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We present an organic compound exhibiting a spin-Peierls (SP) transition to an effective spin-1 antiferromagnetic uniform chain, that is, the Haldane chain. The clear disappearance of magnetization, accompanied by a structural phase transition, is well explained by the deformation to an effective spin-1 Haldane chain. The flexibility of the molecular orbitals in the organic radical compound allows the transformation of the exchange interactions into the Haldane state with different topologies. The SP transition in the present compound demonstrates a mechanism different from that of the conventional systems, paving another path for research in quantum phenomena originating from spin-lattice couplings., 6 pages, 3 figures

The $S=2$ quantum spin chain with the single-ion anisotropy $D$ and the biquadratic exchange interaction $J_{\rm BQ}$ is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that the intermediate-$D$ phase corresponding to the symmetry protected topological (SPT) phase appears in a wide region of the ground state phase diagram. We also obtain the phase diagram at the half of the saturation magnetization which includes the SPT plateau phase., to be published in J. Phys. Soc. Jpn

The magnetization process of the $S=1/2$ distorted diamond spin chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the spin nematic and SDW Tomonaga-Luttinger liquids can appear for sufficiently large easy axis anisotropy., Comment: The 67th Annual Conference on Magnetism and Magnetic Materials (MMM 2022), to be published in AIP Advances

The magnetization plateau of the $S=2$ antiferromagnetic chain with interaction and single-ion anisotropies is investigated using the numerical diagonalization of finite-size clusters and some size scaling analyses. The previous level spectroscopy analysis indicated that two different magnetization plateau phases appear at half of the saturation magnetization. One is due to the large-$D$ mechanism and the other is due to the Haldane one. In the present study the phase diagram is extended to wider region of the anisotropies. As a result we find another half magnetization plateau phase, where the translational symmetry is spontaneously broken ., Comment: to be published in JPS Conference Proceedings (LT29)

The magnetization process of the S = 1 antiferromagnetic chain with the single-ion anisotropy D and the biquadratic interaction is investigated using the numerical diagonalization. Both interactions stabilize the 2-magnon Tomonaga-Luttinger liquid (TLL) phase in the magnetization process. Based on several excitation gaps calculated by the numerical diagonalization, some phase diagrams of the magnetization process are presented. These phase diagrams reveal that the spin nematic dominant TLL phase appears at higher magnetizations for sufficiently large negative D.

By using mainly numerical methods, we investigate the ground-state phase diagram (GSPD) of an $S=1$ ferromagnetic-antiferromagnetic bond-alternating chain with the $XXZ$ and the on-site anisotropies. This system can be mapped onto an anisotropic spin-2 chain when the ferromagnetic interaction is much stronger than the antiferromagnetic interaction. Since there are many quantum parameters in this system, we numerically obtained the GSPD on the plane of the magnitude of the antiferromagnetic coupling versus its $XXZ$ anisotropy, by use of the exact diagonalization, the level spectroscopy as well as the phenomenological renormalization group. The obtained GSPD consists of six phases. They are the $XY$1, the large-$D$ (LD), the intermediate-$D$ (ID), the Haldane (H), the spin-1 singlet dimer (SD), and the N\'eel phases. Among them, the LD, the H, and the SD phases are the trivial phases, while the ID phase is the symmetry-protected topological phase. The former three are smoothly connected without any quantum phase transitions. It is also emphasized that the ID phase appears in a wider region compared with the case of the GSPD of the anisotropic spin-2 chain with the $XXZ$ and the on-site anisotropies. We also compare the obtained GSPD with the result of the perturbation theory., Comment: to be published in JPS Conf. Ser

The frustrated quantum spin system on the distorted diamond chain lattice suitable for the alumoklyuchevskite is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. It is found that this model exhibits three quantum phases; the ferrimagnetic phase, the spin gap one, and the gapless Tomonaga-Luttinger liquid depending on the exchange coupling parameters. The ground state phase diagram is presented., to be published in JPS Conf. Ser

The $S=1/2$ twisted three-leg spin tube with the lattice distortion from the regular triangle to the isosceles one is investigated using the numerical diagonalization of finite-size clusters and the phenomenological renormalization group analysis. It is found that the quantum phase transition occurs from the spin gap phase to another one with respect to this lattice distortion., to be published in JPS Conference Proceedings

