Field Theory Research Team

Home , Numerical sign problem

Chapter 6

6.1 Members

Yoshinobu Kuramashi (Team Leader)

Yoshifumi Nakamura (Research Scientist)

Hiroya Suno (Research Scientist, Joint Position with the Nishina Center for Accelerator-based Research)

Eigo Shintani (Research Scientist)

Yuya Shimizu (Postdoctoral Researcher)

Ken-Ichi Ishikawa (Visiting Scientist, Hiroshima University)

Shoichi Sasaki (Visiting Scientist, Tohoku University)

Takeshi Yamazaki (Visiting Scientist, University of Tsukuba)

Shinji Takeda (Visiting Scientist, Kanazawa University)

6.2 Research Activities

Our research field is physics of elementary particles and nuclei, which tries to answer questions in history of mankind: what is the smallest component of matter and what is the most fundamental interactions? This research subject is related to the early universe and the nucleosynthesis through Big Bang cosmology. Another important aspect is quantum properties, which play an essential role in the world of elementary particles and nuclei as well as in the material physics at the atomic or molecular level. We investigate nonperturbative properties of elementary particles and nuclei through numerical simulations with the use of lattice QCD (Quantum ChromoDynamics). The research is performed in collaboration with applied mathematicians, who are experts in developing and improving algorithms, and computer scientists responsible for research and development of software and hardware systems. Lattice QCD is one of the most advanced case in quantum sciences: interactions between quarks, which are elementary particles known to date, are described by QCD formulated with the quantum field theory. We currently focus on two research subjects: (1) QCD at finite temperature and finite density. We try to understand the early universe and the inside of neutron star by investigating the phase structure and the equation of state. (2) First principle calculation of nucleon form factors. Proton and neutron, which are called nucleon, consist of three quarks. We investigate their internal structure and low energy properties by the measurement of various form factors. Successful numerical simulations heavily depend on an increase of computer performance by improving algorithms and computational techniques. However, we now face a tough problem that the trend of computer architecture becomes large-scale hierarchical parallel structures consisting of tens of thousands of nodes which individually have increasing number of cores in CPU and arithmetic accelerators with even higher degree of parallelism: we need to develop a new type of algorithms and computational techniques, which should be different from the conventional ones, to achieve better computer performance. For optimized use of K computer

63 0.17

0.16

0.15

0.14 E

T 0.13 0 √ t 0.12 Nf = 4 0.11 Nf = 3 2 0.1 c0+c1/Nt c +c /N2+c /N3 0.09 0 1 t 2 t

0.08 0 0.01 0.02 0.03 0.04 0.05 0.06 2 1/Nt

4 E /T 3 PS,E m N = 4 2 f Nf = 3 2 c0+c1/Nt 1 2 3 c0+c1/Nt+c2/Nt

0 0 0.01 0.02 0.03 0.04 0.05 0.06 64 2 CHAPTER 6. FIELD THEORY RESEARCH TEAM 1/Nt

0.9 0.17

0.8 0.16

0.7 0.15

0.6 0.14 E PS,E 0.5 T 0.13 0 m t 0 √ t

√ 0.4 0.12 Nf = 4 Nf = 4 0.3 0.11 Nf = 3 Nf = 3 2 2 0.2 c0+c1/Nt 0.1 c0+c1/Nt 2 3 c +c /N +c /N c +c /N2+c /N3 0.1 0 1 t 2 t 0.09 0 1 t 2 t

