In this presentation, I will discuss applications of machine learning techniques in Lattice QCD. Lattice QCD has physical symmetries and quantum-statistical features compared to standard machine learning in image processing. I mainly explain the gauge covariant neural network, capable of these symmetries and features, and its applications in the context of exact simulations. I will also...
We demonstrate that a state-of-the art multi-grid preconditioner can be learned efficiently by gauge-equivariant neural networks. We show that the models require minimal re-training on different gauge configurations of the same gauge ensemble and to a large extent remain efficient under modest modifications of ensemble parameters. We also demonstrate that important paradigms such as...
We present results for the axial charge and root-mean-square (RMS) radii of the nucleon obtained from 2+1 flavor lattice QCD at the physical point with a large spatial extent of about 10 fm. Our calculations are performed with the PACS10 gauge configurations generated by the PACS Collaboration with the six stout-smeared $O(a)$ improved Wilson-clover quark action and Iwasaki gauge action at...
In this talk, I will discuss the method of the heavy-quark operator product expansion (HOPE) in lattice-QCD computations for parton physics. The extraction of the Mellin moments of the pion light-cone distribution amplitude is employed as an illustration of this approach. I will present numerical results of the second and the fourth moments (the latter being exploratory).
We report on JLQCD's studies on B meson semileptonic decays.
We perform a non-perturbative lattice calculation of the decay rates for inclusive semi-leptonic decays of charmed mesons. In view of the long-standing tension in the determination of the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ from exclusive and inclusive processes, recently, the use of lattice QCD has been extended towards the description of inclusive decays. Since the determination of...
The type IIB matrix model, also known as the IKKT model, is a promising candidate for the non-perturbative formulation of the string theory. Its Lorentzian version, in which the indices are contracted using the Lorentzian metric, has a sign problem stemming from e^{iS} in the partition function (where S is the action). It has turned out that the Lorentzian version is equivalent to the...
We consider fermion systems on a square lattice with a mass term having a curved domain-wall. It is shown that massless and chiral edge states appear on the wall. In the cases of $S^1$ and $S^2$ domain-walls embedded into flat cubic lattices, we find that these edge modes feel gravity through the induced Spin or Spin$^c$ connections. The gravitational effect is encoded in the Dirac eigenvalue...
We present the results of nucleon structure studies measured in 2+1 flavor QCD with physical light quarks in large spatial extents of about 10 and 5 fm. Our calculations are performed on 2+1 flavor gauge configurations generated by the PACS Collaboration with the stout-smeared O(a) improved Wilson fermions and Iwasaki gauge action at beta=1.82 corresponding to the lattice spacing of 0.085 fm....
It is a fundamental question: what is the origin of the glueball masses? In the pure Yang-Mills theory, there is no mass scale in the classical level, while the breaking of scale invariance is induced by quantum effects. This is regarded as the trace anomaly, which is associated with the non-vanishing trace of the energy-momentum tensor (EMT) operator. In this context, the origin of the...
Investigation of QCD thermodynamics for $N_f$=2+1 along the lines of constant physics with Möbius domain wall fermions is underway. At our coarsest lattice $N_t$=12, reweighting to overlap fermions is not successful. To use domain wall fermions with the residual mass larger than average physical $ud$ quarks, careful treatments of the residual chiral symmetry breaking are necessary. One of the...
We have been developing a general purpose lattice QCD code set Bridge++ [1] and its new version contains an optimization for A64FX systems like supercomputer Fugaku. In this presentation, we show the benchmark results of Bridge++ on Fugaku.
The bottleneck of LQCD application is solving linear equations, Dx = b, where fermion matrix D is a large sparse matrix and its operation is a stencil...
One of the motivation for studying QCD thermodynamics is to understand the chiral symmetry restoration at finite temperature. Lattice QCD (LQCD) calculations with chiral fermions at finite temperature can be carried out on modern supercomputers nowadays. M\"{o}bius Domain Wall fermions in 5-d represent one realization of chiral fermions, with slight chiral symmetry breaking due to the finite...
Similarity between the Yang-Mills gradient flow and the stout smearing was first implied by M. Lüscher in 2010 and the rigorous proof of the equivalence was recently given by K. Sakai and S. Sasaki at the zero limit of the lattice spacing and the smearing parameter.
However, it is not obvious that they remain equivalent even with finite parameters within some numerical precision,...
We apply the tensor renormalization group method to the (1+1)-dimensional SU(2) principal chiral model at finite chemical potential with the use of the Gauss-Legendre quadrature to discretize the SU(2) Lie group. The internal energy at vanishing chemical potential $µ = 0$ shows good consistency with the prediction of the strong and weak coupling expansions. This indicates an effectiveness of...
In this work, we investigate the CP(1) model using the tensor renormalization group technic, which does not suffer from the sign problem. The phase structure of the CP(1) model with the theta term is an interesting topic since it could be related to the well-known Haldane's conjectures. We apply the recent tensor renormalization technic to the CP(1) model and show that the CP(1) model has no...