The magnetization process of the $S=1$ spin ladder system is investigated using the numerical exact diagonalization of finite-size clusters. The field-induced spin nematic liquid phase was predicted to appear by our previous work. Several ground-state phase diagrams in the plane of the single-ion anisotropy and the external magnetic field are obtained in the present study., Comment: to be published in JPS Conference Proceedings

The frustrated quantum spin system on the distorted diamond chain lattice is investigated using the numerical diagonalization of finite-size clusters and the level spectroscopy analysis. In the previous work this system was revealed to exhibit the 1/3 magnetization plateau due to two different mechanisms depending on the coupling parameters, and the phase diagram at the 1/3 magnetization was obtained. In the present work it is found that the 1/3 magnetization plateau vanishes for sufficiently large $XY$-like coupling anisotropy. The phase diagram based on the level spectroscopy analysis is also presented., Comment: to be published in JPS Conference Proceedings

The $S=1$ spin ladder with the easy-axis single-ion anisotropy is investigated using the numerical diagonalization and the finite-size scaling analysis. It is found that the field-induced nematic Tomonaga-Luttinger liquid phase appears above the critical field. In addition, there exists another critical field at which the quantum phase transition from the nematic Tomonaga-Luttinger liquid phase to the conventional field-induced Tomonaga- Luttinger liquid phase occurs. Besides some phase diagrams are presented.

We investigate the spin-1/2 twisted three-leg antiferromagnetic quantum spin tube in the presence of the easy-plane anisotropy, using the numerical diagonalization of finite-size clusters. We show cases of the existence and the absence of magnetization plateau at 1/3 height of saturation magnetization when the anisotropy is tuned. The phenomenological-renormalization group analysis indicates a quantum phase transition between the 1/3 magnetization plateau phase and the plateauless one. The phase diagram is also presented.

We study quantum phase transitions in the 1/3 plateau state of the three-leg spin-1/2 tube, where the low-energy effective chirality degree of freedom plays an essential role. Using the density matrix renormalization group and the effective chirality model, we find that, as the leg coupling increases, the chirality liquid, a novel spin imbalance phase and the vector-spin-chirality ordered phase emerge without closing the plateau spin gap. We also clarify the role of the S 3-symmetry of the spin tube, behind these quantum phase transitions.

We investigate the ground-state phase diagram of the bond-alternating S = 2 quantum spin chain with the XXZ and on-site anisotropies. For the on-site anisotropies, in addition to the popular \(D_{2}\sum\nolimits_{j} (S_{j}^{z})^{2}\) term, we consider the \(D_{4}\sum\nolimits_{j} (S_{j}^{z})^{4}\) term. Mainly we use the exact diagonalization and the level spectroscopy analysis. We show that the Haldane state, large-D state and the Dimer2 state belong to the same trivial phase, by finding the existence of adiabatic paths directly connecting these states without the quantum phase transition. Similarly, we show that the intermediate-D state and the Dimer1 state belong to the same symmetry protected topological phase.

The magnetization process of the S=1/2 three-leg spin tube with an asymmetric exchange interaction in each triangle unit is investigated by the numerical exact diagonalization and the density matrix renormalization group calculation. It is found that the 1/3 magnetization plateau appears due to two different mechanisms depending on the asymmetry. The phase diagrams of the 1/3 plateau is presented. In addition some cusp-like anomalies are found in the magnetization curve.

The S = 1 2 three-leg spin nanotube is theoretically investigated, using the numerical diagonalization and the density matrix renormalization group (DMRG) calculation. The system has a magnetization plateau at 1 3 of the saturation magnetization for sufficiently large rung interaction. We mainly focus on the effect of the asymmetric distortion from the regular triangle to the isosceles one. We find an anomalous increase of the plateau width near the symmetric point (i.e., regular triangle) when the asymmetric parameter is varied.

We explore the ground-state phase diagram of the $S=1/2$ two-leg ladder with different leg interactions. The $xy$ and $z$ components of the leg interactions between nearest-neighbor spins in the $a$ ($b$) leg are respectively denoted by $J_{{\rm l},a}$ and $\Delta_{\rm l} J_{{\rm l},a}$ ($J_{{\rm l},b}$ and $\Delta_{\rm l} J_{{\rm l},b}$). On the other hand, the $xy$ and $z$ components of the uniform rung interactions are respectively denoted by $\Gamma_{\rm r} J_{{\rm r}}$ and $J_{{\rm r}}$. In the above, $\Delta_{\rm l}$ and $\Gamma_{\rm r}$ are the $XXZ$-type anisotropy parameters for the leg and rung interactions, respectively. This system has a frustration when $J_{{\rm l},a} J_{{\rm l},b}

The magnetization process of the S=1/2 three-leg spin tube with an asymmetric exchange interaction in each triangle unit is investigated by the numerical exact diagonalization and the density matrix renormalization group calculation. It is found that the 1/3 magnetization plateau appears due to two different mechanisms depending on the asymmetry. The phase diagrams of the 1/3 plateau is presented. In addition some cusp-like anomalies are found in the magnetization curve.