0 0.08 0 0.01 0.02 0.03 0.04 0.05 0.06 0 0.01 0.02 0.03 0.04 0.05 0.06 2 2 1/Nt 1/Nt √ √ √ Figure 15: CutoFigureff dependence 6.1: Continuum of √t T (top) extrapolationm /T of(middle) the critical and √ pointt m t0(bottom).mPS,E (left) and t0TE (right) with t0 the Wilson flow scale. Red0 E and bluePS symbols,E E denote 4 and 30 flavorPS,E cases, respectively. Results for N = 3 [2] are also shown. f 5

our research team aims at (1)13 developing a Monte Carlo algorithm 4 to simulate physical system with negative E

weight eﬀectively and (2) improving iterative methods to solve/T large system of linear equations. These technical 3

development and improvement are carried out in the researchPS,E of physics of elementary particles and nuclei based m on lattice QCD. N = 4 2 f Nf = 3 2 c0+c1/Nt 6.2.1 QCD at ﬁnite temperature and ﬁnite 1 density 2 3 c0+c1/Nt+c2/Nt

Establishing the QCD phase diagram spanned by the temperature 0 T and the quark chemical potential µ in 0 0.01 0.02 0.03 0.04 0.05 0.06 a quantitative way is an important task of lattice QCD. We have been working on2 tracing the critical end line in the parameter space of temperature, chemical potential and quark masses in1/N 4,t 3 and 2+1 flavor QCD using the O(a)-improved Wilson quark action and the Iwasaki gauge action. We have determined the critical end point at zero chemical potential µ = 0 in 3 flavor case. 0.9 Our strategy is to identify at which temperature the Kurtosis of physical observable at the transition point on 0.8 several different spatial volumes intersects. This

method is based on the property of opposite spatial volume 0.7 dependence of the Kurtosis at the transition point between the ﬁrst order phase transition side and the crossover one. We have carried out a systematic study of 0.6 the critical end point changing the temporal lattice size from Nt = 4 to 10 in 3 ﬂavor case, which corresponds PS,E 0.5 m

to change the lattice spacing. In Fig. 6.1 (left and right panels)0 we show the continuum extrapolation of the

√ t 0.4 critical pseudoscalar meson mass mPS,E and the critical temperature TE normalized by √t0, where √t0 denotes Nf = 4 the Wilson flow scale. We also make the same study in 4 0.3 flavor case for comparison. We observe that the Nf = 3 2 2 critical temperature seems to follow the O(a ) scaling property 0.2 both in 3 mad 4 flavor cases.c0+c1/N Ont the other c +c /N2+c /N3 hand, √t0mPS,E shows significantly large scaling violation and 0.1 its continuum extrapolation0 gives1 t different2 t values for 3 and 4 flavor cases: rather close to zero for the former and sufficiently deviated from zero for the latter. 0 The origin of the difference between 3 and 4 flavor cases and ,especially, 0 0.01 whether 0.02 0.03mPS,E 0.04in 3 flavor 0.05 case 0.06 may 2 vanish in the continuum limit are intriguing theoretical issues. Currently we are performing1/Nt a simulation at finer lattice spacing to investigate the possibility that mPS,E may vanish in the continuum limit. Figure 15: Cutoff dependence of √t0TE (top) mPS,E/TE (middle) and √t0mPS,E (bottom). 6.2.2 Nucleon form factorsResults for Nf = 3 [2] are also shown. Nucleon form factors are good probes to investigate the internal structure of the nucleon which is a bound state of quarks. Study of their properties requires nonperturbative method and much13 effort has been devoted to calculate them with lattice QCD since 1980’s. Unfortunately, the current situation is that we are still struggling for reproducing the well-established experimental results, e.g., the electric charge radius and the axial vector coupling. This means that we have not yet achieved proper treatment of a single hadron in lattice QCD calculation. The left panel of Fig. 6.2 shows a summary plot of the electric charge radius calculated with lattice QCD as of 2014. We focus on two major systematic uncertainties in the current lattice QCD simulations: one is heavier quark masses than the physical values and the other is finite spatial volume effects. In order to get rid of them we have carried out calculation of the nucleon form factors on a (10.8 fm)4 lattice at the physical point in 2+1 flavor QCD. Thanks to the large spatial volume we can get access to small momentum transfer region up to q2 =0.013 GeV2. The right panel of Fig. 6.2 plots our results for the electric charge radius, whose 6.2.Hadron RESEARCH Structure ACTIVITIES Martha Constantinou 65

