arXiv subjects

Masaaki Nakamura

Publications and source records attributed to Masaaki Nakamura.

At least 19 recordsLinked to original sources

arXiv2026

Nontrivial three-sublattice magnetization in the easy-axis spin-1/2 XXZ antiferromagnet on the triangular lattice

We investigate the ground-state magnetic structure of the spin-$1/2$ XXZ antiferromagnet on the triangular lattice in the easy-axis regime using the density-matrix renormalization group. By applying spiral boundary conditions, we exactly map finite $L\times L$ clusters onto one-dimensional chains while avoiding the spatial anisotropy inherent in cylindrical geometries. From symmetry-broken local magnetization profiles, we extract the three-sublattice moments and track their evolution with anisotropy. At the isotropic point, we obtain a positive sublattice moment of $0.217(3)$, consistent with previous numerical estimates. In the easy-axis regime ($Δ=J_z/J_\perp>1$), the ordered moments remain close to a Y-like zero-magnetization three-sublattice state, whose $z$-component pattern is of the form $(2m,-m,-m)$, over a broad range of $Δ$. Extrapolation in $1/Δ$ shows that the positive sublattice moment stays well below the classical saturation value $1/2$, approaching $0.419(7)$ as $Δ\to\infty$, while the magnitude of the negative sublattice moment approaches $0.209(4)$. We further compare the energies of the Y state and the up-down-down state and find that the Y state is favored at zero field. Independent thermodynamic-limit energy calculations, performed without assuming any particular ordered pattern, yield an energy consistent with the Y-state solution. These results show that the easy-axis ground state does not simply cross over to a trivially saturated collinear Ising state, but instead remains a nontrivial three-sublattice ordered state selected from the macroscopically degenerate Ising manifold by quantum fluctuations.

cond-mat.str-el↗

arXiv2026

Vectorial Imaging of the Photodissociation of 2-Bromobutane Oriented via Hexapolar State Selection

Molecular orientation techniques are becoming available in the study of elementary chemical processes, in order to highlight those structural and dynamical properties that would be concealed by random rotational motions. Recently successful orientation was achieved for asymmetric-top and chiral molecules of much larger complexity than hitherto. In this work, we report and discuss the correlation between the vectors photofragment recoil velocity v, transition dipole moment μ, and permanent dipole moment d in a dissociation experiment on hexapole oriented 2-bromobutane, photoinitiated by a linearly polarized laser. The sliced ion images of the Br* (2P1/2) and Br (2P3/2) photofragment were acquired at 234.0 and 254.1 nm, respectively, by (2+1) resonance-enhanced multiphoton ionization technique. A detailed analysis of the sliced ion images obtained at a tilting angle 45o of the laser polarization provides the information on correlation of the three vectors, which are confined by two polar angles α, \c{hi} and one azimuthal angle ϕμd in the recoil frame. The sliced ion images of Br fragments eliminated individually from the enantiomers at 254.1 nm yield the asymmetric factor close to zero; for this reason the photofragment angular distributions do not show significant differences. The elimination of Br* fragment at 234.0 nm is mainly correlated with a parallel transition, giving rise to a large anisotropy parameter of 1.85, and thus can be considered as a single state excitation. The resulting recoil frame angles are optimized to 163.8° and 164.1° for α and \c{hi}, respectively, whereas ϕμd approaches close to 0o for the best fit. Since in the present case, the three vectors have an only slight spatial arrangement, the photofragment angular distributions of the two enantiomers do not show appreciable differences...

physics.chem-ph↗

arXiv2026

Lieb-Schultz-Mattis-Type and Laughlin-Type Argument for the Quantum Hall Effect in Lattice Fermions with Spiral Boundary Conditions

We derive the condition for the occurrence of the integer quantum Hall effect in two-dimensional lattice systems with interactions, expressed as $ϕν-ρ\in\mathbb{Z}$, where $ϕ$, $ν$, and $ρ$ denote the magnetic flux, the Chern number, and the electron density, respectively. By employing spiral boundary conditions, which treat the system as an extended one-dimensional chain, this condition is obtained directly through a Lieb-Schultz-Mattis-type and Laughlin-type argument. This approach improves upon the preceding work based on conventional periodic boundary conditions, where the condition was derived indirectly with redundant system-size dependence. The key to this approach is that the spatial directions of the external force and the response can be systematically controlled by a factor of the system size.

