arXiv subjects

Hiroki Nakano

Publications and source records attributed to Hiroki Nakano.

At least 73 records · Page 4Linked to original sources

arXiv2012

Magnetization curve of the kagome-strip-lattice antiferromagnet

We study the magnetization curve of the Heisenberg model on the quasi-one-dimensional kagome-strip lattice that shares the same lattice structure in the inner part with the two-dimensional kagome lattice. Our numerical calculations based on the density matrix renormalization group method reveal that the system shows several magnetization plateaus between zero magnetization and the saturated one; we find the presence of the magnetic plateaus with the n=7 height of the saturation for n =1,2,3,4,5 and 6 in the S =1/2 case, whereas we detect only the magnetic plateaus of n =1,3,5 and 6 in the S =1 case. In the cases of n =2,4 and 6 for the S=1/2 system, the Oshikawa-Yamanaka-Affleck condition suggests the occurrence of the translational symmetry breaking (TSB). We numerically confirm this non-trivial TSB in our results of local magnetizations. We have also found that the macroscopic jump appears near the saturation field irrespective of the spin amplitude as well as the two-dimensional kagome model.

cond-mat.str-el↗

arXiv2012

Ferrimagnetism of the Heisenberg Models on the Quasi-One-Dimensional Kagome Strip Lattices

We study the ground-state properties of the S=1/2 Heisenberg models on the quasi-onedimensional kagome strip lattices by the exact diagonalization and density matrix renormalization group methods. The models with two different strip widths share the same lattice structure in their inner part with the spatially anisotropic two-dimensional kagome lattice. When there is no magnetic frustration, the well-known Lieb-Mattis ferrimagnetic state is realized in both models. When the strength of magnetic frustration is increased, on the other hand, the Lieb-Mattis-type ferrimagnetism is collapsed. We find that there exists a non-Lieb-Mattis ferrimagnetic state between the Lieb-Mattis ferrimagnetic state and the nonmagnetic ground state. The local magnetization clearly shows an incommensurate modulation with long-distance periodicity in the non-Lieb-Mattis ferrimagnetic state. The intermediate non-Lieb-Mattis ferrimagnetic state occurs irrespective of strip width, which suggests that the intermediate phase of the two-dimensional kagome lattice is also the non-Lieb-Mattis-type ferrimagnetism.

cond-mat.str-el↗

arXiv2011

Frustration-Induced Ferrimagnetism in Heisenberg Spin Chains

We study ground-state properties of the Heisenberg frustrated spin chain with interactions up to fourth nearest neighbors by the exact-diagonalization method and the density matrix renormalization group method. We find that ferrimagnetism is realized not only in the case of S=1/2 but also S=1 despite that there is only a single spin site in each unit cell determined from the shape of the Hamiltonian. Our numerical results suggest that a "multi-sublattice structure" is not required for the occurrence of ferrimagnetism in quantum spin systems with isotropic interactions.

cond-mat.str-el↗

arXiv2011

Quantum Magnetization Plateau in Spin-1 Triangular-Lattice Antiferromagnet Ba$_3$NiSb$_2$O$_9$

We report the results of magnetization and specific heat measurements on Ba$_3$NiSb$_2$O$_9$, which is a quasi-two-dimensional spin-1 triangular-lattice antiferromagnet. We observed a nonclassical magnetization plateau at one-third of the saturation magnetization that is driven by spin frustration and quantum fluctuation. Exact diagonalization for a 21-site rhombic cluster was performed to analyze the magnetization process. Experimental and calculated results agree well.

cond-mat.str-el↗

arXiv2011

Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet

We study the system size dependence of the singlet-triplet excitation gap in the $S=1/2$ kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.

cond-mat.mtrl-sci↗

arXiv2011

How to distinguish the Haldane/Large-D state and the intermediate-D state in an S=2 quantum spin chain with the XXZ and on-site anisotropies

We numerically investigate the ground-state phase diagram of an S=2 quantum spin chain with the $XXZ$ and on-site anisotropies described by ${\mathcal H}=\sum_j (S_j^x S_{j+1}^x+S_j^y S_{j+1}^y+ΔS_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $Δ$ denotes the XXZ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the $Δ>0$ and $D>0$ case for simplicity. Our main purpose is to obtain the definite conclusion whether there exists or not the intermediate-$D$ (ID) phase, which was proposed by Oshikawa in 1992 and has been believed to be absent since the DMRG studies in the latter half of 1990's. In the phase diagram with $Δ>0$ and $D>0$ there appear the XY state, the Haldane state, the ID state, the large-$D$ (LD) state and the Néel state. In the analysis of the numerical data it is important to distinguish three gapped states; the Haldane state, the ID state and the LD state. We give a physical and intuitive explanation for our level spectroscopy method how to distinguish these three phases.