1.0

0.6 0.9 Experiment (ep scatt.) 1 Experiment (µH atom) 0.8 Isovector, t /a={14,16} 0.5 sep 0.7 0.95

) 0.4 )

2 2 0.6 fm

(fm (fm 0.5 0.3 1/2 > u-d u-d > > E 2

2 2 0.40.9 1 2

RBC/UKQCD ’09 (DWF, Nf =2+1) 0.1 RBC/UKQCD ’09 (DWF, Nf =2+1) 0.2 RBC/UKQCD ’13 (DWF, Nf =2+1) RBC/UKQCD ’13 (DWF, Nf =2+1) QCDSF/UKQCD ’11 (Clover, Nf =2) 0.85 ETMC ’10 (TMF, Nf =2) QCDSF/UKQCD ’11 (Clover, Nf =2) ETMC ’10 (TMF, Nf =2) QCDSF ’11 (Clover, Nf =2) 0.1 ETMC ’13 (TMF, Nf =2+1+1) QCDSF ’11 (Clover, Nf =2)

ETMC ’13 (TMF, Nf =2+1+1) ETMC ’14 (TMF&clover, Nf =2) PoS(LATTICE2014)001 0.0 CSL/MAINZ ’12 (Clover, Nf =2) CSL/MAINZ ’12 (Clover, Nf =2) ETMC ’14 (TMF&clover, Nf =2) LHPC ’09 (DWF, Nf=2+1) PNDME ’13 (HISQ, Nf=2+1=1) 0.0 PNDME ’13 (HISQ, Nf=2+1=1) LHPC ’10 (DWF/asqtad, Nf=2+1) PDG ’12 LHPC ’10 (DWF/asqtad, Nf=2+1) PDG ’12 µp LHPC ’14 (Clover, Nf=2+1) 0.8 LHPC ’14 (Clover, Nf=2+1) 0 0.1 0.2 0.3 0.4 0.5 0 Linear0.1 0.2Dipole 0.3 0.4 Quadrature0.5 z-exp, kmax=3 m (GeV) 2 2 m (GeV)2 2 2 2 2 2 π q cut=0.013 GeV π q cut=0.102 GeV q cut=0.102 GeV q cut=0.102 GeV

Figure 10: Dirac (left) and Pauli (right) radii as a function of mπ . The lattice data correspond to: Figure 6.2: Summary plot of lattice QCD results for electric charge radius presented in the international N =2+1 DWF (RBC/UKQCD [12, 39]), N =2 TMF (ETMC [40]), N =2+1 DWF (LHPC [41]), N =2+1 conferencef of “Lattice 2014” (left) andf our result on a (10.8f fm)4 lattice at thef physical point in 2+1 ﬂavor DWF on asqtad sea (LHPC [15]), Nf =2 Clover (QCDSF/UKQCD [17], QCDSF [42], CLS/MAINZ [43]), QCD (right). Experimental results for e-p scattering and muonic hydrogen spectroscopy are represented by “ ” Nf =2+1+1 TMF (ETMC [24]), Nf =2+1+1 HISQ (PNDME [25]), Nf =2 + 1 Clover (LHPC [33]), Nf =2 and “ ” symbols in the left panel and gray and black horizontal bands in the right panel. ∗ TMF× with Clover (ETMC [34]). The experimental points have been taken from Refs. [2, 3].

In the left panel of Fig. 11 we plot r1 for a range of pion mass as the sink-source separation fourincreases. data represent The study four is carried types of out analyses by LHPC to [33] extract and ETMC the electric [34] and charge it include radius the result from of the the form factor. Comparing thesummation left and right method. panels There in is Fig.a clear6.2 upwardour resultstendency show as the a sink-source remarkable time improvement. separation increases. We are now trying further reductionAlthough of the the results magnitude from the of summation the error. method agree with the value extracted from the plateau method for the largest sink-source time separation, the errors on the results at lowest values of the pion masses are still large and currently do not allow to reach a deÞnite conclusion.

