arXiv subjects

Y. Kikukawa

Publications and source records attributed to Y. Kikukawa.

At least 19 recordsLinked to original sources

arXiv2015

Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density

We investigate Lefschetz thimble structure of the complexified path-integration in the one-dimensional lattice massive Thirring model with finite chemical potential. The lattice model is formulated with staggered fermions and a compact auxiliary vector boson (a link field), and the whole set of the critical points (the complex saddle points) are sorted out, where each critical point turns out to be in a one-to-one correspondence with a singular point of the effective action (or a zero point of the fermion determinant). For a subset of critical point solutions in the uniform-field subspace, we examine the upward and downward cycles and the Stokes phenomenon with varying the chemical potential, and we identify the intersection numbers to determine the thimbles contributing to the path-integration of the partition function. We show that the original integration path becomes equivalent to a single Lefschetz thimble at small and large chemical potentials, while in the crossover region multi thimbles must contribute to the path integration. Finally, reducing the model to a uniform field space, we study the relative importance of multiple thimble contributions and their behavior toward continuum and low-temperature limits quantitatively, and see how the rapid crossover behavior is recovered by adding the multi thimble contributions at low temperatures. Those findings will be useful for performing Monte-Carlo simulations on the Lefschetz thimbles.

hep-lat↗

arXiv2013

Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem

We consider a hybrid Monte Carlo algorithm which is applicable to lattice theories defined on Lefschetz thimbles. In the algorithm, any point (field configuration) on a thimble is parametrized uniquely by the flow-direction and the flow-time defined at a certain asymptotic region close to the critical point, and it is generated by solving the gradient flow equation downward. The associated complete set of tangent vectors is also generated in the same manner. Molecular dynamics is then formulated as a constrained dynamical system, where the equations of motion with Lagrange multipliers are solved by the second-order constraint-preserving symmetric integrator. The algorithm is tested in the lambda phi^4 model at finite density, by choosing the thimbles associated with the classical vacua for subcritical and supercritical values of chemical potential. For the lattice size L=4, we find that the residual sign factors average to not less than 0.99 and are safely included by reweighting and that the results of the number density are consistent with those obtained by the complex Langevin simulations.

hep-lat↗

arXiv2009

The strongly coupled fourth family and a first-order electroweak phase transition (I) quark sector

In models of dynamical electroweak symmetry breaking due to strongly coupled fourth-family quarks and leptons, their low-energy effective descriptions may involve multiple composite Higgs fields, leading to a possibility that the electroweak phase transition at finite temperature is first order due to the Coleman-Weinberg mechanism. We examine the behavior of the electroweak phase transition based on the effective renormalizable Yukawa theory which consists of the fourth-family quarks and two SU(2)-doublet Higgs fields corresponding to the bilinear operators of the fourth-family quarks with/without imposing the compositeness condition. The strength of the first-order phase transition is estimated by using the finite-temperature effective potential at one-loop with the ring-improvement. In the Yukawa theory without the compositeness condition, it is found that there is a parameter region where the first-order phase transition is strong enough for the electroweak baryogenesis with the experimentally acceptable Higgs boson and fourth-family quark masses. On the other hand, when the compositeness condition is imposed, the phase transition turns out to be weakly first order, or possibly second order, although the result is rather sensitive to the details of the compositeness condition. Combining with the result of the Yukawa theory without the compositeness condition, it is argued that with the fourth-family quark masses in the range of 330-480 GeV, corresponding to the compositeness scale in the range of 1.0-2.3 TeV, the four-fermion interaction among the fourth-family quarks does not lead to the strongly first-order electroweak phase transition.

hep-ph↗

arXiv2007

First-order restoration of SU(Nf) x SU(Nf) chiral symmetry with large Nf and Electroweak phase transition

It has been argued by Pisarski and Wilczek that finite temperature restoration of the chiral symmetry SU(Nf) x SU(Nf) is first-order for Nf >=3. This type of chiral symmetry with a large Nf may appear in the Higgs sector if one considers models such as walking technicolor theories. We examine the first-order restoration of the chiral symmetry from the point of view of the electroweak phase transition. The strength of the transition is estimated in SU(2) x U(1) gauged linear sigma model by means of the finite temperature effective potential at one-loop with the ring improvement. Even if the mass of the neutral scalar boson corresponding to the Higgs boson is larger than 114 GeV, the first-order transition can be strong enough for the electroweak baryogenesis, as long as the extra massive scalar bosons (required for the linear realization) are kept heavier than the neutral scalar boson. Explicit symmetry breaking terms reduce the strength of the first-order transition, but the transition can remain strongly first-order even when the masses of pseudo Nambu-Goldstone bosons become as large as the current lower bound of direct search experiments.

hep-ph↗

arXiv2007

Neutron electric dipole moment with external electric field method in lattice QCD