cond-mat.str-el↗

arXiv2024

Comparing quantum fluctuations in the spin-$\frac{1}{2}$ and spin-$1$ XXZ Heisenberg models on square and honeycomb lattices

We present a detailed investigation of the XXZ Heisenberg model for spin-$1/2$ and spin-$1$ systems on square and honeycomb lattices. Utilizing the density-matrix renormalization group (DMRG) method, complemented by Spiral Boundary Conditions (SBC) for mapping two-dimensional (2D) clusters onto one-dimensional (1D) chains, we meticulously explore the evolution of staggered magnetization and spin gaps across a broad spectrum of easy-axis anisotropies. Our study reveals that, despite the lower site coordination number of honeycomb lattice, which intuitively suggests increased quantum fluctuations in its Néel phase compared to the square lattice, the staggered magnetization in the honeycomb structure exhibits only a marginal reduction. Furthermore, our analysis demonstrates that the dependence of staggered magnetization on the XXZ anisotropy $Δ$, except in close proximity to $Δ=1$, aligns with series expansion predictions up to the 12th order. Notably, for the $S=1/2$ honeycomb lattice, deviations from the 10th order series expansion predictions near the isotropic Heisenberg limit emphasize the critical influence of quantum fluctuations on the spin excitation in its Néel state. Additionally, our findings are numerically consistent with the singular behavior of the spin gap near the isotropic Heisenberg limit as forecasted by spin-wave theory. The successful implementation of SBC marks a methodological advancement, streamlining the computational complexity involved in analyzing 2D models and paving the way for more precise determinations of physical properties in complex lattice systems.

cond-mat.str-el↗

arXiv2024

Chern numbers in two-dimensional systems with spiral boundary conditions

We discuss methods for calculating Chern numbers of two-dimensional lattice systems using spiral boundary conditions, which sweep all lattice sites in one-dimensional order. Specifically, we establish the one-dimensional representation of Fukui-Hatsugai-Suzuki's method, based on lattice gauge theory, and the Coh-Vanderbilt's method, which relates to electronic polarization. The essential point of this discussion is that the insertion of flux into the extended one-dimensional chain generates an effective current in the perpendicular direction. These methods are valuable not only for a unified understanding of topological physics in different dimensions but also for numerical calculations, including the density matrix renormalization group.

cond-mat.str-el↗

arXiv2023

Phase diagram of the Kitaev-Heisenberg model using various finite-size clusters

We estimate phase boundaries of four ordered and two spin-liquid phases for the spin-$\frac{1}{2}$ Kitaev-Heisenberg (KH) model using four kinds of relatively-small clusters, based on the second derivative of ground-state energy. The estimated values are compared between the clusters as well as the previous iPEPS results. We thus find that the boundaries can be accurately estimated within limited-size clusters. The used clusters may appropriate to study higher-$S$ KH models having less fluctuations.

cond-mat.str-el↗

arXiv2023

One-dimensional projection of two-dimensional systems using spiral boundary conditions

We introduce spiral boundary conditions (SBCs) as a useful tool for handling the shape of finite-size periodic clusters. Using SBCs, a lattice model for more than two dimensions can be exactly projected onto a one-dimensional (1D) periodic chain with translational invariance. Hence, the existing 1D techniques such as density-matrix renormalization group (DMRG), bosonization, Jordan-Wigner transformation, etc., can be effectively applied to the projected 1D model. First, we describe the 1D projection scheme for the two-dimensional (2D) square- and honeycomb-lattice tight-binding models in real and momentum space. Next, we discuss how the density of states and the ground-state energy approach their thermodynamic limits. Finally, to demonstrate the utility of SBCs in DMRG simulations, we estimate the magnitude of staggered magnetization of the 2D XXZ Heisenberg model as a function of XXZ anisotropy.

cond-mat.str-el↗

arXiv2022

Study of Staggered Magnetization in the Spin-$S$ Square-Lattice Heisenberg Model Using Spiral Boundary Conditions

We propose an efficient numerical method to obtain local order parameter in two-dimensional systems using spiral boundary conditions. As a benchmark, we first estimate the magnitude of staggered magnetization for the $S=1/2$ XXZ Heisenberg model on a square lattice in the whole range of the XXZ anisotropy by density-matrix renormalization group technique. The validity of our method is confirmed by comparing our results with the previous analytical and numerical studies. Then, as further demonstration, we apply our method to obtain the staggered magnetization for the higher-spin cases from $S=1$ to $S=6$. The accuracy of the obtained results is validated using the series expansion and the spin-wave theory.

