Hiroki Nakano

The magnetization process of the S=1/2 delta chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization of finite-size clusters. It is found that the spin nematic liquid phase appears in higher magnetization region, as well as the SDW liquid one in lower region.

The magnetization process of the S = 1/2 distorted diamond spin chain with anisotropic ferromagnetic interaction is investigated using 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.

Abstract For the spin-1/2 spherical kagomé cluster, as well as for the 2D kagomé lattice, many low-energy singlet excitations have been expected to exist in the energy region below the spin gap, which has been actually confirmed by Kihara et al. in their specific heat measurements up to 10 K in {W72V30}, for which the exchange interaction was estimated as J = 115 K. However, the experimental result of the specific heat cannot be reproduced by the theoretical result in the Heisenberg model. Although the theoretical result has a peak around 2 K, the experimental one does not. To elucidate this difference, we incorporate Dzyaloshinskii–Moriya (DM) interactions and bond-randomness into the model Hamiltonian for {W72V30} and calculate the density of states, entropy, and specific heat at low temperatures by using the Lanczos method. We find that DM interactions do not significantly affect the energy distribution of about 10 singlet states above the ground state, which are involved in the peak structure of the specific heat around 2 K, while even 10% bond-randomness disperses this distribution to collapse the 2 K peak. Kihara et al. also reported experimental specific heats under magnetic fields up to 15 T (= 0.17J), and found that the specific heats show almost no magnetic field dependence, which strongly suggests that the bond-randomness is much stronger than the magnetic fields. For example, our calculated specific heats with 50% randomness reproduce the experimental ones up to about 5 K.

Abstract 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.

The S = 1/2 distorted diamond spin chain with the anisotropic ferromagnetic interaction is investigated using the numerical diagonalization and the level spectroscopy analysis. It is known that the system exhibits a plateau of the magnetization curve at the 1/3 of the saturation. The present study indicates that as the anisotropy is varied the quantum phase transition occurs between two different mechanisms of the 1/3 magnetization plateau. The phase diagram with respect to the anisotropy and the ferromagnetic coupling is also presented.

<title>Abstract</title> We study the <italic>S</italic> = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice by numerical diagonalization method. This system shows various behaviours that are different from that of the Cairo-pentagonal-lattice antiferromagnet. The ground-state energy without magnetic field and the magnetization process of this system are reported. Magnetization plateaux appear at one-ninth height of the saturation magnetization, at one-third height, and at seven-ninth height. The magnetization plateaux at one-third and seven-ninth heights come from interactions linking the sixfold-coordinated spin sites. A magnetization jump appears from the plateau at one-ninth height to the plateau at one-third height. Another magnetization jump is observed between the heights corresponding to the one-third and seven-ninth plateaux; however the jump is away from the two plateaux, namely, the jump is not accompanied with any magnetization plateaux. The jump is a peculiar phenomenon that has not been reported.

We synthesized a kagome fluoride Cs2LiTi3F12 with S = 1/2 spins, and studied magnetic properties of the compound. The temperature dependence of the magnetic susceptibility indicates that it has dominant antiferromagnetic interactions and that it has no magnetic order down to 2 K. We found two magnetization plateaus in its magnetization process approximately at 1/3 and 0.8 mu(B) per Ti. The monoclinic crystal structure gives four inequivalent nearest-neighbor exchange interactions. Our density functional theory calculations suggest that three of them are antiferromagnetic and one of them is weakly ferromagnetic, resulting in a magnetic system composed of antiferromagnetically coupled linear chains and Delta chains. This explains the observed suppression of magnetic order. Numerical diagonalization gives a magnetization curve in good agreement with the experimental results.

The one-dimensional Heisenberg antiferromagnets of large-integer-S spins are studied; their Haldane gaps are estimated by the numerical diagonalization method for S = 5 and 6. We successfully obtain a monotonically increasing sequence of finite-size energy difference data corresponding to the Haldane gaps from the huge-scale parallel calculations of diagonalization under the twisted boundary condition and create a monotonically decreasing sequence within the range of system sizes treated in this study from the monotonically increasing sequence. Consequently, the gaps for S = 5 and 6 are estimated to be 0.000050 +/- 0.000005 and 0.0000030 +/- 0.0000005, respectively. The asymptotic formula of the Haldane gap for S -> infinity is examined from the new estimates to determine the coefficient in the formula more precisely.

We investigate the connection between highly frustrated kagome based Hamiltonians and a recently synthesized family of materials containing Ti3+ S = 1/2 ions. Employing a combination of all electron density functional theory and numerical diagonalization techniques, we establish the Heisenberg Hamiltonians for the distorted kagome antiferromagnets Rb2NaTi3F12, Cs-2 NaTi3F12, and Cs-2 KTi3F12. We determine magnetization curves in excellent agreement with experimental observations. Our calculations successfully clarify the relationship between the experimental observations and the magnetization-plateau behavior at 1/3 height of the saturation and predict characteristic behaviors under fields that are higher than the experimentally measured region. We demonstrate that the studied Ti(III) family of materials interpolates between the kagome strip and kagome lattice.