5 y-summation, qmax = 4, 300 confs 2 y-summation GM (kˆ = 0) sequential method, 1200 confs 6.2.3 Tensor network scheme in path-integral4 formalism

3 ) 2 ˆ k ( M

The Monte Carlo simulation of lattice gauge theoryG is quite powerful to study nonperturbative phenomena of 2 particle physics. However, when the action has an imaginary component like the θ term, it suffers from the numerical sign problem, which is failure of importance1 sampling techniques. The effect of the θ term on the non-Abelian gauge theory, especially quantum chromodynamics (QCD), is important, because it is related to a famous unsolved problem, “ strong CP problem ”. The0 difficulty is also shared with the finite density lattice 0 0.2 0.4 0.6 QCD. So development of effective techniques to solve or by-pass(a thekˆ)2 sign problem leads to a lot of progress in the study of the QCD phase diagram at finite temperature and density. The tensor network scheme is a Figure 11: Left: Isovector ⟨r2⟩ for various ensembles and different source-sink separations [33, 34]. Right: promising theoretical and1 computational framework to overcome these difficulties. So far we have developed Isovector GM for TMF extracted from a position space method [44]. the Grassmann version of the tensor renormalization group (GTRG) algorithm in the tensor network scheme, which allows us to deal with the Grassmann variables directly. The GTRG2 algorithm was successfully applied In order to extract the anomalous magnetic moment one needs to Þt the Q -dependence of GM. to the analysis of the phase structure of one-flavor lattice Schwinger model (2D QED) with and without the Typically one employs a dipole form to extrapolate at Q2 = 0 introducing a model-dependence. θ term showing that the algorithm is free from the sign problem and the computational cost is comparable to Exploratory studies based on a position space method can yield G (0) directly without having to the bosonic case thanks to the direct manipulation of the GrassmannM variables. This was the first successful perform a Þt. This method involves taking the derivative of the relevant correlator with respect application of the tensor network scheme to a Euclidean lattice gauge theory including the relativistic fermions in path-integralto the momentum, formalism. allowing access Toward to zero the momentum final target data. of 4D Thus, QCD there we is no are need currently to assume working a on three research subjectsfunctional in the form tensor for the network momentum scheme: dependence. (i) non-Abelian Such a study isgauge performed theories,for GM (ii)[44] higher and the dimensional (3D or 4D) models,results and are (iii)shown development in the right panel of computational of Fig. 11. techniques for physical observables. In 2017 we have succeeded in applying the tensor network scheme to three dimensional finite temperature Z gauge theory. The left panel 11 2 of Fig. 6.3 shows the Nσ dependence of the specific heat as a function of 1/β at Nτ = 3, where Nσ and Nτ denote the spatial and temporal extent of the lattice, respectively, and 1/β is proportional to temperature. We observe the clear peak structure at all the values of Nσ and the peak height Cmax(Nσ) grows as Nσ increases. We can determine the critical exponent ν from the finite size scaling behavior of the peak position βc(Nσ). In the right panel of Fig. 6.3 we plot the Nσ dependence of βc(Nσ) at Nτ = 3. The solid curve represents 1/ν the fit result obtained with the fit function of β (N )=β ( )+BNσ for N [512, 4096], which gives c σ c ∞ σ ∈ βc( )=0.711150(4) and ν =0.99(4). The value of the critical exponent is consistent with ν = 1 in the universality∞ class of the two dimensional Ising model as expected by the Svetitsky-Yaffe conjecture. Next step may be an application of the tensor network scheme to non-commutative gauge theories. 5

TABLE I. Fit results for the critical point βc( ) and the critical exponent ⌫ at N⌧ =2, 3, 5. The value of ⌫ at N⌧ = 2 in 1 Ref. [19] is evaluated using the pair of data at Nσ = 16 and 32.