cond-mat.str-el↗

arXiv2022

Electronic polarization in non-Bloch band theory

Hermitian topological materials are characterized by the nontrivial relation between topological numbers and edge modes, i.e. the bulk-boundary correspondence. In non-Hermitian systems, the conventional correspondence breaks down. Instead, in the non-Hermitian Su-Schrieffer-Heeger model, the non-Bloch bulk-boundary correspondence, which is the relation between the non-Bloch winding number and the non-Hermitian skin effect, is proposed by S. Yao and Z. Wang. We introduce the non-Bloch polarization as a topological quantity to detect the non-Hermitian skin effect. Moreover, we also discuss the non-Bloch bulk-boundary correspondence in two-dimensional systems using the non-Bloch polarization with spiral boundary conditions.

cond-mat.str-el↗

arXiv2022

Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems

We discuss an extension of the Resta's electronic polarization to non-Hermitian systems with periodic boundary conditions. We introduce the ``electronic polarization'' as an expectation value of the exponential of the position operator in terms of the biorthogonal basis. We found that there appears a finite region where the polarization is zero between two topologically distinguished regions, and there is one-to-one correspondence between the polarization and the winding number which takes half-odd integers as well as integers. We demonstrate this argument in the non-Hermitian Su-Schrieffer-Heeger model.

cond-mat.str-el↗

arXiv2021

Characterization of topological insulators based on the electronic polarization with spiral boundary conditions

We introduce the electronic polarization originally defined in one-dimensional lattice systems to characterize two-dimensional topological insulators. The main idea is to use spiral boundary conditions which sweep all lattice sites in one-dimensional order. We find that the sign of the polarization changes at topological transition points of the two-dimensional Wilson-Dirac model (the lattice version of the Bernevig-Hughes-Zhang model) in the same way as in one-dimensional systems. Thus the polarization plays the role of "order parameter" to characterize the topological insulating state and enables us to study topological phases in different dimensions in a unified way.

cond-mat.str-el↗

arXiv2021

Stereodynamics Imaging of Bromine Atomic Photofragments Eliminated from 1-Bromo-2-methylbutane Oriented via Hexapole State Selector

Both single-laser and two-laser experiments were conducted to look into the ion-imaging of Br*(2P1/2) and Br(2P3/2) photo-fragmented from 1-bromo-2-methylbutane in the range 232-240 nm via a detection scheme of (2+1) resonance-enhanced multiphoton ionization. The angular analysis of these photofragment distributions yields the anisotropy parameter beta = 1.88 +/- 0.06 for the Br* excited state which arises from a parallel transition, while beta = 0.63 +/- 0.09 for the Br ground state indicates the contribution from both a perpendicular transition and a non-adiabatic transition. When a hexapole coupled with an orienting field was implemented, the parent molecules are spatially oriented to yield an orientation efficiency | | of 0.15. Besides the chi angle between the recoil velocity v and the transition dipole moment mu, orienting molecules allows for the evaluation of the angle alpha between v and the permanent molecular dipole moment d. The angular analysis of Br* photofragment distribution yields chi to be 11.5 degrees and alpha in the range from 160 degrees to 180 degrees with weak dependency. In the two-laser experiments, the angular anisotropy of Br photofragment distribution was found to be smaller (0.38 +/- 0.10) when the photolysis wavelength was red-shifted to 240 nm, suggesting the increasing contributions from perpendicular transitions.

physics.atom-ph↗

arXiv2020

Exact Plaquette-Ordered Ground States with Exact Edge States of the Generalized Hubbard Model in Corner Sharing Lattices

We discuss exact plaquette-ordered ground states of the generalized Hubbard model based on the projection operator method for several corner sharing lattices: Kagome, checkerboard, and pyrochlore lattices. The obtained exact ground states are interpreted as Néel ordered states on the plaquette-located electrons. We demonstrate that these models also have exact edge states. We also calculate the entanglement entropy exactly in these systems.

