HPCI project field 5“The origin of matter and the universe”

2014/06/05 ARIS2014
at Ito Hall, Tokyo

Frontier of Nuclear ShellModel Calculations and HighPerformance Computing
Noritaka SHIMIZU
CNS, University of Tokyo
T. Abe (Tokyo), M. Honma (Aizu), T. Mizusaki (Senshu),
T. Otsuka (Tokyo), T. Togashi (CNS),
Y. Tsunoda (Tokyo), and T. Yoshida (CNS)1

Recipe for shell-model calculations
large-scale shell-model calc.

no-core shell model

model space: valence shell (+ extention)

excitation energy (Nmax hw)

phenomenologicalcorrection

Realistic NN force

Realistic NN (+NNN) force

Effective interaction

Effective interaction

Diagonalization of
many-body Hamiltonian
NNN forceHigh Performance ComputingΨ = ∑ vm mmm

Diagonalization of
many-body Hamiltonian∑ m H m' v = E mm'm': configuration, “spherical” Slater determinant of harmonic oscillator

1  N p  N p   
The number of m ≈f  Z  Z Hamiltonian matrix is sparse⇒ Lanczos algorithm

2Frontier of large-scale shell-model calculations
Evolution of LSSM calc.
w/ Lanczos method: Lanczos●• The maximum dimension of the M-scheme Hamiltonian matrix of theLSSM evolve exponentially as the performance development ofsupercomputers• Present limitation ≈ 1010-11 (as expected by the extrapolation in 2000)
e.g. 68Ni in pf+g9/2+d5/2 5x1015

2040 for 1015 dim.?

Large-scale shell model calculations
valence shell or its extention
as model space

f5pg9-shell

sd shell, pf shell,

pf-shell

f5pg9 shelldiagonalizablesd-shell

60Zn in pf-shell : 2x109
78Y in f5pg9-shell: 1.3x1010
4

Example of the large-scale shell-model calculationsNS, Y. Utsuno, S. Ebata, T. Otsuka, M. Honma and T. Mizusaki, in preparation

1hw/3hw sd-pf-sdg shell calculations
for negative-parity states of Ca isotopes
to describe E1 excitations

Photo-absorption cross section of 48Ca

1hw
0g1d2s

exp.

0f1p
0d1s

protonneutron1hw : upto 1hw excitation in sd-pf-sdg shell
4.1x106 M-scheme dim.
at PC

We develop M-scheme shellmodel code with Lanczos method (1+3)hw: up to 3hw excitation in sd-pf-sdg shell
1.2x1010 M-scheme dim.
for massive parallel computation
at supercomputer 5“KSHELL”.

HPCI Strategic Program for Innovative Research
by MEXT, Japan FY2011 – FY2015
to facilitate efficient use of K computer and HPC• Strategic 5 Fields:– Field1: “Supercomputational Life Science”– Field2: “Computational Materials Science Initiative”– Field 3: “Projection of Planet Earth Variations for Mitigating Natural Disasters”– Field 4: “Industrial Innovation”– Field 5: “The origin of matter and the universe”••••

lattice QCD
Nucleus
Supernova Explosion
Early Star Formation

Our group
Head: Takaharu Otsuka (Tokyo)nuclear shell-model calculations using Monte Carlo shell modelMonte Carlo Shell Model

Otsuka, Honma, Mizusaki, Shimizu,Utsuno, PPNP47, 319 (2001)

a tool to go beyond the conventional Lanczos diagonalization methodfor Large-Scale Shell Model calculations∗ ∗ ∗ ∗ ∗∗ ∗ ∗ ∗∗ ∗ ∗∗ ∗H =ε1ε2ε3
diagonalization

Stochasticallyselected basis

Conventional Shell Model
all Slater determinantsH∗ ∗ ∗∗ ∗ ∗∗ ∗ε’1diagonalization

Monte Carlo Shell Modelbases important for a specific eigenstateφ (σ ) = ∏ e∆β ⋅h (σ )ε’2

⋅ φ (0)hˆ(σ ) one-body HamiltonianN MCSM

Ψ = ∑ f k P J ,π φkk =1

σ... auxiliary fieldrandom numbers

 N sp † ( k ) φk = ∏  ∑ ci Diα  −α =1  i =1N

MCSM basis, deformed Slater det.

