Spin Gap in Two-Dimensional Heisenberg Model for CaV4_4O9_9

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.Comment: 8 pages, 6 figures available upon request (Revtex

An Efficient Algorithm for a Bicriteria Single-Machine Scheduling Problem

This paper considers a single-machine scheduling problem in which the maximum tardiness and the total flowtime are two objectives to be minimized. Instead of enumerating all efficient schedules, the author considers the problem of minimizing the maximum of the weighted values of these two objective functions, which arises in interactive multicriteria decision making. The author proposes a strongly polynomial algorithm for this problem which runs in O(n^2 log n) time

An Epsilon-Approximation Scheme for Minimum Variance Combinatorial Problems

Suppose that we are given a finite set E, a family of feasible subsets of E and an integer cost associated with each element in E. The author considers the problem of finding a feasible subset such that the variance among the costs of elements in the subset is minimized. The author shows that if one can solve the corresponding minimum cost problem in polynomial time, it is possible to construct a fully polynomial time approximation scheme for the above minimum variance problem

An Efficient Algorithm for Bicriteria Minimum-Cost Circulation Problem

This paper is concerned with a bicriteria minimum-cost circulation problem which arises in interactive multicriteria decision making. The author presents a strongly polynomial algorithm for this problem, that is achieved by making use of the parametric characterization of optimal solutions and a strongly polynomial algorithm for the single objective minimum-cost circulation problem

An (*e-Approximation Scheme for Minimum Variance Resource Allocation Problems

The minimum variance resource allocation problem asks to allocate a given amount of discrete resource to a given set of activities so that the variance of the profits among activities is minimized. The author presents a fully polynomial time approximation scheme for this problem

Phase diagram of depleted Heisenberg model for CaV4O9

We have numerically investigated the 1/5-depleted Heisenberg square lattice representing CaV4O9 using the Quantum Monte Carlo loop algorithm. We have determined the phase diagram of the model as a function of the ratio of the two different couplings: bonds within a plaquette and dimer bonds between plaquettes. By calculating both the spin gap and the staggered magnetization we determine the range of stability of the long range ordered (LRO) phase. At isotropic coupling LRO survives the depletion. But the close vicinity of the isotropic point to the spin gap phase leads us to the conclusion that already a small frustrating next nearest neighbor interaction can drive the system into the quantum disordered phase and thus explain the spin gap behavior of CaV4O9

Magnetic Susceptibility for CaV4O9CaV_4O_9

We examine experimental magnetic susceptibility $\chi^{tot}(T)$ for CaV$_4$O$_9$ by fitting with fitting function $\alpha \chi^{mag}(T) + c$. The function $\chi^{mag}(T)$ is a power series of 1/T and the lowest order term is fixed as $C/T$, where $C$ is the Curie constant as determined by the experimental $g$-value (g=1.96). Fitting parameters are $\alpha$, $c$ and expansion coefficients except for the first one in $\chi^{mag}(T)$. We determine $\alpha$ and $c$ as $\alpha \simeq$ 0.73 and $c\simeq$ 0 for an experimental sample. We interpret $\alpha$ as the volume fraction of CaV$_4$O$_9$ in the sample and $\chi^{mag}(T)$ as the susceptibility for the pure CaV$_4$O$_9$. The result of $\alpha \ne 1$ means that the sample includes nonmagnetic components. This interpretation consists with the result of a perturbation theory and a neutron scattering experiment.Comment: 4pages, 4figure

Effect of Quantum Fluctuations on Magnetic Ordering in CaV3_3O7_7

We present a theoretical model for CaV$_3$O$_7$: the $1/4$-depleted square spin-$1/2$ Heisenberg model which includes both the nearest-neighbor coupling ($J$) and the next-nearest-neighbor coupling ($J'$), where $J$ and $J'$ are antiferromagnetic. Recent experiments of the neutron diffraction by Harashina et.al. report the magnetic ordering at low temperatures, which may be called as a stripe phase. It is shown that the observed spin structure is not stable in the classical theory. By employing the modified spin wave theory, we show that the stripe phase is stabilized by the quantum fluctuations for $J'/J > 0.69$. In CaV$_3$O$_7$, the coupling constants are estimated as $J \sim J'$ by comparing the theoretical and experimental results.Comment: submitted to J. Phys. Soc. Jp