This work Ref. [19] 2 N⌧ Nσ βc( ) ⌫ B χ /d.o.f. Nσ βc( ) ⌫ 1 1 2 [512, 4096] 0.656097(1) 1.00(1) 0.116(6) 0.086 4, 8, 16, 32 0.65608(5) 1.012(21) 3 [512, 4096] 0.711150(4) 0.99(4) 0.10(3) 0.047 24 0.71102(8) 5 [512, 4096] 0.740730(3) 0.96(5) 0.08(3) 0.012 40 0.74057(3) 66 4CHAPTER 6. FIELD THEORY RESEARCH TEAM that the value of (ln Z)/V monotonically converges12.0 as 12.0 0.712 D2 increases. Since we ﬁnd similar behaviors at other β C(Nσ) Cmax(Nσ) β (Nσ) values, we take the results with D2 = 128 as the central 0.711 c 10.0 10.0 values and their errors are estimated by the di↵erence Nσ=32 N =64 from those with D2 = 144. σ Nσ=128

Nσ=256 0.710

0.7810 8.0 Nσ=512

8.0 Nσ=1024

Nσ=2048

0.7808 Nσ=4096 0.709 6.0 0.7806 6.0 0.708

0.7804 (lnZ)/V 4.0

4.0 0.707 10 100 1000 10000 0.00 0.01 0.02 0.03 0.04 0.7802 1.40 1.41 1.42 Nσ 1/β 1/Nσ

0.7800 FIG. 9.Figure PeakFIG. height 8. 6.3: Specific ofN specificσ dependence heat heatC(NσC)max at of(N specificN⌧σ=) at 3 asN heat⌧ a= function 3 as as a a function of 1FIG./β 10.of 1 Peak/β (left) position and of scaling the specific property heat ofβc(βNcσ()N atσ)N (right).⌧ =3 function ofwithN .N Theσ [32 horizontal, 4096]. axis is logarithmic. Solid line as a function of 1/N . Solid curve represents the fit result. σ 2 σ 0.7798 is to guide your eyes. 0 40 80 120 160 D 6.3 Schedule and Future Plan 2 with P another constant. This procedure su↵ers from IV. SUMMARY AND OUTLOOK