We investigate the elementary excitations and magnetization dynamics of the recently synthesized single-chain magnets, which consist of Mn and Ni ions, and some related systems, using the numerical exact diagonalization of finite-size clusters and the density matrix renormalization group method. It is found that, as the easy-axis anisotropy D increases, a crossover of the lowest-lying elementary excitation should exist between the spin wave and Ising-like excitations. For the realistic trimer single-chain magnet, we estimate several crossover temperatures. In addition we predict that a magnetization plateau at 2/3 of the saturation magnetization would appear in the (s, S) = (1, 2) spin-alternating chain. The phase diagram of the plateau is also presented.

Recently a ferrimagnetic quantum spin chain consisting of Ni and Mn ions has been synthesized to create a new type of magnet with a long life time, based on the Glauber's slow dynamics. Its magnetic properties are well described by the ( s , S ) = ( 1 , 2 ) spin alternating chain model, with single-ion anisotropies D 1 and D 2 at Ni and Mn sites, respectively. Thus we investigate the magnetization process of this model, using the numerical exact diagonalization and finite-size scaling technique. It predicts a new field-induced quantum phase transition between two different Tomonaga–Luttinger liquid phases; TLL1 and TLL2 for some negative values of D 1 and D 2 . This transition corresponds to a quantum version of the spin flop. Some typical phase diagrams are presented.

The magnetization process of the S = 1 and S = 2 spin alternating ferrimagnetic chain with the single-ion anisotropies is investigated by the numerical exact diagonalization and the density matrix renormalization group method. It is found that the mechanism of the 2/3 magnetization plateau formation due to quantum effects depends on the anisotropy constants. The obtained phase diagram of the 2/3 plateau is revealed to include three different phases.

We study an incommensurate long-range order induced by an external magnetic field in a quasi-one-dimensional bond-alternating spin system, F5PNN, focusing on the role of the frustrating interaction which can be enhanced by a high-pressure effect. On the basis of the density matrix renormalization group analysis of a microscopic model for F5PNN, we present several H-T phase diagrams for typical parameters of the frustrating next-nearest-neighbour coupling and the interchain interaction, and then discuss how the field-induced incommensurate order develops by the frustration effect in such phase diagrams. A magnetization plateau at half the saturation moment is also mentioned., 9 pages, 9 figures, submitted to J. Phys.: Condens. Matter

Using mainly numerical methods, we investigate the ground-state magnetization curve of a mixed spin chain with uniaxial single-ion anisotropies, where S = 1 and S = 2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the 1/3-plateau, which appears at one third of the saturation magnetization in the magnetization curve. It is found that there appear three kinds of 1/3-plateaux, one of which has a quantum nature, while the remaining two have a classical (Ising) nature.

Recently some quantum spin systems on tube lattices, so-called spin nanotubes, have been synthesized. They are expected to be interesting low-dimensional systems like the carbon nanotubes. As a first step of theoretical study on the spin nanotube, we investigate the S = 1 2 three-leg spin tube, which is the simplest one, using numerical analyses of finite clusters and a finite-size scaling technique. The spin gap, which is one of the most interesting quantities reflecting the macroscopic quantum effect, was revealed to be open for any finite rung exchange couplings, in contrast to the three-leg spin ladder system which is gapless. We also found a quantum phase transition caused by an asymmetric rung interaction. When one of the three rung coupling constants is changed, the spin gap vanishes very rapidly.

The exact diagonalization study on the magnetization process of the S =1/2 spin ladder system revealed that the incommensurate spin correlation parallel to H would be possibly dominant around half the saturation magnetization, with the ring exchange. In such a situation, an interladder coupling would yield the field-induced long-range incommensurate order. Several phase diagrams including the magnetization plateau are also presented.

We study the finite-field ground state of an anisotropic S = 1/2 antiferromagnetic chain with bond-alternating nearest-neighbor and uniform next-nearest-neighbor interactions. The ground-state magnetization curve of this model has a plateau at a half of the saturation magnetization in a certain parameter region. We analytically investigate the plateau phase of this model by use of tlie degenerate perturbation theory up to the second order.

