The reweighting method is applied to improve the chiral property of domain-wall fermions. One way to achieve this is to enlarge $L_s$, the size of fifth dimension, which controls the size of the induced chiral symmetry breaking. While this is a type of reweighting method for shifting the action parameter, it seems non-trivial since this reweighting means change of the five dimensional lattice volume. In this report, we address issues in this direction of reweighting and evaluate its effectiveness.
Machine Learning-Based Estimation of Cumulants of Chiral Condensate via Multi-Ensemble Reweighting with Deborah.jl
Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）；Department of Information and Mathematical Sciences, Tokyo Woman’s Christian University（东京女子基督教大学信息与数学科学系）；RIKEN Center for Computational Science（理化学研究所计算科学中心）；Department of Physics, Kyoto University（京都大学物理学系）
We consider a massive fermion system having a curved domain-wall embedded in a square lattice. In a similar way to the conventional flat domain-wall fermion, chiral massless modes appear at the domain-wall but these modes feel "gravity" through the induced spin connections. In this work, we embed $S^1$ and $S^2$ domain-walls into a Euclidean space and show how the gravity is detected from the spectrum of the Dirac operator.
We report on our finite temperature 2+1 flavor lattice QCD simulation to study the thermodynamic properties of QCD near the (pseudo) critical point employing $N_T=12$ and $16$. The simulation points are chosen along the lines of constant physics. The quark mass for Möbius domain-wall fermion are tuned by taking into account the residual mass either by fine-tuning the input quark masses or by post-process using reweighting. In this talk, we focus on simulation details and present some preliminary results.
State-of-the-art lattice QCD studies of hot and dense strongly interacting matter currently rely on extrapolation from zero or imaginary chemical potentials. The ill-posedness of numerical analytic continuation puts severe limitations on the reliability of such methods. Here we use the more direct sign reweighting method to perform lattice QCD simulation of the QCD chiral transition at finite real baryon density on phenomenologically relevant lattices. This method does not require analytic continuation and avoids the overlap problem associated with generic reweighting schemes, so has only stat…
We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared to usual domain wall fermions. Moreover, we present first results for four-dimensional quantum chromodynamics, where we also observe significant reductions of chiral symmetry violations for staggered domain wall fermions.
We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, utilizing both Wilson and staggered kernels. In the process, we generalize the staggered kernels to arbitrary even dimensions and introduce both truncated and optimal staggered domain wall fermions. Some numerical investigations are carried out in the (1+1)-dimensional setting of the Schwinger model, where we explore spectral properties of t…
We investigate the effects of the violation of the Ginsparg-Wilson (GW) relation in the Möbius domain-wall fermion formulation on the lattice with finite fifth dimension. Using a decomposion in terms of the eigenmodes of its four-dimensional effective Dirac operator, we isolate the GW-violating terms for various physical quantities including the residual mass and the meson susceptibilities relevant for the effective restoration of the axial U(1) symmetry at finite temperature. Numerical result shows that the GW-violating effect is more significant, or even overwhelming, for the quantities that…
We investigate the axial $U(1)$ symmetry restoration at finite temperature in two flavor QCD. We employ the Möbius domain-wall formalism that is designed to achieve good chiral symmetry. We show the measurements of a difference of meson susceptibilities, sensitive to the $U(1)_A$ symmetry breaking. The signal is dominated by zero and near-zero modes. By reweighting the measure to that of overlap fermions we find a suppression of the $U(1)_A$ breaking effects above the chiral transition temperature.
We study the axial U(1) symmetry at finite temperature in two-flavor lattice QCD. Employing the Mobius domain-wall fermions, we generate gauge configurations slightly above the critical temperature Tc with different lattice sizes L = 2-4 fm. Our action allows frequent topology tunneling while keeping good chiral symmetry close enough to that of overlap fermions. This allows us to recover full chiral symmetry by an overlap/domain-wall reweighting. Above the phase transition, a strong suppression of the low-lying modes is observed in both of overlap and domain-wall Dirac spectra. We, however, fi…
Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The fram…
Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions
在QCD真空的稀释瞬子气体模型中，我们预期手征性和狄拉克本征向量的最大值之间存在很强的空间相关性。继Horvath之后，{ \it et al.}我们在猝灭近似下用格点规范理论研究这个问题。我们通过使用较弱的耦合，$β=6.0$，较大的晶格，$16^4$，和一个改进的费米子配方，畴壁费米子扩展这些作者的工作。与之前的工作相比，我们发现低狄拉克本征向量的手征性密度$|ψ^\dagger(x)γ^5ψ(x)|$和正常密度$ψ^\dagger(x)ψ(x)$的大小之间存在显著的相关性。
We investigate the chiral phase transition in the soft-wall model of AdS/QCD at zero chemical potential for two-flavor and three-flavor cases, respectively. We show that there is no spontaneous chiral symmetry breaking in the original soft-wall model. After detailed analysis, we find that in order to realize chiral symmetry breaking and restoration, both profiles for the scalar potential and the dilaton field are essential. The scalar potential determines the possible solution structure of the chiral condensate, except the mass term, it takes another quartic term for the two-flavor case, and f…
