Picard-Fuchs Equations and Whitham Hierarchy in N=2 Supersymmetric SU(r+1) Yang-Mills Theory

In general, Whitham dynamics involves infinitely many parameters called Whitham times, but in the context of N=2 supersymmetric Yang-Mills theory it can be regarded as a finite system by restricting the number of Whitham times appropriately. For example, in the case of SU(r+1) gauge theory without hypermultiplets, there are r Whitham times and they play an essential role in the theory. In this situation, the generating meromorphic 1-form of the Whitham hierarchy on Seiberg-Witten curve is represented by a finite linear combination of meromorphic 1-forms associated with these Whitham times, but it turns out that there are various differential relations among these differentials. Since these relations can be written only in terms of the Seiberg-Witten 1-form, their consistency conditions are found to give the Picard-Fuchs equations for the Seiberg-Witten periods.Comment: to be published in J. Math. Phys, revtex, 14 page

Chemical potential shift in La(1-x)Sr(x)MnO(3): Photoemission test of the phase separation scenario

We have studied the chemical potential shift in La(1-x)Sr(x)MnO(3) as a function of doped hole concentration by core-level x-ray photoemission. The shift is monotonous, which means that there is no electronic phase separation on a macroscopic scale, whereas it is consistent with the nano-meter scale cluster formation induced by chemical disorder. Comparison of the observed shift with the shift deduced from the electronic specific heat indicates that hole doping in La(1-x)Sr(x)MnO(3) is well described by the rigid-band picture. In particular no mass enhancement toward the metal-insulator boundary was implied by the chemical potential shift, consistent with the electronic specific heat data.Comment: 7 pages, 3 figures, to be published in Europhysics Letter

Ground states with cluster structures in a frustrated Heisenberg chain

We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interactions which frustrate each other. The system undergoes phase changes when the ratio $\lambda$ between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of $\lambda$ in the S=1/2 case. For S=1/2 we show that there are three ground state phases and determine their boundaries.Comment: 4 pages, uses revtex.sty, 2 figures available on request from [email protected], to be published in J. Phys.: Cond. Mat

Spin Gap of Two-Dimensional Antiferromagnet Representing CaV4_4O9_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 $\Delta \sim 0.2J_e \simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.Comment: 12 pages of LaTex, 4 figures availavule upon reques