Quantum Phase Transitions to Charge Order and Wigner Crystal Under Interplay of Lattice Commensurability and Long-Range Coulomb Interaction

Relationship among Wigner crystal, charge order and Mott insulator is studied by the path-integral renormalization group method for two-dimensional lattices with long-range Coulomb interaction. In contrast to Hartree-Fock results, the solid stability drastically increases with lattice commensurability. The transition to liquid occurs at the electron gas parameter $r_s \sim 2$ for the filling $n=1/2$ showing large reduction from $r_s \sim 35$ in the continuum limit. Correct account of quantum fluctuations are crucial to understand charge-order stability generally observed only at simple fractional fillings and nature of quantum liquids away from them.Comment: 4 pages including 7 figure

Quantum-number projection in the path-integral renormalization group method

We present a quantum-number projection technique which enables us to exactly treat spin, momentum and other symmetries embedded in the Hubbard model. By combining this projection technique, we extend the path-integral renormalization group method to improve the efficiency of numerical computations. By taking numerical calculations for the standard Hubbard model and the Hubbard model with next nearest neighbor transfer, we show that the present extended method can extremely enhance numerical accuracy and that it can handle excited states, in addition to the ground state.Comment: 11 pages, 7 figures, submitted to Phys. Rev.

Absence of Translational Symmetry Breaking in Nonmagnetic Insulator Phase on Two-Dimensional Lattice with Geometrical Frustration

The ground-state properties of the two-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hoppings at half filling are studied by the path-integral-renormalization-group method. The nonmagnetic-insulator phase sandwiched by the the paramagnetic-metal phase and the antiferromagnetic-insulator phase shows evidence against translational symmetry breaking of the dimerized state, plaquette singlet state, staggered flux state, and charge ordered state. These results support that the genuine Mott insulator which cannot be adiabatically continued to the band insulator is realized generically by Umklapp scattering through the effects of geometrical frustration and quantum fluctuation in the two-dimensional system.Comment: 4 pages and 7 figure

Numerical investigations of mechanical stress caused in dendrite by melt convection and gravity

In order to investigate the effects of stress around dendrite neck cased by the convection and gravity on the dendrite fragmentation, the novel numerical model, where phase-field method, Navier-Stokes equations and finite element method are continuously and independently employed, has been developed. By applying the model to the dendritic solidification of Al-Si alloy, the maximum stress variations by melt convection and gravity with dendrite growth were evaluated

Precise estimation of shell model energy by second order extrapolation method

A second order extrapolation method is presented for shell model calculations, where shell model energies of truncated spaces are well described as a function of energy variance by quadratic curves and exact shell model energies can be obtained by the extrapolation. This new extrapolation can give more precise energy than those of first order extrapolation method. It is also clarified that first order extrapolation gives a lower limit of shell model energy. In addition to the energy, we derive the second order extrapolation formula for expectation values of other observables.Comment: PRC in pres

Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for κ\kappa-(ET)2_2Cu2(CN)3_2(CN)_3

We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for $\kappa$-type BEDT-TTF compounds. In contrast with mean-field predictions, path-integral renormalization group calculations show a universal presence of nonmagnetic insulator sandwitched by antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does not show a simple translational symmetry breakings such as flux phases, implying a genuine Mott insulator. We discuss possible relevance on the nonmagnetic insulating phase found in $\kappa$-(ET)$_2$Cu$_2(CN)_3$.Comment: 4pages including 7 figure

Thermodynamic Relations in Correlated Systems

Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they relate several thermodynamic quantities to the slope of the metal-insulator phase boundary drawn in the plane of the chemical potential and the Coulomb interaction in the phase diagram of the Hubbard model. The relations impose constraints on the critical properties of the Mott transition. These thermodynamic relations are indeed confirmed to be satisfied in the cases of the one- and two-dimensional Hubbard models. One of these relations yields that at the continuous Mott transition with a diverging charge compressibility, the doublon susceptibility also diverges. The constraints on the shapes of the phase boundary containing a first-order metal-insulator transition at finite temperatures are clarified based on the thermodynamic relations. For example, the first-order phase boundary is parallel to the temperature axis asymptotically in the zero temperature limit. The applicability of the thermodynamic relations are not restricted only to the metal-insulator transition of the Hubbard model, but also hold in correlated systems with any types of phases in general. We demonstrate such examples in an extended Hubbard model with intersite Coulomb repulsion containing the charge order phase.Comment: 10 pages, 9 figure

From Display to Labelled Proofs for Tense Logics

We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt

Kernels for graphs

This chapter contains sections titled: Introduction, Label Sequence Kernel between Labeled Graphs, Experiments, Related Works, Conclusion

A Hamiltonian-based solution to the mixed sensitivity optimization problem for stable pseudorational plants

This paper considers the mixed sensitivity optimization problem for a class of infinite-dimensional stable plants. This problem is reducible to a two- or one-block H∞ control problem with structured weighting functions. We first show that these weighting functions violate the genericity assumptions of existing Hamiltonian-based solutions such as the well-known Zhou-Khargonekar formula. Then, we derive a new closed form formula for the computation of the optimal performance level, when the underlying plant structure is specified by a pseudorational transfer function. © 2005 Elsevier B.V. All rights reserved