The Shastry-Sutherland model-the S = 1/2 Heisenberg antiferromagnet on the square lattice accompanied by orthogonal dimerized interactions-is studied by the numerical-diagonalization method. Large-scale calculations provide results for larger clusters that have not been reported yet. The present study successfully captures the phase boundary between the dimer and plaquette-singlet phases and clarifies that the spin gap increases once when the interaction forming the square lattice is increased from the boundary. Our calculations strongly suggest that in addition to the edge of the dimer phase given by J(2)/J(1) similar to 0.675 and the edge of the Neel-ordered phase given by J(2)/J(1) similar to 0.76, there exists a third boundary ratio J(2)/J(1) similar to 0.70 that divides the intermediate region into two parts, where J(1) and J(2) denote dimer and square-lattice interactions, respectively.

The Haldane gap of the S = 2 Heisenberg antiferromagnet in a one-dimensional linear chain is examined by a numerical-diagonalization method. A precise estimate for the magnitude of the gap is successfully obtained by a multistep convergence-acceleration procedure applied to finite-size diagonalization data under the twisted boundary condition.

The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice is studied by the numerical-diagonalization method. This lattice is obtained by the combination of the Lieb lattice and the square lattice. It is known that when interaction on the square lattice is increased from the ferrimagnetic limit of strong interaction on the Lieb lattice, this system shows gradual decrease and disappearance of spontaneous magnetization in the ground state. The present study treats the region near the case of the square-lattice antiferromagnet accompanied by isolated spins by numerical-diagonalization calculations of finite-size clusters with the maximum size of 39 sites. Our numerical results suggest the existence of a new phase with small but nonzero spontaneous magnetization between two zero-spontaneous-magnetization phases. (c) 2018 Author(s).

The S=1/2 kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.

The spin-1/2 triangular-lattice Heisenberg antiferromagnet with a-Type distortion is studied by the numerical-diagonalization method. We examine this model between the two cases, one is the undistorted triangular lattice and the other is the model on the honeycomb lattice with isolated spins. When the distortion is controlled, we find a nontrivial region where the ground states shows spontaneous magnetization the magnitude increases gradually as the distortion is larger and is smaller than one third of the saturated magnetization.

The S=1/2 kagome-lattice antiferromagnet is investigated using the numerical diagonalization of finite-size clusters. The analysis of the susceptibility at the zero magnetization indicates that the magnetic excitation of the system is gapless. It is consistent with our previous finite-scaling analysis of the spin gap. The application of the method for the triangular-lattice antiferromagnet confirms the validity of the analysis.

The magnetization process of the spin-1/2 antiferromagnetic Heisenberg model on two-dimensional square-kagome lattice is studied theoretically. The metamagnetic jumps exist in the magnetization process at the higher edge of the 1/3 and 2/3 plateaus. The parameter-dependencies of the critical field and the magnitude of the magnetization jump at the higher edge of the 1 /3 plateau are obtained by using the approximated state in the unit cell and compared with the numerical results of the exact diagonalization of 42 sites.

The S = 1=2 triangular-lattice Heisenberg antiferromagnet with distortion is investigated by the numerical-diagonalization method. The examined distortion type is √3 x √3. We study the case when the distortion connects the undistorted triangular lattice and the dice lattice. For the intermediate phase reported previously in this system, we obtain results of the boundaries of the intermediate phase for a larger system than those in the previous report and examine the system size dependence of the boundaries in detail. We also report the specific heat of this system, which shows a marked peak structure related to the appearance of the intermediate state.

The S = 1=2 triangular- and kagome-lattice Heisenberg antiferromagnets are investigated under a magnetic field using the numerical-diagonalization method. A procedure is proposed to extract data points with very small finite-size deviations using the numerical-diagonalization results for capturing the magnetization curve. For the triangular-lattice antiferromagnet, the plateau edges at one-third the height of the saturation and the saturation field are successfully estimated. This study additionally presents results of magnetization process for a 45-site cluster of the kagome-lattice antiferromagnet the present analysis suggests that the plateau does not open at one-ninth the height of the saturation.

An S = 1/2 triangular-lattice Heisenberg antiferromagnet with next-nearest-neighbor (NNN) interactions is investigated under a magnetic field by the numerical-diagonalization method. It is known that, in both cases of weak and strong NNN interactions, this system reveals a magnetization plateau at one-third of the saturated magnetization. We examine the stability of this magnetization plateau when the amplitude of NNN interactions is varied. We find that a nonplateau region appears between the plateau phases in the cases of weak and strong NNN interactions.

