arXiv subjects
Publications and source records attributed to A. Matsuo.
We show that the Hilbert series of the projective variety $X=P(O_{min}),$ corresponding to the minimal nilpotent orbit $\mathcal O_{min},$ is universal in the sense of Vogel: it is written uniformly for all simple Lie algebras in terms of Vogel's parameters $α,β,γ$ and represents a special case of the generalized hypergeometric function ${}_{4}F_{3}.$ A universal formula for the degree of $X$ is then deduced.
We report magnetization, specific heat, and NMR measurements of 3-Br-4-F-V [=3-(3-bromo-4-fluorophenyl)-1,5-diphenylverdazyl], a strong-rung S=1/2 Heisenberg spin ladder with ferromagnetic leg interactions. We explain the magnetic and thermodynamic properties based on the strong-rung regime. Furthermore, we find a field-induced successive phase transition in the specific heat and the nuclear spin-lattice relaxation rate 1/T1. 19F-NMR spectra for higher- and lower-temperature phases indicate partial magnetic order and incommensurate long-range order, respectively, evidencing the presence of frustration due to weak interladder couplings.
A spin-singlet ground state with a spin gap has been discovered in antiferromagnetic spin chain substances when the spin value is 1/2, 1 or 2. To find spin gap (singlet-triplet) excitations in spin-3/2 chain substances, we performed inelastic neutron scattering and magnetization measurements on {\it R}CrGeO$_5$ ({\it R} = Y or Sm) powders. As expected, we observed spin gap excitations and the dispersion relation of the lowest magnetic excitations. We proved that the spin system of Cr$^{3+}$ was an antiferromagnetic alternating spin-3/2 chain.
We have succeeded in synthesizing single crystals of the verdazyl radical beta-2,6-Cl2-V [= beta-3-(2,6-dichlorophenyl)-1,5-diphenylverdazyl]. The ab initio MO calculation indicated the formation of an S = 1/2 Heisenberg antiferromagnetic chain with four-fold magnetic periodicity consisting of three types of exchange interactions.We have successfully explained the magnetic and thermodynamic properties based on the expected spin model by using the quantum Monte Carlo method. Furthermore, we revealed that the alternating and unique Ising ferromagnetic chains become effective in the specific field regions and observed a cooperative phenomenon caused by the magnetic order and quantum fluctuations. These results demonstrate that verdazyl radical could form unconventional spin model with interesting quantum behavior and provide a new way to study a variety of quantum spin systems.
The magnetic and dielectric properties under high magnetic fields are studied in the single crystal of Cu3Mo2O9. This multiferroic compound has distorted tetrahedral spin chains. The effects of the quasi-one dimensionality and the geometrical spin frustration are expected to appear simultaneously. We measure the magnetoelectric current and the differential magnetization under the pulsed magnetic field up to 74 T. We also measure the electric polarization versus the electric field curve/loop under the static field up to 23 T. Dielectric properties change at the magnetic fields where the magnetization jumps are observed in the magnetization curve. Moreover, the magnetization plateaus are found at high magnetic fields.
Pb2V3O9 was found to have antiferromagnetic alternating chains of S=1/2 and show the antiferromagnetic long range ordered (AFLRO) state under the magnetic field between 4 and 38 T. We succeeded in growing single crystals of Pb2V3O9 by floating zone method and determined the asymmetric H-T phase diagram of Pb2V3O9 from measurements of the magnetization and the heat capacity. Previous reports focused on the AFLRO state in the low magnetic field region and that in high magnetic field region was not discussed so much. In this paper, we examined the AFLRO state in terms of the mean field theory and the picture of Bose-Einstein condensation of magnons to discuss the whole phase diagram. Consequently, the asymmetry of the phase boundary in Pb2V3O9 is explained by the mixing contribution of excited states and by interchain interactions.
The $q$-vertex operators of Frenkel and Reshetikhin are studied by means of a $q$-deformation of the Wakimoto module for the quantum affine algebra $U_q(\widehat{\sl}_2)$ at an arbitrary level $k\ne 0,-2$. A Fock module version of the $q$-deformed primary field of spin $j$ is introduced, as well as the screening operators which (anti-)commute with the action of $U_q(\widehat{\sl}_2)$ up to a total difference of a field. A proof of the intertwining property is given for the $q$-vertex operators corresponding to the primary fields of spin $j\notin {1 \over2}\Z_{\geq0}$, which is enough to treat a general case. A sample calculation of the correlation function is also given.
A Fock representation of the quantum affine algebra $U_q(\widehat{\sl}_2)$ is constructed by three bosonic fields for an arbitrary level with the help of the Drinfeld realization.