arXiv subjects

Katsumasa Nakayama

Publications and source records attributed to Katsumasa Nakayama.

36 records · Page 2Linked to original sources

arXiv2021

Kondo effect with Wilson fermions

We investigate the Kondo effect with Wilson fermions. This is based on a mean-field approach for the chiral Gross-Neveu model including four-point interactions between a light Wilson fermion and a heavy fermion. For massless Wilson fermions, we demonstrate the appearance of the Kondo effect. We point out that there is a coexistence phase with both the light-fermion scalar condensate and Kondo condensate, and the critical chemical potentials of the scalar condensate are shifted by the Kondo effect. For negative-mass Wilson fermions, we find that the Kondo effect is favored near the parameter region realizing the Aoki phase. Our findings will be useful for understanding the roles of heavy impurities in Dirac semimetals, topological insulators, and lattice simulations.

hep-lat↗

arXiv2021

Lattice-fermionic Casimir effect and topological insulators

The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the Möbius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.

hep-lat↗

arXiv2020

Casimir effect for lattice fermions

We propose a definition of the Casimir energy for free lattice fermions. From this definition, we study the Casimir effects for the massless or massive naive fermion, Wilson fermion, and (Möbius) domain-wall fermion in $1+1$ dimensional spacetime with the spatial periodic or antiperiodic boundary condition. For the naive fermion, we find an oscillatory behavior of the Casimir energy, which is caused by the difference between odd and even lattice sizes. For the Wilson fermion, in the small lattice size of $N \geq 3$, the Casimir energy agrees very well with that of the continuum theory, which suggests that we can control the discretization artifacts for the Casimir effect measured in lattice simulations. We also investigate the dependence on the parameters tunable in Möbius domain-wall fermions. Our findings will be observed both in condensed matter systems and in lattice simulations with a small size.

hep-lat↗

arXiv2020

Atiyah-Patodi-Singer index on a lattice

We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the $η$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set of the free domain-wall fermion, we perturbatively show in the continuum limit that the curvature term in the APS theorem appears as the contribution from the massive bulk extended modes, while the boundary $η$ invariant comes entirely from the massless edge-localized modes.

hep-lat↗

arXiv2020

Charmonium contribution to $B \rightarrow K\ell^+\ell^-: testing the factorization approximation on the lattice

We report the current status of a study of charmonium contribution to $B \rightarrow K\ell^+\ell^-$ on the lattice. Our lattice calculation tests the factorization approximation for this contribution. In order to control the problem of the artificial divergence, we focus on the low $q^2$ region with a small b-quark mass. We also take into account the renormalization constants of relevant four-quark operators calculated through the temporal moments. Results suggest a violation of the factorization approximation.

hep-lat↗

arXiv2020

Renormalization of bilinear and four-fermion operators through temporal moments

We propose a renormalization scheme that can be simply implemented on the lattice. It consists of the temporal moments of two-point and three-point functions calculated with finite valence quark mass. The scheme is confirmed to yield a consistent result with another renormalization scheme in the continuum limit for the bilinear operators. We apply a similar renormalization scheme for the non-perturbative renormalization of four-fermion operators appearing in the weak effective Hamiltonian.

hep-lat↗

arXiv2020

A lattice formulation of the Atiyah-Patodi-Singer index

Atiyah-Singer index theorem on a lattice without boundary is well understood owing to the seminal work by Hasenfratz et al. But its extension to the system with boundary (the so-called Atiyah- Patodi-Singer index theorem), which plays a crucial role in T-anomaly cancellation between bulk- and edge-modes in 3+1 dimensional topological matters, is known only in the continuum theory and no lattice realization has been made so far. In this work, we try to non-perturbatively define an alternative index from the lattice domain-wall fermion in 3+1 dimensions. We will show that this new index in the continuum limit, converges to the Atiyah-Patodi-Singer index defined on a manifold with boundary, which coincides with the surface of the domain-wall.

hep-lat↗

arXiv2019

Renormalization group on a triad network

We propose a new renormalization scheme of tensor networks made only of third order tensors. The isometry used for coarse-graining the network can be prepared at an $O(D^6)$ computational cost in any $d$ dimension ($d \ge 2$), where $D$ is the truncated bond dimension of tensors. Although it is reduced to $O(D^5)$ if a randomized singular value decomposition is employed, the total cost is $O(D^{d+3})$ because the contraction part for creating a renormalized tensor with isometries has $D^{d+3}$ multiplications. We test our method in three dimensional Ising model and find that the numerical results are obtained for large $D$s with reasonable errors.

hep-lat↗

arXiv2019

$D$ mesons as a probe of Casimir effect for chiral symmetry breaking

We propose $D$ mesons as probes to investigate finite-volume effects for chiral symmetry breaking at zero and finite temperature. By using the $2+1$-flavor linear-sigma model with constituent light quarks, we analyze the Casimir effects for the $σ$ mean fields: The chiral symmetry is rapidly restored by the antiperiodic boundary for light quarks, and the chiral symmetry breaking is catalyzed by the periodic boundary. We also show the phase diagram of the $σ$ mean fields on the volume and temperature plane. For $D$ mesons, we employ an effective model based on the chiral-partner structure, where the volume dependence of $D$ mesons is induced by the $σ$ mean fields. We find that $D_s$ mesons are less sensitive to finite volume than $D$ mesons, which is caused by the insensitivity of $σ_s$ mean fields. An anomalous mass shift of $D$ mesons at high temperature with the periodic boundary will be useful in examinations with lattice QCD simulations. The dependence on the number of compactified spatial dimensions is also studied.

