Magnetic properties and Mott transition in the Hubbard model on the anisotropic triangular lattice

Magnetic phase diagram and Mott transition are studied in the Hubbard model on the anisotropic triangular lattice at zero temperature and half-filling by the variational cluster approximation, taking into account N\'eel, 120$^\circ$ N\'eel, and collinear orderings. Paramagnetic insulator (spin liquid) is realized above the metallic phase around the isotropic point. In general, this spin liquid state, continuously connected with the metallic state, changes to a magnetic state as the on-site Coulomb repulsion $U$ increases, but it persists up to large $U$ limit in a small window between 120$^\circ$ N\'eel and collinear phases. For very large $U$ another spin liquid state, separated from the metallic state by magnetic states, emerges around a narrow region where both N\'eel and 120$^\circ$ N\'eel orderings are highly suppressed due to the frustration and anisotropy. Implications for the $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ are discussed. As for the Mott transition, the structure of the self-energy in the spectral representation is studied in detail. As $U$ increases around the Mott transition point, single dispersion evolves in the spectral weights of the self-energy which splits the non-interacting band into the upper and lower Hubbard bands.Comment: 10 pages, 10 figures.

Monopole Excitation to Cluster States

We discuss strength of monopole excitation of the ground state to cluster states in light nuclei. We clarify that the monopole excitation to cluster states is in general strong as to be comparable with the single particle strength and shares an appreciable portion of the sum rule value in spite of large difference of the structure between the cluster state and the shell-model-like ground state. We argue that the essential reasons of the large strength are twofold. One is the fact that the clustering degree of freedom is possessed even by simple shell model wave functions. The detailed feature of this fact is described by the so-called Bayman-Bohr theorem which tells us that SU(3) shell model wave function is equivalent to cluster model wave function. The other is the ground state correlation induced by the activation of the cluster degrees of freedom described by the Bayman-Bohr theorem. We demonstrate, by deriving analytical expressions of monopole matrix elements, that the order of magnitude of the monopole strength is governed by the first reason, while the second reason plays a sufficient role in reproducing the data up to the factor of magnitude of the monopole strength. Our explanation is made by analysing three examples which are the monopole excitations to the $0^+_2$ and $0^+_3$ states in $^{16}$O and the one to the $0^+_2$ state in $^{12}$C. The present results imply that the measurement of strong monopole transitions or excitations is in general very useful for the study of cluster states.Comment: 11 pages, 1 figure: revised versio

A new method of determining ∣Vub∣|V_{ub}| by the processes Bˉ→ρlνˉ\bar{B} \to \rho l \bar{\nu} and \bar{B} \to K^* l \lbar

The differential decay width of the process $\bar{B} \rightarrow \rho l \bar{\nu}$ is related to that of the process \bar{B} \rightarrow K^* l \lbar by using $SU(3)$-flavor symmetry and the heavy quark symmetry. The ratio of the Kobayashi-Maskawa matrix elements is obtained in the zero recoil limit of $\rho$ and $K^*$, allowing a determination of $|V_{ub}|$.Comment: Latex file 9 pag

Chiral dynamics of Σ\Sigma-hyperons in the nuclear medium

Using SU(3) chiral perturbation theory we calculate the density-dependent complex mean field $U_\Sigma(k_f)+ i W_\Sigma(k_f)$ of a $\Sigma$-hyperon in isospin-symmetric nuclear matter. The leading long-range $\Sigma N$-interaction arises from one-kaon exchange and from two-pion exchange with a $\Sigma$- or a $\Lambda$-hyperon in the intermediate state. We find from the $\Sigma N\to \Lambda N$ conversion process at nuclear matter saturation density $\rho_0 = 0.16$fm$^{-3}$ an imaginary single-particle potential of $W_\Sigma(k_{f0}) =-21.5$ MeV, in fair agreement with existing empirical determinations. The genuine long-range contributions from iterated (second order) one-pion exchange with an intermediate $\Sigma$- or $\Lambda$-hyperon sum up to a moderately repulsive real single-particle potential of $U_\Sigma(k_{f0})= 59$ MeV. Recently measured $(\pi^-,K^+$) inclusive spectra related to $\Sigma^-$-formation in heavy nuclei give evidence for a $\Sigma$-nucleus repulsion of similar size. Our results suggest that the net effect of the short-range $\Sigma N$-interaction on the $\Sigma$-nuclear mean field could be small.Comment: 7 pages, 2 figures, published in: Phys. Rev. C 71, 068201 (2005

A Parametric Study of the Acoustic Mechanism for Core-Collapse Supernovae

We investigate the criterion for the acoustic mechanism to work successfully in core-collapse supernovae. The acoustic mechanism is an alternative to the neutrino-heating mechanism. It was proposed by Burrows et al., who claimed that acoustic waves emitted by $g$-mode oscillations in proto-neutron stars (PNS) energize a stalled shock wave and eventually induce an explosion. Previous works mainly studied to which extent the $g$-modes are excited in the PNS. In this paper, on the other hand, we investigate how strong the acoustic wave needs to be if it were to revive a stalled shock wave. By adding the acoustic power as a new axis, we draw a critical surface, an extension of the critical curve commonly employed in the context of neutrino heating. We perform both 1D and 2D parametrized simulations, in which we inject acoustic waves from the inner boundary. In order to quantify the power of acoustic waves, we use the extended Myers theory to take neutrino reactions into proper account. We find for the 1D simulations that rather large acoustic powers are required to relaunch the shock wave, since the additional heating provided by the secondary shocks developed from acoustic waves is partially canceled by the neutrino cooling that is also enhanced. In 2D, the required acoustic powers are consistent with those of Burrows et al. Our results seem to imply, however, that it is the sum of neutrino heating and acoustic powers that matters for shock revival.Comment: 20 pages, 19 figures, accepted by Ap

Modified Laplace transformation method and its application to the anharmonic oscillator

We apply a recently proposed approximation method to the evaluation of non-Gaussian integral and anharmonic oscillator. The method makes use of the truncated perturbation series by recasting it via the modified Laplace integral representation. The modification of the Laplace transformation is such that the upper limit of integration is cut off and an extra term is added for the compensation. For the non-Gaussian integral, we find that the perturbation series can give accurate result and the obtained approximation converges to the exact result in the $N \to \infty$ limit ($N$ denotes the order of perturbation expansion). In the case of anharmonic oscillator, we show that several order result yields good approximation of the ground state energy over the entire parameter space. The large order aspect is also investigated for the anharmonic oscillator.Comment: 26 pages including tables, Late