cond-mat.stat-mech↗

arXiv2011

Frustration-Induced Ferrimagnetism in S=1/2 Heisenberg Spin Chain

The ground-state properties of the S=1/2 frustrated Heisenberg spin chain with interactions up to fourth nearest neighbors are investigated by the exact-diagonalization method and density matrix renormalization group method. Our numerical calculations clarify that the ferrimagnetic state is realized in the ground state in spite of the fact that a multi-sublattice structure in the shape of the system is absent. We find that there are two types of ferrimagnetic phases: one is the well-known ferrimagnetic phase of the Lieb-Mattis type and the other is the nontrivial ferrimagnetic phase that is different from that of the Lieb-Mattis type. Our results suggest that a multi-sublattice structure of the shape is not necessarily required for the occurrence of ferrimagnetism.

cond-mat.str-el↗

arXiv2011

Haldane, Large-D and Intermediate-D States in an S=2 Quantum Spin Chain with On-Site and XXZ Anisotropies

Using mainly numerical methods, we investigate the ground-state phase diagram of the S=2 quantum spin chain described by $H = \sum_j (S_j^x S_{j+1}^x + S_j^y S_{j+1}^y + ΔS_j^z S_{j+1}^z) + D \sum_j (S_j^z)^2$, where $Δ$ denotes the $XXZ$ anisotropy parameter of the nearest-neighbor interactions and $D$ the on-site anisotropy parameter. We restrict ourselves to the case with $Δ\ge 0$ and $D \ge 0$ for simplicity. Each of the phase boundary lines is determined by the level spectroscopy or the phenomenological renormalization analysis of numerical results of exact-diagonalization calculations. The resulting phase diagram on the $Δ$-$D$ plane consists of four phases; the XY 1 phase, the Haldane/large-$D$ phase, the intermediate-$D$ phase and the Néel phase. The remarkable natures of the phase diagram are: (1) the Haldane state and the large-$D$ state belong to the same phase; (2) there exists the intermediate-$D$ phase which was predicted by Oshikawa in 1992; (3) the shape of the phase diagram on the $Δ$-$D$ plane is different from that believed so far. We note that this is the first report of the observation of the intermediate-$D$ phase.

cond-mat.str-el↗

arXiv2011

Critical magnetization behaviors of the triangular and Kagome lattice quantum antiferromagnets

We investigate the $S=1/2$ quantum spin antiferromagnets on the triangular and Kagome lattices in magnetic field, using the numerical exact diagonalization. Particularly we focus on an anomalous magnetization behavior of each system at 1/3 of the saturation magnetization. The critical exponent analyses suggest that it is a conventional magnetization plateau on the triangular lattice, while an unconventional phenomenon, called the magnetization ramp, on the Kagome lattice.

cond-mat.mtrl-sci↗

arXiv2011

Collapse of Ferrimagnetism in Two-Dimensional Heisenberg Antiferromagnet due to Frustration

We study ferrimagnetism in the ground state of the antiferromagnetic Heisenberg model on the spatially anisotropic kagome lattice, in which ferrimagnetism of the conventional Lieb-Mattis type appears in the region of weak frustration whereas the ground state is nonmagnetic in the isotropic case. Numerical diagonalizations of small finite-size clusters are carried out to examine the spontaneous magnetization. We find that the spontaneous magnetization changes continuously in the intermediate region between conventional ferrimagnetism and the nonmagnetic phase. Local magnetization of the intermediate state shows strong dependence on the site position, which suggests non-Lieb-Mattis ferrimagnetism.

cond-mat.str-el↗

arXiv2011

Hyperbolic Deformation Applied to S = 1 Spin Chains - Scaling Relation in Excitation Energy -

We investigate excitation energies of hyperbolically deformed S = 1 spin chains, which are specified by the local energy scale f_j^{~} = \cosh j λ, where j is the lattice index and λis the deformation parameter. The elementary excitation is well described by a quasiparticle hopping model, which is also expressed in the form of hyperbolic deformation. It is possible to estimate the excitation gap Δin the uniform limit λ\rightarrow 0, by means of a finite size scaling with respect to the system size N and the deformation parameter λ.

cond-mat.str-el↗

arXiv2010

Scaling Relation for Excitation Energy Under Hyperbolic Deformation

We introduce a one-parameter deformation for one-dimensional (1D) quantum lattice models, the hyperbolic deformation, where the scale of the local energy is proportional to cosh lambda j at the j-th site. Corresponding to a 2D classical system, the deformation does not strongly modify the ground state. In this situation, the effective Hamiltonian of the quantum system shows that the quasi particle is weakly bounded around the center of the system. By analyzing this binding effect, we derive scaling relations for the mean-square width of confinement, the energy correction with respect to the excitation gap Δ, and the deformation parameter $λ$. This finite-size scaling allows us to investigate excitation gap of 1D non-deformed bulk quantum systems.

