Yoshiyuki Fukumoto

Theory of the Superconductivity of MgB2

We consider MgB 2 to be a structure-dependent superconductor, the B 2 plane of the MgB 2 crystal to be superconducting and the Mg plane to be a tunneling junction plane between the B 2 planes. We set up the superconducting interaction within the B 2 plane between two adjacent planes and the coupling pair interactions in the perpendicular direction of the B 2 plane. Using the mean field approximation for the equation of motion of the superconducting electron, we solve the Green function of the electron and obtain the order parameters Δ∥(T) and Δ⊥(T) of the intra B 2 plane and inter B 2 plane electrons, respectively. It is found that these two order parameters have the same T c with an appropriate choice of model parameters. Our gap function in the form Δ∥ + const × Δ⊥ cos q, where q represents the momentum along the c-axis direction, leads to a two-peak structure in the density of states, which explains the experimental measurement of two gaps in MgB 2 . The bulk properties of the specific heat, the NMR and the thermal conductivity are also calculated.

Theoretical study of quantum spin icosidodecahedron (S = 1=2) with next-nearest neighbor interactions and analysis of experimental susceptibility for Mo72V30

We study integrated density of states (DOS) and thermodynamic properties for the S = 1=2 quantum spin icosidodecahedron, using a numerical method for calculating an eigenvalue distribution function. For the ideal quantum spin icosidodecahedron with next-nearest neighbor interactions, we find that there exist many singlet states before the first triplet state, which is an evidence of the resonating valence bond (RVB) state, and the experimental susceptibilities of Mo72V30 measured by Muller et al. and Botar et al. cannot be reproduced within the ideal model. Because V4+ ions are on vertices of a slightly distorted icosidodecahedron in Mo72V30, we study the distorted version of the model and find that agreement between theoretical and experimental susceptibilities is improved. For this distorted model, there exist about ten singlet states before the first triplet state.

Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like-Decorated Square Lattice

We study the ground-state phase diagram of a Heisenberg model with spin S = 1/2 on a diamond-like-decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the length of the diagonal bond to that of the other four edges determines the strength of frustration. It has been pointed out [J. Phys. Soc. Jpn 85, 033705 (2016)] that the so-called tetramer–dimer states, which are expected to be stabilized in an intermediate region of λc < λ < 2, are identical to the square-lattice dimer-covering states, which ignited renewed interest in high-dimensional diamond-like-decorated lattices. In order to determine the phase boundary λc, we employ the modified spin wave method to estimate the energy of the ferrimagnetic state and obtain λc = 0.974. Furthermore, our numerical diagonalization study suggests that other cluster states do not appear in the ground-state phase diagram.

Exact Solutions on the Ground States of Ising Models in Magnetic Fields with Frustration on a Diamond Hierarchical Lattice

Abstract Magnetization processes of Ising models with frustration on diamond hierarchical lattices, which contain vertices with high coordination numbers, are exactly obtained at zero temperature. In antiferromagnetic systems, the magnetization cannot saturate under finite magnetic fields owing to the competition between the antiferromagnetic and Zeeman interactions and the intrinsic long-range nature of hierarchical lattices. For the zero-field classical spin-liquid phase found in [Kobayashi et al., J. Phys. Soc. Jpn. 78, 074004 (2009)], an infinitely small applied magnetic field can induce an infinitely small magnetization, despite Ising models that have discrete energy levels. By examining the structure of the partition function, we obtain the ground state spinconfigurations and clarify the mechanism of the “gapless like behavior”.

Superconductivity in the Three-Fold Charge-Ordered Metal of the Triangular-Lattice Extended Hubbard Model

The quarter-filling extended Hubbard model on the triangular lattice is studied to explore pairing instability in the three-fold charge-ordered (CO) metal. We derive a second-order strong-coupling ...

Ground-State Phase Diagram of the XXZ Model on a Railroad–Trestle Lattice with Asymmetric Leg Interactions

Using the bosonization and level spectroscopy methods, we study the ground-state phase diagram of a X X Z antiferromagnet on a railroad–trestle lattice with asymmetric leg interactions. It is shown that the asymmetry does not change the dimer/Neel transition line significantly, which agrees with the expectation based on a naive bosonization procedure, but it does change the dimer/spin-fluid transition line. To understand this observation, we analyze eigenvectors of the ground state, dimer excitation, doublet excitation and Neel excitation, and find that only the doublet excitation is affected by the asymmetric interaction.