Wave function is described as a linear combination of J-projected deformed Slater determinants.
Increase MCSM dimension, or number of deformed Slater det. till energy converges.
7

“Advanced” Monte Carlo Shell Model towards K computer
T. Otsuka, M. Honma, T. Mizusaki, NS, and Y.
Utsuno, Prog. Part. Nucl. Phys. 47, 319 (2001).

PC cluster
100CPUNS, Y. Utsuno, T. Mizusaki, T. Otsuka, T. Abe, and M.
Honma, Phys. Rev. C 82, 061305(R) (2010).

Precise estimation of energy eigenvalues
with energy-variance extrapolation+ basis reordering technique

Parallel efficiency
NS et al., Phys. Rev. C 85054301(2012).

Energy gradient for
optimization of wave function

Computation algorithm
OpenMP+MPI hybrid parallel

100,000 cores
NS, T. Abe, Y. Tsunoda, Y. Utsuno, T.
Yoshida, T. Mizusaki, M. Honma and T.
Otsuka, Prog. Theor. Exp. Phys. 2012
01A205 (2012).

8 timesacceleration
Y. Utsuno, NS, T. Otsuka, and T. Abe,Comp. Phys. Comm. 184 102 (2013).

8

Energy variance extrapolation in the MCSM: 64Ge in pfg9-shell
Energy variance：
64Ge in pfg9-shell, 1014dim

Extrapolate to 1014... impossible

2

As the number of basis states increases,
the approximated w.f. approaches the exact one
and the energy variance approaches zero.
Extrapolate towards ∆H

Number of basis states (dimension)<H>1 <H>2 <H>3 ・・・ Eexact<∆H2>1<∆H2>2 <∆H2>3 ・・・ 0Hij =∆H 2 = H 2 − H

Extrapolate to 0.

2→0Advantages of the MCSM
• computation intensive, rather small memory
access, small I/O ... good at massive parallel
computation
discretized integral
M-scheme Lanczos method

vs~1010Ψ = ∑ f k φmm =1

huge memory and disk I/O• overcome the limitation ofLanczos method• analyze “intrinsic” wave
function and shape(discussed later)of Euler’s angle
MCSM wave function

Ψ =N MCSM ~100J ,πfP
∑ k φkk =1●: Lanczos■: MCSMMCSM broadens applicability of SM calc.
pf-shell + g9/2 + d5/2 MCSM

heavier nuclei
neutron-rich nuclei

f5pg9

pf-shell
20<Z<40, 28<N<56
Sieja & Nowacki
arXiv:1201.0372

Ex(2+) Ni isotopes
sd-shellNeutron-rich nuclei: across two major shells⇒ proton neutron different model space+ truncation⇒ full isospin-invariant space + MCSM

11

Y. Tsunoda AS2-A037, S. Suchyta PS2-A039, Y. Utsuno oral

Neutron-rich Ni isotopes and shell evolution

Exp.: S. Suchyta PS2-A039pf-shell + g9/2, d5/2 orbits w/o truncation
Y. Tsunoda, T. Otsuka, NS, M. Honma and Y. Utsuno,... 5.1 x 1015 M-scheme dim.
PRC 89, 031301(R) (2014)
8+68Ni
6+4+2+

Energy0+

Neutron number

68Ni 0+ states ⇔ different shapes
MCSM w.f.

Ψ =0+2 : oblate β ～ -0.2

N MCSM ~100

J ,πfP∑ k φkk =1PES is calculated by Q-constraint Hartree-Fock calc.
Location of circle : quadrupole deformation ofArea of circle : overlap probability

φk21Ψ P J ,π φkNk0+1 : spherical β ～ 00+3 : prolate β ～ +0.4

Towards 78Ni : prediction
Z=28, N=50
How magic?