-3 less uncertainties associated with the numerical deriva- 10 6.3.1tive compared QCD to at the finite direct fittemperature of the specific heat and itself. finite density δ We have applied the tensor network scheme to a study F We expect that the peak height Cmax(Nσ) scales with We are performing a systematic study of the criticalof end 3D finitepoint temperature in 4 flavor QCD Z2 gauge in comparison theory. Its e withciency 3 flavor is Nσ as -4 case. We also investigates whether or not mPS,E in 3demonstrated flavor QCD vanishes by a numerical in the continuum study of the limit. critical prop- 10 ↵/⌫ Cmax(Nσ) Nσ , (16)erties of the 3D Z2 gauge theory. The tensor network / scheme enables us to make a large scale of finite size scal- 6.3.2with the Nucleon critical exponents form factors↵ and ⌫. We plot the peak -5 ing analysis with the wide range of N thanks to the ln V 10 height Cmax(Nσ) at N⌧ = 3 as a function of Nσ in dependence of the computational cost,4 which allows us a WeFig. are 9. trying We observe to reduce a clear the statistical logarithmic errorNσ ofdependence the nucleon form factors on a (10.8 fm) lattice at the physical precise and reliable estimation of the critical point and point.for C Aftermax(N thatσ). We we haveplan foundto investigate similar features the cutoff ateffect. other -6 the critical exponent at the thermodynamic limit. This 10 N⌧ . These observation indicates ↵ 0. We can determine another critical exponent ⌫ from' the finite sizeis the first successful application of the tensor network scheme to one of the simplest 3D lattice gauge theories. 6.3.3scaling behaviorTensor of network the peak position schemeβc(N inσ), path-integral formalism 0 40 80 120 160 Next step may be the extension of this approach to the D 1/⌫ 2 As stated above,β therec(Nσ) areβc three( ) importantNσ . subjects(17) in research and development of tensor network scheme in − 1 / gauge theories with continuous groups. path-integralFigure 10 shows formalism:Nσ dependence (i) non-Abelian of βc(N gaugeσ) at N theories,⌧ =3 (ii) higher dimensional (3D or 4D) models, and (iii) FIG. 7. D2 dependence of (ln Z)/V (top) and δF (bottom) at β =0.71115 on the 40962 3 lattice. developmentas a representative of computational case. The techniques solid curve forrepresents physical the observables. Future research keeps to follow these three ⇥ directions.fit result obtained with the fit function of βc(Nσ)= ACKNOWLEDGMENTS 1/⌫ β ( )+BNσ . In Table I we list the fit range at each c 1 N⌧ which is chosen to avoid possible finite size e↵ects dueNumerical calculation for the present work was carried B. Results 6.4to the Publications smaller Nσ. The fit results for βc( ), B, ⌫ andout with the COMA (PACS-IX) computer under the In- χ2/d.o.f. are summarized in Table I. The values1 of β ( ) c terdisciplinary1 Computational Science Program of Cen- In Fig. 8 we plot the specific heat of Eq. (15) as a 6.4.1at N⌧ =2 Articles, 3, 5 estimated in Ref. [19] are systematicallyter for Computational Sciences, University of Tsukuba. function of 1/β. We observe the clear peak structure at smaller than ours beyond the error bars. This may beThis at- work is supported by the Ministry of Education, [1]tributed Takeshi to Yamazaki the narrow and range Yoshinobu of N employed Kuramashi, in Ref. ”Relation [19]. between scattering amplitude and Bethe-Salpeter all the values of Nσ and the peak height Cmax(Nσ) grows σ Culture, Sports, Science and Technology (MEXT) as For the values of ⌫ we observe that both of our results as Nσ increases. In order to determine the peak position wave function in quantum field theory”, Phys.“Exploratory Rev. D 96 (2017) Challenge ref. 114511. on Post-K computer (Frontiers and those in Ref. [19] are consistent with ⌫ = 1, which is βc(Nσ) and the peak height Cmax(Nσ) at each Nσ we of Basic Science: Challenging the Limits)” and also [2]the Xiao-Yong expected critical Jin, Yoshinobu exponent Kuramashi,in 2D Ising model. Yoshifumi This Nakamura, Shinji Takeda and Akira Ukawa, ”Critical employ the quadratic approximation of the specific heat in part by Grants-in-Aid for Scientific Research from around β (N ): alsopoint satisfies phase the transition Josephson for law finite of d⌫ temperature=2 ↵ with 3-flavord =2 QCD with non-perturbatively O(a)-improved Wilson c σ − MEXT (No. 15H03651). 2 in thefermions two-dimensional at Nt = 10”, case. Phys. These Rev. are D supporting 96 (2017) evi- ref. 034523. 1 1 dences for Svetitsky-Ya↵e conjecture that the finite tem- C(Nσ) Cmax(Nσ)+R ⇠ β − β (N ) perature transitions in (d + 1)-dimensional SU(N) and ✓ c σ ◆ [3] Yuya Shmizu and Yoshinobu Kuramashi, ”Berezinskii-Kosterlitz-Thouless transition in lattice Schwinger with R a constant. Instead of fitting the specific heat ZN modellatticewith gauge one-flavor theories belong of Wilson to the fermion”, same universal- Phys. Rev. D 97 (2018) ref. 034502. itself we fit the internal energy E with the following form ity class of those in the corresponding d-dimensional ZN spin models [20]. In our case the universality class for around βc(Nσ): [4] Daisuke Kadoh, Yoshinobu Kuramashi, Yoshifumi Nakamura, Ryo Sakai, Shinji Takeda and Yusuke Yoshimura, the finite temperature Z2 lattice gauge theory should co- 3 ”Tensor network formulation for two-dimensional lattice N = 1 Wess-Zumino model”, JHEP 1803 (2018) @ ln Z Cmax(Nσ) R 1 1 incide with that for the 2D Ising model whose critical E = = P + + ref. 141. − V @β β 3 β − β (N ) exponents are ↵ = 0 and ⌫ = 1. ✓ c σ ◆ [5] Yusuke Yoshimura, Yoshinobu Kuramashi, Yoshifumi Nakamura, Ryo Sakai and Shinji Takeda, ”Calculation of fermionic Green functions with Grassmann higher-order tensor renormalization group”, Phys. Rev. D 97 (2018) ref. 034502. 6.4. PUBLICATIONS 67