Thermodynamic Properties of the Transverse-Crystal-Field Ising Model on a Δ Chain: — Three Peak Structure in the Specific Heat —

The specific heat of the S = 1 transverse-crystal-field Ising model with an antiferromagnetic exchange interaction J on a Δ-chain is studied by using the exact-diagonalization, quantum Monte Carlo and finite-temperature Lanczos methods. We find that when the strength of the transverse crystal field Γ is chosen to be sufficiently small, the specific heat exhibits a three-peak structure as a function of temperature, with peaks at T ∼ 0.05Γ, 0.2F and 0.7J. In addition to the two energy scales Γ and J, a new energy scale ∼ 0.1 x F appears due to the geometrical frustration and the existence of the S z = 0 states in the present system.

Ground-state properties of spin-1/2 Heisenberg antiferromagnets with frustration on the diamond-like-decorated square and triangular lattices

We study the ground-state phase diagrams and properties of spin-1/2 Heisenberg models on the diamond-like-decorated square and triangular lattices. The diamond-like-decorated square (triangular) lattice is a lattice in which the bonds of a square (triangular) lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the strength of the diagonal bond to that of the other four edges determines the ground-state properties. In particular, the macroscopically degenerated tetramer-dimer states, which are equivalent to the dimer covering states of the original lattices, are stabilized for λc < λ < 2, where the value of λc depends on the lattices. To determine the phase diagrams and boundaries λc, we employ the modified spin wave (MSW) method and the quantum Monte Carlo (QMC) method to estimate the ground-state energies of the ferrimagnetic states for λ < λc, where we can consider the mixed spin-1 and spin-1/2 Lieb-lattice and triangular Lieb-lattice Heisenberg antiferromagnets instead, and obtain λc(square)=0.974 and λc(triangular)=0.988. We also calculate the long-range order (LRO) parameters using the MSW and QMC methods and find the scaling relations where the spin reductions of each sublattice are inversely proportional to the number of sublattice sites. We prove these scaling relations by applying an infinitesimal uniform magnetic field. Furthermore, by examining the calculation process in the MSW, we clarify the mathematical structure behind the scaling relations for the sublattice LROs.We study the ground-state phase diagrams and properties of spin-1/2 Heisenberg models on the diamond-like-decorated square and triangular lattices. The diamond-like-decorated square (triangular) lattice is a lattice in which the bonds of a square (triangular) lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the strength of the diagonal bond to that of the other four edges determines the ground-state properties. In particular, the macroscopically degenerated tetramer-dimer states, which are equivalent to the dimer covering states of the original lattices, are stabilized for λc < λ < 2, where the value of λc depends on the lattices. To determine the phase diagrams and boundaries λc, we employ the modified spin wave (MSW) method and the quantum Monte Carlo (QMC) method to estimate the ground-state energies of the ferrimagnetic states for λ < λc, where we can consider the mixed spin-1 and spin-1/2 Lieb-lattice and triangular...

Novel constructive method for the quantum dimer model in spin-1/2 Heisenberg antiferromagnets with frustration on a diamond-like-decorated square lattice

We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice. The diamond-like-decorated square lattice is a lattice in which the bonds in a square lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the diagonal bond strength to that of the other four edges controls the frustration strength. For 0.974 0) and repulsive interaction between dimers (v > 0). This suggests the possibility of realizing the resonating valence bond (RVB) state because the RVB state is obtained at v = |t|, which is known as the RK point.We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated square lattice. The diamond-like-decorated square lattice is a lattice in which the bonds in a square lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the diagonal bond strength to that of the other four edges controls the frustration strength. For 0.974 < λ < 2, the present system has a nontrivial macroscopic degeneracy, which is called the macroscopically degenerated tetramer-dimer (MDTD) states. The MDTD states are identical to the Hilbert space of the Rokhsar–Kivelson (RK) quantum dimer model (QDM). By introducing further neighbor couplings in the MDTD states, we calculate the second-order effective Hamiltonian, which is exactly the same as the square-lattice QDM with a finite hopping amplitude t and dimer-dimer interaction v. Furthermore, we calculate v/|t| as a function of the ratio λ in the Heisenberg model and examine which phases of the sq...

An Exact Calculation of the Transverse Susceptibility for an Antiferromagnetic Ising Δ Chain

We study the transverse susceptibility of the fully frustrated antiferromagnetic Ising