We study the ground-state phase diagram of the distorted diamond type S=1/2 quantum spin chain with the XXZ type interaction anisotropy, given by H = J 1 ∑ j { h 3 j − 1 , 3 j ( Δ ) + h 3 j , 3 j + 1 ( Δ ) } + J 2 ∑ j h 3 j + 1 , 3 j + 2 ( Δ ) + J 3 ∑ j { h 3 j − 2 , 3 j ( Δ ) + h 3 j , 3 j + 2 ( Δ ) } where h l , m ( Δ ) = S l x S m x + S l y S m y + Δ S l z S m z , and Δ>0 denotes the XXZ anisotropy. We have used the degenerate perturbation theory, numerically exact diagonalization method, and the level spectroscopy analysis of the diagonalization data. The remarkable nature of the phase diagram is the existence of the inversion areas. Namely, there appears the Neel region even when the interaction is XY-like, and the spin-fluid region when it is Ising-like. This phenomenon is attributed to the interplay among the interaction anisotropy, frustrating interaction, and the trimer nature of the Hamiltonian.

Azurite (Cu 3 (CO 3 ) 2 (OH) 2 ) is a model substance of a diamond spin chain, one of frustrated antiferromagnetic quantum spin chains. The high field magnetization up to 60 T, magnetic susceptibility, magnetic entropy, muon spin relaxation and 1 H-NMR of azurite have been measured using single crystals. A distinct 1/3 magnetization plateau is confirmed to be present in the magnetization curve. Two resonance peaks of 1 H-NMR. were observed. By analyzing temperature dependencies of their hyperfine shift. we found two different local susceptibilities which correspond to susceptibility of dimer and monomer spins, respectively. New field induced phase transition was found to occur at a critical field where the magnetic plateau onsets. A short range magnetic ordering developed in a peculiar two-stage process, which was revealed by temperature dependence of the magnetic specific heat and susceptibility.

A mechanism of the magnetization plateau observed in the high-field magnetizatiom measurement of the organic S = 1 spin ladder system BIP-TENO is investigated. Assuming possible lattice distortion, we propose a possible scenario of the plateau formation on the basis of the bond-alternating ladder. Some unsolved problems are also discussed.

We investigate, analytically and numerically, the ground state of the S = 1/2 distorted diamond type spin chain having three kinds of couplings, where one or two types of the couplings are ferromagnetic. We obtained the phase diagram at zero-magnetic field and also at M s /3, where M s is the saturation magnetization. We also discuss the plateau at (2/3)M s .

Using numerical methods, we study the finite-field ground state of an anisotropic S= 1 2 antiferromagnetic chain with bond-alternating nearest-neighbor and uniform next-nearest-neighbor interactions. Special attention is paid to the magnetization plateaux at a half and one-third of the saturation magnetization, which appear in the ground-state magnetization curve.

The experimental magnetization curve of the first synthesized S = 1 organic spin ladder compound BIP-TENO is presented. It reveals a clear plateau at 1/4 of the saturation magnetization. We propose a mechanism of the 1/4 plateau formation based on the frustration due to third-neighbor exchange interactions. We also compare the numerically calculated magnetization curve and susceptibility with the experimental results to estimate the exchange coupling constants.

We investigate the inversion phenomenon between the XXZ anisotropies of the Hamiltonian and the wave function in quantum spin chains, mainly focusing on the S=1/2 trimerized XXZ model with the next-nearest-neighbor interactions. We have obtained the ground-state phase diagram by use of the degenerate perturbation theory and the level spectroscopy analysis of the numerical data calculated by the Lanczos method. In some parameter regions, the spin-fluid is realized for the Ising-like anisotropy, and the Neel state for the XY-like anisotropy, against the ordinary situation., Comment: 4 pages, 4 figures (embedded): Conference paper: Yukawa-Institute-for-Theoretical-Physics International Workshop "Order, Disorder, and Dynamics in Quantum Spin Systems" (Nov.15-16,2001): will be published as a special issue of Supplement Prog. Theor. Phys

