arXiv subjects

T. Fukui

Publications and source records attributed to T. Fukui.

At least 19 recordsLinked to original sources

arXiv2026

Gradient flow towards quantum states with ideal quantum geometry

We propose a gradient-flow method for quantum states in lattice models, generated by an action consisting of the quantum-metric and the square of the Berry curvature. These two terms drive the spectral projector toward Bogomolny saturation and uniform Berry curvature, respectively. We show that, due to a no-go theorem for finite-dimensional projectors, the two conditions cannot in general be satisfied simultaneously in lattice models. Hence the flow is expected to approach a nontrivial fixed point that balances the two geometric requirements. For the Wilson-Dirac model, we demonstrate that the flowed projector exhibits almost uniform Berry curvature while remaining close to the Bogomolny bound. We further construct a short-range truncated flattened Hamiltonian from the flowed projector and obtain a lattice model with nearly flat bands and nearly uniform Berry curvature. We also apply the method to the Hofstadter model and confirm the roles of the metric and Berry-curvature terms in a Chern band with higher Chern number.

quant-ph↗

arXiv2025

Gradient flow and Bogomolny bounds for quantum metric actions

We formulate gradient flow dynamics generated by two natural actions of the quantum metric for an isolated set of Bloch bands. Specializing to two spatial dimensions, we derive Bogomolny-type lower bounds that relate these actions to the Chern number and show that the bounds are saturated by (anti-)holomorphic projector configurations. Along the flows, the actions decrease monotonically while the Chern number is conserved, giving a constructive route to simplify models within a fixed topological phase toward canonical, low-complexity representatives.

cond-mat.mes-hall↗

arXiv2025

Realistic shell model for ordinary muon capture of sd-shell nuclei

We report about a study of the ordinary muon capture in nuclei belonging to the sd shell, an electroweak process that occurs with exchange momenta far larger than ordinary beta decays (approximately 100 MeV). Such a characteristic places this transition in an energy range that is consistent with the neutrinoless double-beta decay, and represents an interesting test for nuclear models to support their predictions of the nuclear matrix elements for such an unobserved process. For the first time, the calculations are carried out within the realistic shell model (RSM), namely employing effective shell-model Hamiltonians and decay operators derived from realistic nuclear forces, without resorting to any empirical adjustment of the coupling constants. This is a chapter of a research program that is aimed to assess the realistic shell model in reproducing the observables related to electroweak processes in nuclei, and then to evaluate the reliability of nuclear matrix elements for the neutrinoless double-beta decay that are calculated within this approach. We calculate the partial capture rates for many nuclear systems in the sd-shell region, as well as their spectroscopic properties, and compare the results with the available experimental counterparts. Such a comparison tests the relevance of a microscopic approach to the renormalization of transition operators to reproduce data and provide solid predictions of unknown observables.

nucl-th↗

arXiv2025

A formally exact real-space representation of the Berry phase on infinite lattices: Applications to dipole and quadrupole moments

Inspired by Kitaev's real-space representation of Chern numbers, we develop a real-space formulation of the Berry phase for infinite lattices. While the well-known Resta formula for the Berry phase is defined under periodic boundary conditions for finite lattices, our approach constructs the Berry phase directly on an infinite lattice without requiring momentum-space discretization. We apply this method to several disordered models to examine its validity. Furthermore, we attempt to generalize the real-space representation to the quadrupole moment, drawing an analogy to the generalization of the Resta formula for the quadrupole moment.

cond-mat.mes-hall↗

arXiv2025

Real-space representation of the second Chern number

We extend Kitaev's real-space formulation of the first Chern number to the second Chern number and establish a computational framework for its evaluation. To test its validity, we apply the derived formula to the disordered Wilson-Dirac model and analyze its ability to capture topological properties in the presence of disorder. Our results demonstrate that the real-space approach provides a viable method for characterizing higher-dimensional topological phases beyond momentum-space formulations.