cond-mat.other↗

arXiv2010

Magnetization Process of Kagome-Lattice Heisenberg Antiferromagnet

The magnetization process of the isotropic Heisenberg antiferromagnet on the kagome lattice is studied. Data obtained from the numerical-diagonalization method are reexamined from the viewpoint of the derivative of the magnetization with respect to the magnetic field. We find that the behavior of the derivative at approximately one-third of the height of the magnetization saturation is markedly different from that for the cases of typical magnetization plateaux. The magnetization process of the kagome-lattice antiferromagnet reveals a new phenomenon, which we call the "magnetization ramp".

cond-mat.str-el↗

arXiv2009

Gap Estimation by means of Hyperbolic Deformation

We present a way of numerical gap estimation applicable for one-dimensional infinite uniform quantum systems. Using the density matrix renormalization group method for a non-uniform Hamiltonian, which has deformed interaction strength of $j$-th bond proportional to $\cosh λj$, the uniform Hamiltonian is analyzed as a limit of $λ\to 0$. As a consequence of the deformation, an excited quasi-particle is weakly bounded around the center of the system, and kept away from the system boundary. Therefore, insensitivity of an estimated excitation gap of the deformed system to the boundary allows us to have the bulk excitation gap $Δ(λ)$, and shift in $Δ(λ)$ from $Δ(0)$ is nearly linear in $λ$ when $λ\ll 1$. Efficiency of this estimation is demonstrated through application to the S=1 antiferromagnetic Heisenberg chain. Combining the above estimation and another one obtained from the technique of convergence acceleration for finite-size gaps estimated by numerical diagonalizations, we conclude that the Haldane gap is in $[0.41047905,~0.41047931]$.

cond-mat.stat-mech↗

arXiv2008

Reexamination of Finite-Lattice Extrapolation of Haldane Gaps

We propose two methods of estimating a systematic error in extrapolation to the infinite-size limit in the study of measuring the Haldane gaps of the one-dimensional Heisenberg antiferromagnet with the integer spin up to S=5. The finite-size gaps obtained by numerical diagonalizations based on Lanczos algorithm are presented for sizes that have not previously been reported. The changes of boundary conditions are also examined. We successfully demonstrate that our methods of extrapolation work well. The Haldane gap for S=1 is stimated to be $0.4104789 \pm 0.0000013$. We successfully obtain the gaps up to S=5, which make us confirm the asymptotic formula of the Haldane gap in $S\to\infty$.

cond-mat.str-el↗

arXiv2008

Finite-size scaling of string order parameters characterizing the Haldane phase

We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi-point correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the S = 1 XXZ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density matrix renormalization group method. We focus on the gradient of the inversedsystem- size dependence of the correlation function on a logarithmic plot. This quantity shows that the finite-size scaling sensitively changes at the critical point. The behavior of the gradient with increasing system size is divergent, stable at a finite value, or rapidly decreases to zero when the system is in the disordered phase, at the critical point, or in the ordered phase, respectively. The analysis of the finite-size string correlation functions allows precise determination of the boundary of the Haldane phase and estimation of the critical exponent of the correlation length. Our estimates of the transition point and the critical exponents, which are determined only by the ground-state quantities, are consistent with results obtained from the analysis of the energy-level structure. Our analysis requires only the correlation functions of several finite sizes under the same condition as a candidate for the long-range order. The quantity is treated in the same manner irrespective of the kind of elements which destroy the order concerned. This work will assist in the development of a method to directly observe quantum phase transitions.

cond-mat.str-el↗

arXiv2007

Drude Weight of the Two-Dimensional Hubbard Model -- Reexamination of Finite-Size Effect in Exact Diagonalization Study --

The Drude weight of the Hubbard model on the two-dimensional square lattice is studied by the exact diagonalizations applied to clusters up to 20 sites. We carefully examine finite-size effects by consideration of the appropriate shapes of clusters and the appropriate boundary condition beyond the imitation of employing only the simple periodic boundary condition. We successfully capture the behavior of the Drude weight that is proportional to the squared hole doping concentration. Our present result gives a consistent understanding of the transition between the Mott insulator and doped metals. We also find, in the frequency dependence of the optical conductivity, that the mid-gap incoherent part emerges more quickly than the coherent part and rather insensitive to the doping concentration in accordance with the scaling of the Drude weight.

cond-mat.str-el↗

arXiv2006

Zero modes of tight binding electrons on the honeycomb lattice

Tight binding electrons on the honeycomb lattice are studied where nearest neighbor hoppings in the three directions are $t_a,t_b$ and $t_c$, respectively. For the isotropic case, namely for $t_a=t_b=t_c$, two zero modes exist where the energy dispersions at the vanishing points are linear in momentum $k$. Positions of zero modes move in the momentum space as $t_a,t_b$ and $t_c$ are varied. It is shown that zero modes exist if $||\frac{t_b}{t_a}| -1| \leq |\frac{t_c}{t_a}| \leq ||\frac{t_b}{t_a}|+1|$. The density of states near a zero mode is proportional to $|E|$ but it is propotional to $\sqrt{|E|}$ at the boundary of this condition.

cond-mat.mes-hall↗