We study frustrated quantum spin systems consisting of dimers of spin-1/2 spins. We derive several models that have the exact ground state of the form of the direct product of dimer states. The ground states realized include the product state of dimer singlets, that of dimer triplets with zero magnetization, those of dimer-spin-nematic states, and those of a mixture of the dimer states. Pseudo spin-1/2 operators emerging in each dimer are also introduced., Comment: 9 pages, 4 figures, 1 table. v2: accepted version, Sec.IIIE and a few references added, some sentences revised, to appear in J. Phys. Soc. Jpn

The spin nanotubes have attracted a lot of interest in the field of the condensed matter physics [1]. Particularly, the S = 1/2 three-leg spin tube is the most important because it has the largest frustration and quantum fluctuation. One of interesting features is that the system has a spin gap [2], while the S = 1/2 three-leg spin ladder is gapless. Although no clear evidence of the spin gap was observed in any candidate materials of the three-leg spin tube so far [3, 4], many theoretical works [5–11] have supported the existence of it. In this paper, we theoretically investigate the stability of the spin gap in the S = 1/2 three-leg spin tube against the XXZ anisotropy. The discovery of a quantum phase transition from the gapped phase to the gapless one due to the anisotropy would be another evidence of the existence of the spin gap in the isotropic spin tube.

We numerically investigate the finite-field ground state of an antiferromagnetic spin- 1 2 chain with bond-alternating nearest-neighbor and uniform next-nearest-neighbor interactions, analyzing the data for finite-size systems of up to 144 spins. Special attention is paid to the magnetization curve, and the obtained results are discussed with major emphasis on the half-plateau.

We investigate the ground state magnetization curve of an S=1/2 distorted diamond chain. It is found that, in a certain region of the exchange interaction constants, a (2/3)-plateau appears in addition to a (1/3)-plateau, which appears in a much wider region. In the (2/3)-plateau state the translational symmetry of the Hamiltonian is spontaneously broken. We also discuss the phase diagram on an interaction constant plane that shows the region of the appearance of the (2/3)-plateau.

We numerically investigate the magnetization plateau at M=MS/3 (MS is the saturation magnetization) of the S=3/2 spin chain having the isotropic nearest-neighbor spin–spin interactions and also the on-site anisotropy D(Sjz)2with D>0. When D is varied, we find a no-plateau region (D

In recent studies we find that three kinds of magnetization plateaux appear at one-third of the saturation magnetization in the ground-state magnetization curve of an anisotropic (S, S') = (1, 2) spin-alternating chain, in which S = 1 and S' = 2 spins with on-site anisotropies are altematingly arranged and coupled antiferromagnetically. One of these plateaux is a quantum plateau, while the other two are classical plateaux. We here show that the first-order phase transition between the two classical one-third plateau states occurs when the on-site anisotropy for the S= 1 spin is of easy-axis type and its magnitude is sufficiently large. We numerically determine the phase transition line for this first-order transition and briefly discuss the origin of its occurrence.

The spin ladder system with the easy-axis anisotropy in magnetic field is theoretically investigated using the numerically exact diagonalization, the density matrix renormalization group (DMRG) and the finite-size scaling analysis. It is found that the field-induced nematic phase appears above the critical field. In addition, there exists another critical field at which the quantum phase transition from the nematic phase to the conventional field-induced Tomonaga-Luttinger liquid (TLL) phase occurs. The phase diagram on the coupling anisotropy versus magnetization plane is given by the numerical diagonalization. Furthermore, a typical magnetization curve calculated by the DMRG is presented.

We study the magnetization process of the $S=1/2$ antiferromagnetic spin ladder in the presence of the second and the third-neighbor couplings which lead to frustration with the typical nearest-neighbor coupling. We use degenerate perturbation theory and level spectroscopy analysis of the numerical diagonalization data of the Hamiltonian for finite systems. We find two kinds of plateaux at half the saturation moment in the magnetization curve. One is mainly due to the second-neighbor couplings and the other to the third-neighbor couplings. The mechanisms of these two plateaux are quite different with each other., 9 pages,7figures, other comments

We reexamine the numerical study of the magnetized state of the S=3/2 spin chain with single ion anisotropy D(> 0) for the magnetization M=M_{S}/3, where M_{S} is the saturation magnetization. We find at this magnetization that for D D_{c1}, the parameter region is divided into two parts D_{c1} < D < D_{c2}=0.943 and D_{c2} < D. In each region, the system is gapful and the M=M_{S}/3 magnetization plateau appears in the magnetization process. From our numerical calculation, the intermediate region D_{c1} < D < D_{c2} should be characterized by a magnetized valence-bond-solid state., Comment: 6 pages, 8 figures