cond-mat.mes-hall↗

arXiv2024

Cuspidal edges and generalized cuspidal edges in the Lorentz-Minkowski 3-space

It is well-known that every cuspidal edge in the Euclidean space E^3 cannot have a bounded mean curvature function. On the other hand, in the Lorentz-Minkowski space L^3, zero mean curvature surfaces admit cuspidal edges. One natural question is to ask when a cuspidal edge has bounded mean curvature in L^3. We show that such a phenomenon occurs only when the image of the singular set is a light-like curve in L^3. Moreover, we also investigate the behavior of principal curvatures in this case as well as other possible cases. In this paper, almost all calculations are given for generalized cuspidal edges as well as for cuspidal edges. We define the "order" at each generalized cuspidal edge singular point is introduced. As nice classes of zero-mean curvature surfaces in L^3,"maxfaces" and "minfaces" are known, and generalized cuspidal edge singular points on maxfaces and minfaces are of order four. One of the important results is that the generalized cuspidal edges of order four exhibit a quite similar behaviors as those on maxfaces and minfaces.

math.DG↗

arXiv2024

Flow of unitary matrices: Real-space winding numbers in one and three dimensions

The notion of the flow introduced by Kitaev is a manifestly topological formulation of the winding number on a real lattice. First, we show in this paper that the flow is quite useful for practical numerical computations for systems without translational invariance. Second, we extend it to three dimensions. Namely, we derive a formula of the flow on a three-dimensional lattice, which corresponds to the conventional winding number when systems have translational invariance.

nlin.CD↗

arXiv2023

The role of three-nucleon potentials within the shell model: past and present

We survey the impact of nuclear three-body forces on structure properties of nuclei within the shell model. It has long been acknowledged, since the seminal works of Zuker and coworkers, that three-body forces play a fundamental role in making the monopole component of shell-model Hamiltonians, derived from realistic nucleon-nucleon potentials, able to reproduce the observed evolution of the shell structure. In the vast majority of calculations, however, their effects have been taken into account by shell-model practitioners by introducing ad hoc modifications of the monopole matrix elements. During last twenty years, a new theoretical approach, framed within the chiral perturbation theory, has progressed in developing nuclear potentials, where two- and many-body components are naturally and consistently built in. This new class of nuclear forces allows to carry out nuclear structure studies that are improving our ability to understand nuclear phenomena in a microscopic approach. We provide in this work an update on the status of the nuclear shell model based on realistic Hamiltonians that are derived from two- and three-nucleon chiral potentials, focusing on the role of the three-body component to provide the observed shell evolution and closure properties, as well as the location of driplines. To this end, we present the results of shell-model calculations and their comparison with recent experimental measurements, which enlighten the relevance of the inclusion of three-nucleon forces to master our knowledge of the physics of atomic nuclei.

nucl-th↗

arXiv2023

Chern numbers associated with the periodic Toda lattice

The periodic Toda lattice is solved by exploiting the spectral properties of the Lax operator, in which the boundary states play an important role. We show that these boundary states have a topological origin similar to that of the edge states in topological insulators, and consequently, that the bulk wave functions of the Lax operator yield nontrivial Chern numbers. This implies that the periodic Toda lattice belongs to the same topological class as the Thouless pump. We demonstrate that the cnoidal wave of the Toda lattice exhibits a Chern number of $-1$ per period.

cond-mat.mes-hall↗

arXiv2023

Higher-order topological heat conduction on a lattice for detection of corner states

A heat conduction equation on a lattice composed of nodes and bonds is formulated assuming the Fourier law and the energy conservation law. Based on this equation, we propose a higher-order topological heat conduction model on the breathing kagome lattice. We show that the temperature measurement at a conner node can detect the corner state which causes rapid heat conduction toward the heat bath, and that several-nodes measurement can determine the precise energy of the corner states.

cond-mat.mes-hall↗

arXiv2022

Moir\'e Landau levels of a $C_4$-symmetric twisted bilayer system in the absence of a magnetic field

