情報基盤研究開発センターハンズオン：HΦ講習会­ITOを用いたハンズオン­

今後の将来展望: HΦ山地 洋平
東京大学大学院工学系物理工学専攻
Youhei Yamaji
Department of Applied Physics, The University of Tokyo

1. Kωの応用: Finite-T linear response
2. 今後の開発目標 Perspective1	

New function will be implemented:
Finite-T linear response
Combination of TPQ and Kω
Y. Yamaji, T. Suzuki, & M. Kawamura, arXiv:1802.02854.
Dr. Mitsuaki Kawamura
The Institute for Solid State Physics,
The University of Tokyo

Prof. Takafumi Suzuki
Graduate School of Engineering,
University of Hyogo

Finite-Temperature Spectra

ComplexityMemoryIs it necessary? Answer is NoFinite-Temperature Spectra by
Real-Time Evolution of Wave Functions
T. Iitaka and T. Ebisuzaki, Phys. Rev. Lett. 90, 047203 (2003).
R. Steinigeweg, J. Gemmer, and W. Brenig, Phys. Rev. Lett. 112, 120601 (2014).
T. Monnai and A. Sugita, J. Phys. Soc. Jpn. 83, 094001 (2014).
C. Karrasch, D. M. Kennes, and J. E. Moore, Phys. Rev. B 90, 155104 (2014).
F. Jin, R. Steinigeweg, F. Heidrich-Meisner, K. Michielsen, and H. De Raedt,Phys. Rev. B 92, 205103 (2015).

Finite-Temperature Spectra byMicorocanonical EnsembleM. W. Long, P. Prelovsek, S. El Shawish, J. Karadamoglou, and X. Zotos,Phys. Rev. B 68, 235106 (2003).
X. Zotos, Phys. Rev. Lett. 92, 067202 (2004).	

An Intuitive Description of TPQ States andGreenʼs Function at Finite Temperature
A normalized TPQ state

Spectral projector
Greenʼs function rewritten by using a TPQ stateAn Alternative to Spectral Projection
T. Kato, Progress of Theoretical Physics 4, 514 (1949).

Discretized by Riemann sum

T. Sakurai and H. Sugiura,J. Comput. Appl. Math. 159, 119 (2003).
T. Ikegami, T. Sakurai, and U. Nagashima,
J. Comput. Appl. Math. 233, 1927 (2010).

Shifted Krylov Subspace Method

Liner equations←Solvable by Shifted Krylov subspace method
A. Frommer (1995, 2003)
T. Sogabe, T. Hoshi, S. L. Zhang, and T. Fujiwara, A numerical method for
calculating the Greenʼs function arising from electronic structure theory,
In Frontiers of Computational Science. pp.189-195, 2007.

7	Shifted CG: Algorithm
Seed switch
S. Yamamoto, et al.,J. Phys. Soc. Jpn. 77, 114713 (2008).

-Seed equations-Shifted equations

Library Kω
by Dr. Kawamura (ISSP)

Finite-Temperature Greenʼs Function byTypical Pure States
321MM-2

M-1

Greenʼs funtion

Probability distributioncf.) N. Shimizu, Y. Utsuno, Y. Futamura, T. Sakurai,T. Mizusaki, and T. Otsuka, Physics Letters B 753, 13 (2016).	

12 site AF Kitaev Standard deviation of averaged values
0.4
0.3
0.2
0.1
00.6
0.4
0.2
000.5

1

1.5

2

2.5

3

18 site AF Kitaev Standard deviation
0.4
0.3
0.2
0.1
00.6
0.4
0.2
000.5

1

1.5

22.5

3

Finite-T S(Q,ω) of a Frustrated Magnets: Γ model
A. M. Samarakoon, G. Wachtel, Y. Yamaji,
D. A. Tennant, C. D. Batista, and Y. B. Kim
Phys. Rev. B 98, 045121 (2018)
443

322

11
1.4
1.2

0

100.8
40.6

40.4
876
54
32
100.2
30322

110012	

Future Plan
New functions will be implemented
1. Finite-T linear response:
Combination of TPQ and Kω
2. N spin/body interaction and Greenʼs function
3. Tool for optimizing model parameters toﬁt experimental measurements-Example: Find an eﬀective spin Hamiltonian that
reproduces an observed magnetizaion process
4. Symmetry-Reduction of dimension of Hilbert space-Analysis of wave fucntions

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