hep-ph↗

arXiv2019

Casimir effect for nucleon parity doublets

Finite-volume effects for the nucleon chiral partners are studied within the framework of the parity-doublet model. Our model includes the vacuum energy shift for nucleons, which is the Casimir effect. We find that for the antiperiodic boundary the finite-volume effect leads to chiral symmetry restoration, and the masses of the nucleon parity doublets degenerate. For the periodic boundary, the chiral symmetry breaking is enhanced, and the masses of the nucleons also increase. We also discuss the finite-temperature effect and the dependence on the number of compactified spatial dimensions.

hep-ph↗

arXiv2019

Test of factorization for the long-distance effects from charmonium on $B\to K\ell^+\ell^-$

We report on a calculation of the charmonium contribution to the decay $B \rightarrow K\ell^+\ell^-$ using lattice simulations with 2+1 flavors of Mobius domain wall fermions. We focus on the region of $q^2$ below the $J/ψ$ resonance and test the factorization approximation to estimate the amplitude. We show a possible discrepancy between the lattice calculation and the factorization method for the non-factorizable contribution.

hep-lat↗

arXiv2018

Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics

We study supersymmetry breaking from a lattice model of N=2 supersymmetric quantum mechanics using the direct computational method proposed in arXiv:1803.07960. The vanishing Witten index is realized as a numerical result in high precision. The expectation value of Hamiltonian is evaluated for the double-well potential. Compared with the previous Monte-Carlo results, the obtained vacuum energy coincides with the known values within small errors for strong couplings. The instanton effect is also reproduced for weak couplings. The used computational method helps us to evaluate the effect of finite lattice spacings more precisely and to study the mechanism of non-perturbative supersymmetry breaking from lattice computations.

hep-lat↗

arXiv2018

Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD

The eigenvalue spectrum $ρ(λ)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract them at the leading order and then take the continuum limit with lattice data at three lattice spacings. Lattice results for the exponent $\partial\lnρ/\partial\lnλ$ are matched to continuum perturbation theory, which is known up to $O(α_s^4)$, to extract the strong coupling constant $α_s$.

hep-lat↗

arXiv2018

Direct computational approach to lattice supersymmetric quantum mechanics

We propose a numerical method of estimating various physical quantities in lattice (supersymmetric) quantum mechanics. The method consists only of deterministic processes such as computing a product of transfer matrix, and has no statistical uncertainties. We use the numerical quadrature to define the transfer matrix as a finite dimensional matrix, and find that it effectively works by rescaling variable for sufficiently small lattice spacings. For a lattice supersymmetric quantum mechanics, the correlators can be estimated without statistical errors, and the effective masses coincide with the exact solution within very small errors less than 0.001%. The SUSY Ward identity is also precisely studied in compared with the Monte-Carlo method. Our method is not limited to a lattice SUSY quantum mechanics, but is also applicable to any other lattice models of quantum mechanics.

hep-lat↗

arXiv2017

Dirac spectral density and mass anomalous dimension in 2+1 flavor QCD

We compute the Dirac spectral density of QCD in a wide range of eigenvalues by using a stochastic method. We use 2+1 flavor lattice ensembles generated with Mobius domain-wall fermion at three lattice spacings ($a=0.083, 0.055, 0.044$ fm) to estimate the continuum limit. The discretization effect can be minimized by a generalization of the valence domain-wall fermion. The spectral density at relatively high eigenvalues can be matched with perturbation theory. We compare the lattice results with the perturbative expansion available to $O(α_s^4)$.

hep-lat↗

arXiv2017

Determination of charm quark mass from temporal moments of charmonium correlator with Mobius domain-wall fermion

We extract the charm quark mass and the strong coupling constant from the charmonium current correlators calculated with $n_f = 2 + 1$ Mobius domain wall fermions. We match our lattice calculation for the temporal moments of the correlator with perturbative result known up to four-loop order, and extract the charm quark mass with uncertainty less than 1%. Using the temporal moments, we also confirm the correlators in the vector channel to be consistent with the experimental data for the R-ratio. We used the ensembles generated by the JLQCD collaboration at lattice spacings $a$ = 0.080 fm, 0.055 fm and 0.044 fm.

hep-lat↗

arXiv2016

Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass

We calculate charmonium correlators on the lattice with 2+1-flavors of sea quarks and charm valence quark both described by the Möbius domain-wall fermion. Temporal moments of the correlators are calculated and matched to perturbative QCD formulae to extract the charm quark mass $m_c(μ)$ and strong coupling constant $α_s(μ)$. Lattice data at three lattice spacings, 0.044, 0.055, and 0.080~fm, are extrapolated to the continuum limit. The correlators in the vector channel are confirmed to be consistent with the experimental data for $e^+e^-\to c\bar{c}$, while the pseudo-scalar channel is used to extract $m_c(μ)$ and $α_s(μ)$. We obtain $m_\mathrm{c}(3 \mathrm{\ GeV})$ = 1.003(10)~GeV and $α_s^{\bar{\mathrm{MS}}(4)}(3\mathrm{\ GeV})$ = 0.253(13). Dominant source of the error is the truncation of perturbative expansion at $α_s^3$.

hep-lat↗

arXiv2015

Charmonium current-current correlators with Mobius domain-wall fermion

We calculate the charmonium correlators on the lattice with $n_f = 2+ 1$ Moebius domain wall fermion, and extract the charm quark mass and the strong coupling constant. Time moments are defined by current-current correlators, which have been calculated in the continuum theory by perturbation theory. We extract the charm quark mass by matching the lattice results with the corresponding perturbative QCD calculations, using the recently generated ensembles by the JLQCD collaboration at lattice spacings $a = 0.083, 0.055$, and $0.044$ fm.

hep-lat↗