cond-mat.str-el↗

arXiv2019

Polarization amplitude near quantum critical points

We discuss the polarization amplitude of quantum spin systems in one dimension. In particular, we closely investigate it in gapless phases of those systems based on the two-dimensional conformal field theory. The polarization amplitude is defined as the ground-state average of a twist operator which induces a large gauge transformation attaching the unit amount of the U(1) flux to the system. We show that the polarization amplitude under the periodic boundary condition is sensitive to perturbations around the fixed point of the renormalization-group flow rather than the fixed point itself even when the perturbation is irrelevant. This dependence is encoded into the scaling law with respect to the system size. In this paper, we show how and why the scaling law of the polarization amplitude encodes the information of the renormalization-group flow. In addition, we show that the polarization amplitude under the antiperiodic boundary condition is determined fully by the fixed point in contrast to that under the periodic one and that it visualizes clearly the nontriviality of spin systems in the sense of the Lieb-Schultz-Mattis theorem.

cond-mat.stat-mech↗

arXiv2019

Extraction of topological information in Tomonaga-Luttinger liquids

We discuss expectation values of the twist operator $U$ appearing in the Lieb-Schultz-Mattis theorem (or the polarization operator for periodic systems) in excited states of the one-dimensional correlated systems $z_L^{(q,\pm)}\equiv\braket{Ψ_{q/2}^{\pm}|U^q|Ψ_{q/2}^{\pm}}$, where $\ket{Ψ_{p}^{\pm}}$ denotes the excited states given by linear combinations of momentum $2pk_{\rm F}$ with parity $\pm 1$. We found that $z_L^{(q,\pm)}$ gives universal values $\pm 1/2$ on the Tomonaga-Luttinger (TL) fixed point, and its signs identify the topology of the dominant phases. Therefore, this expectation value changes between $\pm 1/2$ discontinuously at a phase transition point with the U(1) or SU(2) symmetric Gaussian universality class. This means that $z_L^{(q,\pm)}$ extracts the topological information of TL liquids. We explain these results based on the free-fermion picture and the bosonization theory, and also demonstrate them in several physical systems.

cond-mat.str-el↗

arXiv2018

Exact Ground States of the Extended Hubbard Model on the Kagome lattice

We discuss the exact plaquette-ordered ground states of the generalized Hubbard model on the Kagomé lattice for several fillings, by constructing the Hamiltonian as a sum of products of projection operators for up and down spin sectors. The obtained exact ground states are interpreted as Néel ordered states on the bond-located electrons. We determine several parameter regions of the exact ground states, and calculate the entanglement entropy. We examine the above results by numerical calculations based on exact diagonalization and density-matrix renormalization group methods.

cond-mat.str-el↗

arXiv2017

Hexapole-Oriented Asymmetric-Top Molecules and Their Stereodirectional Photodissociation Dynamics

Molecular orientation is a fundamental requisite in the study of stereodirected dynamics of collisional and photoinitiated processes. In this last decade, variable hexapolar electric filters have been developed and employed for the rotational-state selection and the alignment of molecules of increasing complexity, for which main difficulties are their mass, their low symmetry and the very dense rotational manifold. In this work, for the first time, a complex molecule such as 2-bromobutane, an asymmetric-top containing a heavy atom (the bromine), has been successfully oriented by a weak homogeneous field placed downstream the hexapolar filter. Efficiency of the orientation has been characterized experimentally, by combining time-of-flight measurements and a slice-ion-imaging detection technique. The application is described to the photodissociation dynamics of the oriented 2-bromobutane, which was carried out at a laser wavelength of 234 nm, corresponding to the breaking of the C Br bond. The Br photofragment is produced in both the ground Br (2P3/2) and the excited Br (2P1/2) electronic states and both channels are studied by the slice imaging technique, revealing new features in the velocity and angular distributions with respect to previous investigations on non-oriented molecules.

physics.chem-ph↗

arXiv2017

Stereodirectional Photodynamics: Experimental and Theoretical Perspectives

Hexapole oriented 2-bromobutane is photodissociated and detected by a slice ion imaging technique at 234 nm. The laser wavelength corresponds to the C Br bond breaking with emission of a Br atom fragment in two accessible fine structure states: the ground state Br and the excited state Br*, both observable separately by resonance enhanced multiphoton ionization (REMPI). Orientation is evaluated by time of flight measurements combined with slice ion imaging.

physics.chem-ph↗