[6] Taisuke Boku, Ken-Ichi Ishikawa, Yoshinobu Kuramashi and Lawrence Meadows, ”Mixed precision solver scalable to 16000 MPI processes for lattice quantum chromodynamics simulations on the Oakforest-PACS system”, arXiv:1709.08785 [physics.comp-ph].

[7] Yasumichi Aoki, Taku Izubuchi, Eigo Shintani and Amarjit Soni, ”Improved lattice computation of proton decay matrix elements”, Phys. Rev. D 96 (2017) ref. 014506.

[8] V. G. Bornyakov et al., ”Flavour breaking eﬀects in the pseudoscalar meson decay constants”, Phys. Lett. B767 (2017) p. 366.

[9] T. Haar et al., ”Applying polynomial ﬁltering to mass preconditioned Hybrid Monte Carlo”, Comput. Phys. Commun. 215 (2017) p. 113.

[10] A. J. Chambers et al., ”Nucleon structure functions from lattice operatorproduct expansion”, Phys. Rev. Lett. 118 (2017) ref. 242001.

[11] A. J. Chambers et al., ”Electromagnetic form factors at large momenta from lattice QCD”, Phys. Rev. D 96 (2017) ref. 114509 .

[12] R. Sakai, S. Takeda and Y. Yoshimura, ”Higher order tensor renormalization group for relativistic fermion systems”, Prog. Theor. Exp. Phys. (2017) 063B07.

6.4.2 Conference Papers [13] Natsuki Tsukamoto, Ken-Ichi Ishikawa, Yoshinobu Kuramashi, Shoichi Sasaki, and Takeshi Yamazaki for PACS Collaboration, ”Nucleon structure from 2+1 ﬂavor lattice QCD near the physical point”, EPJ Web Conf., 175 (2018) ref. 06007.

[14] Taku Izubuchi, Yoshinobu Kuramashi, Christoph Lehner and Eigo Shintani, ”Lattice study of ﬁnite volume eﬀect in HVP for muon g-2”, EPJ Web Conf. 175 (2018) ref. 06020.

[15] Renwick Hudspith, Randy Lewis, Kim Matlman and Eigo Shintani, ”αs from the hadronic vacuum polar- isation”, EPJ Web Conf. 175 (2018) ref. 10006.

[16] Xiao-Yong Jin, Yoshinobu Kuramashi, Yoshifumi Nakamura, Shinji Takeda and Akira Ukawa, ”Continuum extrapolation of critical point for ﬁnite temperature QCD with Nf = 3”, arXiv:1710.08057 [hep-lat]. [17] R. Sakai, D. Kadoh, Y. Kuramashi, Y. Nakamura, S. Takeda, and Y. Yoshimura, ”Application of tensor network method to two-dimensional lattice N = 1 Wess-Zumino model”, EPJ Web Conf. 175 (2018) ref. 11019.