It is widely known that the twisted bilayer graphene (TBG) shows flat bands at magic angles, which can be well described by the effective continuum model derived by Bistritzer and MacDonald (BM). We propose in this paper a similar twisted bilayer system but defined on the square lattice with $\pi$-flux per plaquette, and study its spectrum using the BM Hamiltonian with a mass term which is originated from the staggered potential. The basic difference between the TBG and the present model is simply rotational symmetry, $C_3$ vs $C_4$, as well as a mass term. Nevertheless, the feature of the flat bands is quite different: Those of the TBG appear at magic angles only, while the present model shows many flat bands, which are reminiscent of Landau levels, quite stably at any angles even in the absence of a magnetic field other than $\pi$-flux which keeps time reversal (TR) symmetry. Moreover, flat bands emerge in the mass gap of the Dirac spectrum, and each state composing these flat bands is well-localized at the position forming the moir\'e lattice. It turns out that the moir\'e potential serves as a periodic magnetic field, which can give energies smaller that the gap around moir\'e lattice positions. We derive a local Hamiltonian valid around the moir\'e lattice sites and show that it indeed reproduces the energies of the flat bands within the mass gap. Since these mid-gap states are localized at the moir\'e lattice, they form degenerate levels, which may be referred to as moir\'e Landau levels, although the mechanism of degeneracies are different from the conventional Landau levels. Interestingly, doubled fermions of the BH Hamiltonian associated with two layers have opposite charges when they couple with the effective moir\'e magnetic filed, which concern TR symmetry.

cond-mat.mes-hall↗

arXiv2021

Shell-model study of titanium isotopic chain with chiral two- and three-body forces

The even-even Ti isotopic chain, from A = 42 to 70, has been studied within the nuclear shell-model framework by employing an effective Hamiltonian which is derived by way of many-body perturbation theory from a chiral potential with two- and three-body forces, and includes three-body contributions which account for Pauli principle violations in nuclei with more than two valence particles. We consider 40Ca as a closed core and a model space spanned by the neutron and proton 0f1p orbitals with the addition of the 0g9/2 orbital for neutrons. Calculated two-neutron separation energies and excitation energies of the yrast 2+ states are reported and compared with the experimental data, which are available up to 62Ti. The present study intends to investigate the effects of the adopted effective interactions on the evolution of the shell structure.

nucl-th↗

arXiv2021

Femtoscopic study of coupled-channel $N\Xi$ and $\Lambda\Lambda$ interactions

The momentum correlation functions of S = -2 baryon pairs (p Xi^- and Lambda Lambda) produced in high-energy pp and pA collisions are investigated on the basis of the coupled-channel formalism. The strong interaction is described by the coupled-channel HAL QCD potential obtained by the lattice QCD simulations near physical quark masses, while the hadronic source function is taken to be a static Gaussian form. The coupled-channel effect, the threshold difference, the realistic strong interaction, and the Coulomb interaction are fully taken into account for the first time in the femtoscopic analysis of baryon-baryon correlations. The characteristic features of the experimental data for the p Xi^- and Lambda Lambda pairs at LHC are reproduced quantitatively with a suitable choice of non-femtoscopic parameters and the source size. The agreement between theory and experiment indicates that the N Xi (Lambda Lambda) interaction is moderately (weakly) attractive without having a quasi-bound (bound) state.

hep-ph↗

arXiv2021

Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath

We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature) profile from a given initial distribution, by diagonalising the Hamiltonian, i.e., the Laplacian with alternating diffusion constants, and expanding the temperature profile by its eigenstates. We show that there are basically phases with or without edge states. The edge states affect the heat conduction around heat baths. In particular, rapid heat transfer to heat baths would be observed in a short time regime, which is estimated to be $t<10^{-2}$s for $a\sim 10^{-3}$m system and $t< 1$s for $a\sim 10^{-2}$m system composed of two kinds of familiar metals such as titanium, zirconium and aluminium, gold, etc. We also discuss the effective lattice model which simplifies the calculation of edge states up to high energy. It is suggested that these high energy edge states also contribute to very rapid heat conduction in a very short time regime.