The type IIB matrix model, also known as the IKKT model, is a promising candidate for the non-perturbative formulation of the string theory. Its Lorentzian version, in which the indices are contracted using the Lorentzian metric, has a sign problem stemming from e^{iS} in the partition function (where S is the action). It has turned out that the Lorentzian version is equivalent to the...
We investigate the finite temperature QCD phase transition with three degenerate quark flavors using Mobius domain wall fermions. To explore the order of phase transition on the lower left corner of Columbia plot and if possible, to locate the critical endpoint
we performed simulations at temperatures around 181 and 121 MeV with lattice spacing $a=0.1361(20)$~fm corresponding to temporal...
Understanding the nature of correlated quantum many-body systems is the main purpose of modern condensed matter physics. Current booming quantum computing techniques offer a new way to treat these challenging systems: the quantum simulation approach. Using the quantum computer, which is a controllable quantum many-body system by itself, we can simulate other correlated quantum systems in which...
The renormalization group (RG) $\beta$ function describes the running of the renormalized coupling and connects the ultraviolet and infrared regimes of quantum field theories. Using different gradient flow schemes, we define renormalized couplings and determine the RG $\beta$ function using a more traditional step-scaling method as well as the concept of the continuous $\beta$ function which...
In the early days of QCD, the axial U(1) anomaly was considered to trigger the breaking of the SU(2)_L x SU(2)_R symmetry through topological excitations of gluon fields. However, it has been a challenge for lattice QCD to quantify the effect. In this work, we simulate QCD at high temperatures with chiral symmetric lattice Dirac operator. The exact chiral symmetry enables us to separate the...
I will give an overview of the development directions of Grid on current and future US exascale computers.
I will also give an overview of the USQCD SciDAC-5 algorithm project to develop multiscale algorithms to exploit these.
We investigate the finite temperature QCD phase transition with three degenerate quark flavors using Mobius domain wall fermions. To explore the order of phase transition on the lower left corner of Columbia plot and if possible, to locate the critical endpoint
we performed simulations at temperatures around 181 and 121 MeV with lattice spacing $a=0.1361(20)$~fm corresponding to temporal...
Simulation framework named “braket” for quantum computer with qubits and gates circuit is developed for massively-parallelized HPC systems using the state-vector method. On the “Fugaku” supercomputer, simulation for 40 qubits circuit is achieved using 1,024 or less nodes, and if its full nodes are available, we will reach 48 qubits with double precision and 51 qubits with byte precision....
Understanding the nature of correlated quantum many-body systems is the main purpose of modern condensed matter physics. Current booming quantum computing techniques offer a new way to treat these challenging systems: the quantum simulation approach. Using the quantum computer, which is a controllable quantum many-body system by itself, we can simulate other correlated quantum systems in which...
The numerical sign problem is one of the major obstacles to first-principles calculations in a variety of important systems. Typical examples include finite-density QCD, some condensed matter systems such as strongly correlated electron systems and frustrated spin systems, and real-time dynamics of quantum fields. Until very recently, individual methods were developed for each target system,...
Critical slowing down is one of the major difficulties in lattice QCD. Recently, it is becoming an urgent problem in the field as the precision goal is getting high and small lattice spacings have become demanding. As a promising approach towards conquering this problem, we here study the idea of the trivializing map, proposed by Luscher. In particular, we study the properties of the map at...
The tensor renormalization group (TRG) approach is a variant of the real-space renormalization group to evaluate the path integral defined on the thermodynamic lattice, without resorting to any probabilistic interpretation for the given Boltzmann weight. Moreover, since the TRG can directly deal with the Grassmann variables, this approach can be formulated in the same manner for the systems...
We obtain the equation of state (EoS) for two-color QCD at low temperature and high density from the lattice Monte Carlo simulation. We find that the velocity of sound exceeds the relativistic limit (cs2/c2=1/3) after the BEC-BCS crossover in the superfluid phase. Such an excess of the sound velocity is previously unknown from any lattice calculations for QCD-like theories. This finding might...
We are generating the 2+1 flavor PACS10 configuration, whose
physical volumes are more than (10 fm)$^4$ at the physical point,
using the Iwasaki gauge action and $N_f=2+1$ stout-smeared
nonperturbatively $O(a)$ improved Wilson quark action at
three lattice spacings. We present our results for several physical
quantities calculated from the PACS10 configurations, such as
the...
The stabilised Wilson fermion (SWF) framework combines numerical enhancements and a new discretisation scheme for Wilson-Clover fermions. In this presentation I discuss the components of the framework and give an overview of the status of the application of SWF in two cases: Traditional lattice QCD simulations, i.e. with spatial lengths less than 6 fm, and simulations with large spatial...
We first review theoretical aspects of the HAL QCD method, by comparing its pros and cons with the finite volume method. We then present the latest investigations in the HAL QCD method. In particular, we report on dibaryons and exotics at the almost physical pion mass.
We perform a non-perturbative lattice calculation of the decay rates for inclusive semi-leptonic decays of charmed mesons. In view of the long-standing tension in the determination of the CKM matrix elements $|V_{ub}|$ and $|V_{cb}|$ from exclusive and inclusive processes, recently, the use of lattice QCD has been extended towards the description of inclusive decays. Since the determination of...