[18] Takeshi Yamazaki, Ken-Ichi Ishikawa, Yoshinobu Kuramashi for PACS Collaboration, ”Comparison of diﬀerent source calculations in two-nucleon channel at large quark mass”, EPJ Web Conf., 175 (2018) ref. 05019.

[19] S. Takizawa et al., ”A scalable multi-granular data model for data parallel workﬂows”, HPC ASIA 2018, Proceedings of the International Conference on High Performance Computing in Asia-Paciﬁc Region (2018) p. 251-260.

6.4.3 Invited talks [20] Yoshinobu Kuramashi, ”Lattice QCD approach to proton puzzle”, 2018 Annual (73th) Metteing of the Physical Society of Japan, Tokyo University of Science, Noda, Japan, March 22-25, 2018.

[21] Eigo Shintani, ”Lattice QCD study of nucleon EDM”, RCNP Workshop on Fundamental Physics Using Neutrons and Atoms, RCNP, Osaka, Japan, July 4-5, 2017.

[22] Eigo Shintani, ”Lattice study of ﬁnite size eﬀect in the leading order of hadronic contribution to muon g 2”, First Workshop of the Muon g-2 Theory Initiative, Q Center, Chicago, USA, June 3-6, 2017. − [23] Eigo Shintani, ”Lattice calculation of matrix element on proton decay”, International Workshop on Baryon & Lepton Number Violation 2017, Case Western University, Cleveland, Ohio, USA, May 15-18, 2017. 68 CHAPTER 6. FIELD THEORY RESEARCH TEAM

[24] Takeshi Yamazaki, ”Binding energy of light nucleus from lattice QCD”, QCD Downunder 2017, Novotel Cairns Oasis Resort, Australia, July 10-14, 2017.

[25] Takeshi Yamazaki, ”Study of nucleon structure from lattice QCD”, The Forth Project Report Meeting of the HPCI System Including K computer, KOKUYO Hall, Tokyo, Japan, November 2, 2017.

[26] Takeshi Yamazaki, ”Relation between scattering amplitude and Bethe-Salpeter wave function in quantum ﬁeld theory”, Multi-Hadron Systems from Lattice QCD, University of Washington, Seattle, USA, February 5-9, 2018.

[27] Takeshi Yamazaki, ”A new calculation method of scattering phase shift with Bethe-Salpeter wave function in lattice QCD”, 2018 Annual (73th) Metteing of the Physical Society of Japan, Tokyo University of Science, Noda, Japan, March 22-25, 2018.

[28] Sinji Takeda, ”Tensor networks in particle physics”, Tensor Networks 2017, AICS, Kobe, Japan, August 3, 2017.

6.4.4 Posters and Presentations [29] Yoshinobu Kuramashi for PACS Collaboration, ”A large scale simulation of 2+1 flavor lattice QCD”, The 35th International Symposium on lattice field theory (Lattice 2017), Palacio de Congresos de Granada, Spain, June 19-24, 2017. [30] Eigo Shintani, ”Lattice study of finite volume effect in HVP for muon g 2”, The 35th International Symposium on lattice field theory (Lattice 2017), Palacio de Congresos de− Granada, Spain, June 19-24, 2017. [31] Takeshi Yamazaki, Ken-ichi Ishikawa, Yoshinobu Kuramashi for PACS Collaboration, ”Comparison of different source calculations in two-nucleon channel at large quark mass”, The 35th International Symposium on lattice field theory (Lattice 2017), Palacio de Congresos de Granada, Spain, June 19-24, 2017. [32] S. Takeda, ”Cost reduction of tensor renormalization group algorithm by projective truncation technique”, 2018 Annual (73th) Metteing of the Physical Society of Japan, Tokyo University of Science, Noda, Japan, March 22-25, 2018.

[33] S. Takeda, ”Continuum extrapolation of critical point for ﬁnite temperature QCD with Nf = 3”, The 35th International Symposium on lattice ﬁeld theory (Lattice 2017), Palacio de Congresos de Granada, Spain, June 19-24, 2017.