cond-mat.mes-hall↗

arXiv2021

Diophantine equation for the Rice-Mele model: Topological aspect of filling numbers and associated spatial pump

We introduce a long-period generic spatial modulation into a typical model of the Thouless pump, namely, the Rice--Mele (RM) model, to examine the lattice analog of the fermion charge in quantum field theory. We derive a Diophantine equation relating the fermion charge and the pumped charge, which leads to the one-dimensional (1D) analog of the Streda formula in the quantum Hall effect (QHE). This formula implies that an adiabatic change of the periodicity of the spatial modulation yields a spatial charge pump such that the rightmost charge is pumped to the right by the Chern number compared with the leftmost charge. This causes a change in the length of the fermion chain by an integer, thus providing the opportunity for direct measurement of the Streda formula in 1D systems.

cond-mat.mes-hall↗

arXiv2020

Chiral three-nucleon force and continuum for dripline nuclei and beyond

Three-nucleon force and continuum play important roles in reproducing the properties of atomic nuclei around driplines. Therefore it is valuable to build up a theoretical framework where both effects can be taken into account to solve the nuclear Schr\"odinger equation. To this end, in this letter, we have expressed the chiral three-nucleon force within the continuum Berggren representation, so that bound, resonant and continuum states can be treated on an equal footing in the complex-momentum space. To reduce the model dimension and computational cost, the three-nucleon force is truncated at the normal-ordered two-body level and limited in the $sd$-shell model space, with the residual three-body term being neglected. We choose neutron-rich oxygen isotopes as the test ground because they have been well studied experimentally, with the neutron dripline determined. The calculations have been carried out within the Gamow shell model. The quality of our results in reproducing the properties of oxygen isotopes around the neutron dripline shows the relevance of the interplay between three-nucleon force and the coupling to continuum states. We also analyze the role played by the chiral three-nucleon force, by dissecting the contributions of the $2\pi$ exchange, $1\pi$ exchange and contact terms.

nucl-th↗

arXiv2020

A shell-model study of calcium isotopes towards their drip line

We report in this paper a study in terms of the nuclear shell model about the location of the calcium isotopes drip line. The starting point is considering the realistic two-body potential derived by Entem and Machleidt within chiral perturbation theory at next-to-next-to-next-to-leading order (N3LO), as well as a chiral three-body force at next-to-next-to-leading order (N2LO) whose structure and low-energy constants are consistent with the two-body potential. Then we construct the effective single-particle energies and residual interaction needed to diagonalize the shell-model Hamiltonian. The calculated two-neutron separation energies agree nicely with experiment until 56Ca, which is the heaviest isotope whose mass has been measured, and do not show any sign of two-neutron emission until 70Ca. We discuss the role of the choice of the model space in determining the neutron drip line, and also the dependence of the results on the parameters of the shell-model Hamiltonian.

nucl-th↗

arXiv2020

Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators

We develop a theory of edge states based on the Hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which serve as differential operators in continuum theories. It turns out that such Hamiltonian operators are not necessarily Hermitian on lattices with boundaries, which is due to the boundary terms associated with the summation by parts. The Hermiticity of Hamiltonian operators leads to natural boundary conditions, and for models with nearest-neighbor (NN) hoppings only, there are reference states that satisfy the Hermiticity and boundary conditions simultaneously. Based on such reference states, we develop a Bloch-type theory for edge states of NN models on a half-plane. This enables us to extract Hamiltonians describing edge-states at one end, which are separated from the bulk contributions. It follows that we can describe edge states at the left and right ends separately by distinct Hamiltonians for systems of cylindrical geometry. We show various examples of such edge state Hamiltonians (ESHs), including Hofstadter model, graphene model, and higher-order topological insulators (HOTIs).

cond-mat.mes-hall↗