The S = 1/2 kagome-lattice antiferromagnet is studied using the numerical diagonalization of finite clusters and a finite-size scaling. The susceptibility analysis at the zero magnetization indicates that the system has a gapless spin excitation. It is consistent with our previous finite-size scaling analysis of the spin gap. (C) 2017 Published by Elsevier Ltd.

The ground state of the spin-1/2 Heisenberg antiferromagnet on a distorted triangular lattice is studied using a numerical-diagonalization method. The network of interactions is the root 3 x root 3 type; the interactions are continuously controlled between the undistorted triangular lattice and the dice lattice. We find new states between the nonmagnetic 120-degree-structured state of the undistorted triangular case and the up-up-down state of the dice case. The intermediate states show spontaneous magnetizations that are smaller than one third of the saturated magntization corresponding to the up-up-down state.

The S = 1/2 kagome-lattice antiferromagnet is studied using the numerical diagonalization of finite clusters and a finite-size scaling. The susceptibility analysis at the zero magnetization indicates that the system has a gapless spin excitation. It is consistent with our previous finite-size scaling analysis of the spin gap. (C) 2017 Elsevier Ltd. All rights reserved.

We study the magnetization process of the spin-1/2 Heisenberg antiferromagnet on a distorted square-kagome lattice by the numerical-diagonalization method. The magnetization jump at one-third of the height of the saturation is examined in detail; we find that the jump becomes larger when a small distortion is switched on and that it is accompanied by an abrupt change in lines along microscopic spin directions. Our finite-size results successfully confirm that the magnetization jump in a spin-isotropic system is a macroscopic jump that survives in the thermodynamic limit and that the changes in spin directions are common to a spin-flop phenomenon observed in spin-anisotropic systems.

The S = 1/2 three-leg spin nanotube with the ring exchange interaction at each plaquette is investigated using the numerical diagonalization of finite-size systems. The previous work suggested that the system without the ring exchange interaction has a spin excitation gap between the singlet ground state and the triplet excitation, because a spontaneous dimerization occurs in the ground state. The present study indicates that as the ring exchange increases, a quantum phase transition occurs at some critical value to another spin gap phase where the pattern of the dimerization is different from the initial one. The spin gap is revealed to vanish at the phase boundary. The ground state phase diagram is also presented. (C) 2015 Elsevier B.V. All rights reserved.

The S = 1/2 kagome-lattice antiferromagnet is investigated by the numerical diagonalization of 18-spin finite-size cluster. The matrix elements proportional to the intensity of the singlet--triplet electron spin resonance (ESR) transition are calculated in the presence of the Dzyaloshinsky--Moriya interaction. Some angle-dependent selection rules are also proposed. The present result would be useful to examine whether the kagome-lattice antiferromagnet has a spin gap or not, with the ESR experiment.

The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S = 1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.

To clarify the instability of the ferrimagnetism which is the fundamental magnetism of ferrite, numerical-diagonalization study is carried out for the two-dimensional S = 1/2 Heisenberg antiferromagnet with frustration. We find that the ferrimagnetic ground state has the spontaneous magnetization in small frustration; due to a frustrating interaction above a specific strength, the spontaneous magnetization discontinuously vanishes so that the ferrimagnetic state appears only under some magnetic fields. We also find that, when the interaction is increased further, the ferrimagnetism disappears even under magnetic field. (C) 2015 The Japan Society of Applied Physics

The S=1/2 three-leg quantum spin tube is investigated using the numerical diagonalization. The study indicated a new quantum phase transition between the 1/3 magnetization plateau phase and the plateauless one, with respect to the spin anisotropy. The phase diagram is also presented.

The magnetization process of the S=1/2 kagome-lattice antiferromagnet is investigated using the numerical diagonalization up to 42-spin clusters. The critical exponent analysis confirms the unconventional magnetization behavior around the 1/3 magnetization plateau-like anomaly the field derivative is infinite at the low-field side, while it is zero at the high-field side. We also confirm that a magnetization jump appears at 1/3 of the saturation magnetization in distorted kagome-lattice antiferromagnets.

The S= 1/2 three-leg quantum spin tube is investigated using the numerical diagonalization. The study indicated a new quantum phase transition between the 1/3 magnetization plateau phase and the plateauless one, with respect to the spin anisotropy. The phase diagram is also presented.

The magnetization process of the S=1/2 kagome-lattice antiferromagnet is investigated using the numerical diagonalization up to 42-spin clusters. The critical exponent analysis confirms the unconventional magnetization behavior around the 1/3 magnetization plateau-like anomaly; the field derivative is infinite at the low-field side, while it is zero at the high-field side. We also confirm that a magnetization jump appears at 1/3 of the saturation magnetization in distorted kagome-lattice antiferromagnets.