We discuss a possibility that the Neutron Electric Dipole Moment (NEDM) can be calculated in lattice QCD simulations in the presence of the CP violating $θ$ term. In this paper we measure the energy difference between spin-up and spin-down states of the neutron in the presence of an uniform and static external electric field. We first test this method in quenched QCD with the RG improved gauge action on a $16^3\times 32$ lattice at $a^{-1}\simeq$ 2 GeV, employing two different lattice fermion formulations, the domain-wall fermion and the clover fermion for quarks, at relatively heavy quark mass $(m_{PS}/m_V \simeq 0.85)$. We obtain non-zero values of NEDM from calculations with both fermion formulations. We next consider some systematic uncertainties of our method for NEDM, using $24^3\times 32$ lattice at the same lattice spacing only with the clover fermion. We finally investigate the quark mass dependence of NEDM and observe a non-vanishing behavior of NEDM toward the chiral limit. We interpret this behavior as a manifestation of the pathology in the quenched approximation.

hep-lat↗

arXiv2005

Neutron electric dipole moment on the lattice

We carry out a feasibility study toward a lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the $θ$ term using two different approaches. In the first method, we calculate the CP-odd electromagnetic form factor $F_3$, which becomes the NEDM in the zero momentum transfer limit. At the first order in $θ$, we derive a formula connecting the lattice three-point function to the CP-odd electromagnetic form factor. In the second method we directly extract the NEDM from the energy difference between spin-up and spin-down neutron states in the presence of a constant electric field, without expanding a small but non-zero $θ$. We test both approaches numerically, employing the domain-wall quark action with the RG improved gauge action in quenched QCD at $a^{-1}\simeq 2$ GeV on a $16^3\times 32\times 16$ lattice, and further applying the second method to the clover quark action at a similar lattice spacing and nucleon mass. We obtain good signals from both approaches. In particular the second method works well with both fermion formulations.

hep-lat↗

arXiv2005

Neutron electric dipole moment from lattice QCD

We carry out a feasibility study for the lattice QCD calculation of the neutron electric dipole moment (NEDM) in the presence of the $θ$ term. We develop the strategy to obtain the nucleon EDM from the CP-odd electromagnetic form factor $F_3$ at small $θ$, in which NEDM is given by $\lim_{q^2\to 0}θF_3(q^2)/(2m_N)$ where $q$ is the momentum transfer and $m_N$ is the nucleon mass. We first derive a formula which relates $F_3$, a matrix element of the electromagnetic current between nucleon states, with vacuum expectation values of nucleons and/or the current. In the expansion of $θ$, the parity-odd part of the nucleon-current-nucleon three-point function contains contributions not only from the parity-odd form factors but also from the parity-even form factors multiplied by the parity-odd part of the nucleon two-point function, and therefore the latter contribution must be subtracted to extract $F_3$. We then perform an explicit lattice calculation employing the domain-wall quark action with the RG improved gauge action in quenched QCD at $a^{-1}\simeq 2$ GeV on a $16^3\times 32\times 16$ lattice. At the quark mass $m_f a =0.03$, corresponding to $m_π/m_ρ\simeq 0.63$, we accumulate 730 configurations, which allow us to extract the parity-odd part in both two- and three-point functions. Employing two different Dirac $γ$ matrix projections, we show that a consistent value for $F_3$ cannot be obtained without the subtraction described above. We obtain $F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) =$ $-$0.024(5) $e\cdot$fm for the neutron and $F_3(q^2\simeq 0.58 \textrm{GeV}^2)/(2m_N) =$ 0.021(6) $e\cdot$fm for the proton.

hep-lat↗

arXiv2005

Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice

In the gauge-invariant construction of abelian chiral gauge theories on the lattice based on the Ginsparg-Wilson relation, the gauge anomaly is topological and its cohomologically trivial part plays the role of the local counter term. We give a prescription to solve the local cohomology problem within a finite lattice by reformulating the Poincaré lemma so that it holds true on the finite lattice up to exponentially small corrections. We then argue that the path-integral measure of Weyl fermions can be constructed directly from the quantities defined on the finite lattice.

hep-lat↗

arXiv2000

One-loop analyses of lattice QCD with the overlap Dirac operator

We discuss the weak coupling expansion of lattice QCD with the overlap Dirac operator. The Feynman rules for lattice QCD with the overlap Dirac operator are derived and the quark self-energy and vacuum polarization are studied at the one-loop level. We confirm that their divergent parts agree with those in the continuum theory.

hep-lat↗

arXiv1999

Low energy effective action of domain-wall fermion and the Ginsparg-Wilson relation

