolo=r- inr thiis cfigurhe leg enmd, the areadtert is ereferrred t(o tNhe w eb(cid:6) version oZf this) ar:tic le.)
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4.3. Extractions of potentials and systematic errors+, its existence should be carefully examined
- New shell closures in future studies.
The potential for the spin-singlet sector at NLO can be easily We make a technical comment. We sometimes observe large
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= R($r,!t;J),(Dt−13HN0)R1(5$r,Nt";J) 21N 23N(18) 4.42.7 SNcattering phase shifts and effective potentials
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pared to VCI=S11(r)and VLIS=1(r), and (iii) the spin–orbit potential turns out that the former dominates the systematic error except
;=
Reach of ab-initio theories in
recent years
! Degenerate system (open shells, deformations…)
! Hamiltoninan, including three nucleon forces!
88Ni!
"
2014"
Ab-initio methods zoology
QCD!
Chiral!EFT!
Nuclear!forces:! Phenomenologic!
Derive!from!
!(QCD!symm)!
models!
!NN,!3NF,!etc..!
L#QCD!
(AV18,!CD#Bonn)! 2#,!3#,!N#body!
“hard”! “hard”! “sod”!
“super!sod”!
Hyp!Harm!
SRG!evolu;on!
Self&Cons.&
NCSM! Green’s&fnct&
Monte!Carlo!
IMSRG!
Coupled!
GFMC,!AFDMC!
L#EFT! cluster!
Infinite&maXer&&&&
Light&nuclei&& mid&mass&<&132Sn&
Astroph.&applica#ons!
(cid:1)
(cid:20)(cid:19)(cid:21)(cid:18)(cid:1)(cid:48)(cid:43)(cid:21)(cid:17)(cid:20)(cid:19)(cid:1)(cid:49)(cid:52)(cid:44)(cid:1)(cid:50)(cid:1)(cid:51)(cid:1)(cid:47)(cid:46)(cid:45)(cid:15)(cid:15)
In Green’s Function Monte Carlo one starts with a “trial” wave function, and
lets it propagate in time:

! For t"-i∞, this goes to
the gs wave function!
Better to break the time in many little intervals Δt,
Green’s function (GF)(cid:1)
Monte Carlo
integral (MC)(cid:1)
! GFMC is a method to compute the exact wave function.
(typically works for few bodies, A ≤ 12 in nuclei).(cid:1)
(cid:20)(cid:19)(cid:21)(cid:18)(cid:1)(cid:48)(cid:43)(cid:21)(cid:17)(cid:20)(cid:19)(cid:1)(cid:49)(cid:52)(cid:44)(cid:1)(cid:50)(cid:1)(cid:51)(cid:1)(cid:47)(cid:46)(cid:45)(cid:15)(cid:15)

!M  BGF is a method that DO NOT compute the wave function:
It assumes that the system is in its ground state and attempts at
calculating directly simple excitations from it

•L  arge N (number of particles)
•T  he N-body ground state plays the role of vacuum (of excitations)
•D  egrees of freedom are a few particles (or holes) on top of this vacuum
•I  t is a microscopic method (and capable of “ab-initio” calculations)
(cid:20)(cid:19)(cid:21)(cid:18)(cid:1)(cid:48)(cid:43)(cid:21)(cid:17)(cid:20)(cid:19)(cid:1)(cid:49)(cid:52)(cid:44)(cid:1)(cid:50)(cid:1)(cid:51)(cid:1)(cid:47)(cid:46)(cid:45)(cid:15)(cid:15)
Don’t get confused:

Green’s function Monte Carlo (GFMC) and

Many-body Green’s Functions

are NOT the same method!!!!!!