arXiv subjects

Ken'ichi Takano

Publications and source records attributed to Ken'ichi Takano.

29 records · Page 2Linked to original sources

arXiv2000

Phase diagrams of period-4 spin chains consisting of three kinds of spins

We study a period-4 antiferromagnetic mixed quantum spin chain consisting of three kinds of spins. When the ground state is singlet, the spin magnitudes in a unit cell are arrayed as (s-t, s, s+t, s) with integer or half-odd integer s and t (0 <= t < s). The spin Hamiltonian is mapped onto a nonlinear sigma model (NLSM) in a previously developed method. The resultant NLSM includes only two independent parameters originating from four exchange constants for fixed s and t. The topological angle in the NLSM determines the gapless phase boundaries between disordered phases in the parameter space. The phase diagrams for various s and t shows rich structures. We systematically explain the phases in the singlet-cluster-solid picture.

cond-mat.str-el↗

arXiv2000

Spin Gap of S=1/2 Heisenberg Model on Distorted Diamond Chain

We study the spin gap of the S=1/2 Heisenberg model on the distorted diamond chain, which is recently proposed to represent magnetic properties of Cu_3 Cl_6 (H_2 O)_2 2H_8 C_4 SO_2. This model is composed of stacked trimers and has three kinds of exchange interactions J_1, J_2 and J_3. Using the numerical diagonalization, we obtain a contour map of the spin gap in the J_2/J_1-J_3/J_1 plane. We argue possible values of the exchange constants based on the contour map and the observed value of the spin gap.

cond-mat.str-el↗

arXiv2000

Spin-Gap States of a Periodic Mixed Spin Chain

We examine a chain of periodic arrays of 4 quantum spins with magnitudes of 1/2, 1, 3/2 and 1. There are four kinds of nearest-neighbour exchange parameters among them. We choose two independent parameters for concreteness: one represents the ratio of typical exchange parameters, and the other represents a distortion. We determine the phase diagram of the ground state in the parameter space. The phase boundaries appear as gapless lines which separate gapful disordered phases. They are determined by the gapless equation which was previously derived by mapping a general periodic spin chain to the nonlinear $σ$ model.

cond-mat.str-el↗

arXiv1999

Phase Diagrams of Mixed Spin Chains with Period 4 by the Nonlinear $σ$ Model

We study mixed quantum spin chains consisting of two kinds of spins with magnitudes, s_a and s_b. The spins are arrayed as s_a-s_a-s_b-s_b in a unit cell and the exchange couplings are accordingly periodic with period 4. The spin Hamiltonian is mapped onto a nonlinear $σ$ model based on the general formula for periodic inhomogeneous spin chains. The gapless condition given by the nonlinear $σ$ model determines boundaries between disordered phases in the space of the exchange parameters. The phase diagram has a rich phase structure characterized by the values of s_a and s_b. We explain all phases in the singlet-cluster-solid picture which is an extension of the valence-bond-solid picture.

cond-mat.str-el↗

arXiv1999

Phase Diagram of the 1/2-1/2-1-1 Spin Chain by the Nonlinear Sigma Model

We examine a periodic mixed spin chain with spin magnitudes 1/2 and 1 which are arrayed as 1/2-1/2-1-1. The three independent parameters are ratios of the four exchange couplings. We determine phase boundaries in the parameter space by using the gapless condition which was previously derived by mapping a general inhomogeneous spin chain to the nonlinear sigma model. We find two gapless boundaries separating three disordered phases. The features of the phases are explained in terms of singlet clusters.

cond-mat.str-el↗

arXiv1998

Magnetic Susceptibility for $CaV_4O_9$

We examine experimental magnetic susceptibility $χ^{tot}(T)$ for CaV$_4$O$_9$ by fitting with fitting function $αχ^{mag}(T) + c$. The function $χ^{mag}(T)$ is a power series of 1/T and the lowest order term is fixed as $C/T$, where $C$ is the Curie constant as determined by the experimental $g$-value (g=1.96). Fitting parameters are $α$, $c$ and expansion coefficients except for the first one in $χ^{mag}(T)$. We determine $α$ and $c$ as $α\simeq$ 0.73 and $c\simeq$ 0 for an experimental sample. We interpret $α$ as the volume fraction of CaV$_4$O$_9$ in the sample and $χ^{mag}(T)$ as the susceptibility for the pure CaV$_4$O$_9$. The result of $α\ne 1$ means that the sample includes nonmagnetic components. This interpretation consists with the result of a perturbation theory and a neutron scattering experiment.

cond-mat↗

arXiv1998

Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model

We algebraically construct the Fock space of the Sutherland model in terms of the eigenstates of the pseudomomenta as basis vectors. For this purpose, we derive the raising and lowering operators which increase and decrease eigenvalues of pseudomomenta. The operators exchanging eigenvalues of two pseudomomenta have been known. All the eigenstates are systematically produced by starting from the ground state and multiplying these operators to it.

solv-int↗

arXiv1998

Non-Linear Sigma Model for Inhomogeneous Spin Chains

We derive a non-linear sigma model (NLSM) generally representing antiferromagnetic Heisenberg spin chains with inhomogeneous spin magnitudes and inhomogeneous nearest-neighbor exchange constants arrayed in finite periods. Only a restriction is that the average of spin magnitudes on one sublattice is the same as that on the other sublattice. The NLSM gives the gapless condition explicitly written by the spin magnitudes and the exchange constants. We apply this gapless condition to several cases including systems with impurities.

cond-mat.str-el↗

arXiv1997

Determination of Exchange Parameters from Magnetic Susceptibility

We report a novel practical method to determine exchange parameters by using experimental susceptibility data in a relatively narrow temperature region and a low order high-temperature-expansion equation. This method is applied to a square lattice and a CaV_4O_9-type lattice, and its accuracy is discussed.

cond-mat.str-el↗

arXiv1996

Determination of Exchange Parameters for CaV_4O_9

Magnetic susceptibility measured for CaV$_4$O$_9$ is analyzed by a method with high temperature expansion. The analysis is consistent with the $g$-value which is close to 2 and is observed by an ESR experiment. Four exchange parameters in a two-dimensional Heisenberg model are determined to represent CaV$_4$O$_9$. All the exchange parameters are about 500 K and strongly frustrated. The observed spin gap originates from the frustration.

cond-mat↗

arXiv1995

Spin Gap of Two-Dimensional Antiferromagnet Representing CaV$_4$O$_9$

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, $J_e$ and $J_c$. This model describes localized spins at vanadium ions in a layer of CaV$_4$O$_9$, for which a spin gap is found by a recent experiment. Comparing the high temperature expansion of the magnetic susceptibility to experimental data, we determined the exchange energies as $J_e \simeq$ 610 K and $J_c \simeq$ 150 K. By the numerical diagonalization we estimated the spin gap as $Δ\sim 0.2J_e \simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.

cond-mat↗