We derive the effective action of the light fermion field of the domain-wall fermion, which is referred as $q(x)$ by Furman and Shamir. The inverse of the effective Dirac operator turns out to be identical to the inverse of the truncated overlap Dirac operator, except a local contact term which would give the chiral symmetry breaking in the Ginsparg-Wilson relation. This result allows us to relate the light fermion field and the fermion field described by the truncated overlap Dirac operator and to understand the chiral property of the light fermion through the exact chiral symmetry based on the Ginsparg-Wilson relation.

hep-lat↗

arXiv1998

Symmetry and Symmetry Restoration of Lattice Chiral Fermion in the Overlap Formalism

Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by Luescher is evaluated and is shown to have the correct form of the topological charge density for perturbative backgrounds. Next we discuss the exponential suppression of the self-energy correction of the lightest mode in the domain-wall fermion/truncated overlap. Finally, we consider a supersymmetric extension of the overlap formula in the case of the chiral multiplet and examine the symmetry structure of the action.

hep-lat↗

arXiv1998

Weak coupling expansion of massless QCD with a Ginsparg-Wilson fermion and axial U(1) anomaly

We discuss the weak coupling expansion of massless QCD with the Dirac operator which is derived by Neuberger based on the overlap formalism and satisfies the Ginsparg-Wilson relation. The axial U(1) anomaly associated to the chiral transformation proposed by Luscher is calculated as an application and is shown to have the correct form of the topological charge density for perturbative backgrounds. The coefficient of the anomaly is evaluated as a winding number related to a certain five-dimensional fermion propagator.

hep-lat↗

arXiv1997

Exponential suppression of radiatively induced mass in the truncated overlap

A certain truncation of the overlap (domain wall fermions) contains $k$ flavors of Wilson-Dirac fermions. We show that for sufficiently weak lattice gauge fields the effective mass of the lightest Dirac particle is exponentially suppressed in $k$. This suppression is seen to disappear when lattice topology is non-trivial. We check explicitly that the suppression holds to one loop in perturbation theory. We also provide a new expression for the free fermion propagator with an arbitrary additional mass term.

hep-lat↗

arXiv1997

Overlap in odd dimensions

In odd dimensions the lattice overlap formalism is simpler than in even dimensions. Masslessness of fermions can still be preserved without fine tuning and gauge invariance without gauge averaging can be maintained, although, sometimes, only at the expense of parity invariance. When parity invariance is enforced invariance under small gauge transformations can be maintained and continuum global gauge anomalies are reproduced.

hep-lat↗

arXiv1997

Finite size corrections in two dimensional gauge theories and a quantitative chiral test of the overlap

An argument is presented for a certain universality of finite size corrections in two dimensional gauge theories. In the abelian case a direct calculation is carried out for a particular chiral model. The analytical result confirms the above universality and that the 't Hooft vertex previously measured using the overlap smoothly approaches the correct continuum limit within statistical errors.

hep-th↗

arXiv1996

Gribov Copy and Complex Phase of Chiral Determinant

We calculate the complex phase of chiral determinant by the vacuum overlap formula with configurations of two-dimensional U(1) gauge field fixed in Landau and Laplacian gauge. The complex phase fluctuates over the Gribov copies, which appear in the process of Landau gauge fixing and contain vortex-like singularities. In the Laplacian gauge, the fluctuation can be reduced and the phase can be determined uniquely. If it is used as a preconditioning for Landau gauge fixing, the most smooth configuration is obtained among the copies generated.

hep-lat↗

arXiv1996

Wess-Zumino term by Vacuum Overlap Formula

We examine the vacuum overlap formula for the two-dimensional SU(2) Wess-Zumino term in lattice regularization. Perturbatively it reproduces the Wess-Zumino term correctly in the continuum limit and yields the IR fixed point in the beta function of the chiral model. Nonperturbatively it shows a sharp Gaussian distribution for the SU(2) chiral field configurations in the scaling region, where smooth configurations dominate even in the symmetric phase due to asymptotic freedom. Crossover is sharp from the strong coupling region where the Wess-Zumino term fluctuates hard and the species doublers' contribution is suspected to affect it.

hep-lat↗

arXiv1995

Perturbation Theory at Finite Extent of Fifth Dimension for Vacuum Overlap Formula of Chiral Determinant -- Continuum Limit Case --

Taking into account of the boundary condition in the fifth direction which is derived from the lattice Wilson fermion, we develop a theory of five-dimensional fermion with kink-like and homogeneous masses in finite extent of the fifth dimension. The boundary state wave functions are constructed explicitly and the would-be vacuum overlap is expanded by using the propagator of the theory. The subtraction is performed unambiguously at the finite extent with the help of the dimensional regularization. Then the limit of the infinite extent is evaluated. The consistent anomaly in four dimensional theory is finitely obtained. Each contribution to the vacuum polarization is vector-like. It is the lack of the massless mode in the fermion with negative homogeneous mass that leads to the correct chiral normalization. Gauge noninvariant piece remains due to the breaking of the boundary condition by the dimensional regularization.

hep-lat↗