Excitation energies of Ni isotopes

Both SM results givelarge 2+ energy
78Ni

PES

SM: Sieja and Nowacki, arXiv:1201.0373
MCSM: Y. Tsunoda et al., PRC 89 031301(R) (2014)

π pf, ν f5pg9d5
full pfpg9d5

MCSM

Towards SM calc. w/o phenomenologicalcorrection
3-body force into normal ordered 2-body force
2+1 Energy of calcium isotopes

Normal ordered 2-body force isgood approximation for no-core SM
Ref. R. Roth et al., PRL 109, 052501
Phenomenological fit of SM interaction← 3-body force origin

SM calc. w/o phenom. correction
Normal ordered 2-body force
Ref. J. Holt, T. Otsuka, A. Schwenk and T. Suzuki,
JPG 39 085111 (2012)

No-core shell model

Importance Truncated
NCSM
R. Roth, P. Navratil, et al.
40Ca, 48Ca, ...

Excitation energy (Nmaxhw) truncation
Extrapolation to infinite model space

NCSM
P. Maris, J. P. Vary and A. Shirokov
PRC 79, 014308 (2009)

NCSM and reaction ... S. Quaglioni et al.

MCSM for no-core shell model calc.
• Enhance the applicability toheavier region by MCSM
• Description of clusterstructureby MCSM
• Nshell truncation

NCSM

truncation by single-particle energy

T. Abe, P. Maris, J. Vary et al., AS2-A018

Extrapolation to infinite model space based on EFT
MCSM
Excitation energy (Nnshell) truncation

NCSM

4He 0+ g.s.

Preliminary

JISP16 NN int.
Nshell = 2 - 7

Energy(MeV)

Excitation energy (Nmaxhw) truncation

MCSM(IR- & UV cutoff fit): (w/ Nshell = 7 data)
Error estimates are needed.

Ref. Coon, Avetian, Kruse, van Klock, Maris and Vary
PRC 86 054002 (2012)

On going: 8Be(0+), 12C(0+), 16O(0+), …

T. Yoshida Poster AS2-A005

Density profile of the MCSM wave function
Density distribution of the ground state J π = 0 + of 8Be

k =1

 N MCSM ∑ f k φk  k =1laboratory-frame(spherical sym.)“Intrinsic”
framework

N MCSMΨ = ∑ fk P

J ,πφk = PJ ,πφk[AMD: Y.Enyo et al. PRC 2003 ][C.M. : M.Ito, N.Itagaki et al, PRL 2008]

Matter density of Be isotopes JISP16 interaction
A=8

A=9

A=10

A=11

A=12

Summary• HPCI project promotes nuclear physics. In HPCI Field
5 Subject 2, we developed the “advanced” MCSM torun on K computer– energy-variance extrapolation, code R&D– unified description of neutron-rich Ni isotopes, shellevolution and shape coexistence– test the feasibility of no-core MCSM and propose a new
method to draw the density profile• MCSM purvey analysis of “intrinsic” shapes and theirmixing, which enlighten cluster structure and shapecoexistence.
20

Collaborators
HPCI project, Field 5•••••••••••

Takaharu Otsuka (Tokyo)
Takashi Abe (Tokyo)
Shuichiro Ebata (Hokkaido)
Michio Honma (Aizu)
Yoritaka Iwata (CNS, Tokyo)
Takahiro Mizusaki (Senshu Univ.)
Tomoaki Togashi (CNS, Tokyo)
Naofumi Tsunoda (CNS, Tokyo)
Yusuke Tsunoda (Tokyo)
Yutaka Utsuno (JAEA)
Tooru Yoshida (CNS, Tokyo)• James Vary (Iowa)• Pieter Maris (Iowa)

Co-chair
Poster AS2-A018
Poster PS2-B022
Poster PS2-A061
Poster PS2-A035
Poster PS2-A037
Oral Jun/3
Poster PS2-A005

ICNT workshop, next week

Thank you !