Timelike Entanglement Entropy from Rindler Method

For a Lorentzian invariant theory, the entanglement entropy should be a function of the dependence of domain of the subregion under consideration. More precisely, it should be a function of the dependence of domain and the appropriate cut-off. In this paper, we define the concept of cut-off to make it applicable to timelike regions and assume that the usual entanglement entropy formula also applies to timelike intervals. Using the Rindler method, the timelike entanglement entropy can be regarded as the thermal entropy of the CFT after the Rindler transformation plus a constant $ic\pi/6$ with $c$ the central charge of the CFT. The gravitational dual of the timelike entanglement entropy is finally presented following this method.Comment: 14 pages, 3 figure

The SU(3) bosons and the spin nematic state on the spin-1 bilinear-biquadratic triangular lattice

A bond-operator mean-field theory in the SU(3) bosons representation is developed to describe the antiferro-nematic phase of the spin-1 bilinear-biquadratic model. The calculated static structure factors reveal delicately that the antiferro-nematic state may exhibit both the ferro- and antiferro-quadruple long-range orders, which is reminiscent of the ferrimagnets or the canted antiferromagnets. This result may influence the spin wave theory concerned with this phase. Possible relevance of this unconventional state to the quasi-two-dimensional triangular material NiGa2S4 is addressed.Comment: 8pages, 6figure

Production of proton-rich nuclei around Z=84-90 in fusion-evaporation reactions

Within the framework of the dinuclear system model, production cross sections of proton-rich nuclei with charged numbers of Z=84-90 are investigated systematically. Possible combinations with the $^{28}$Si, $^{32}$S, $^{40}$Ar bombarding the target nuclides $^{165}$Ho, $^{169}$Tm, $^{170-174}$Yb, $^{175,176}$Lu, $^{174,176-180}$Hf and $^{181}$Ta are analyzed thoroughly. The optimal excitation energies and evaporation channels are proposed to produce the proton-rich nuclei. The systems are feasible to be constructed in experiments. It is found that the neutron shell closure of N=126 is of importance during the evaporation of neutrons. The experimental excitation functions in the $^{40}$Ar induced reactions can be nicely reproduced. The charged particle evaporation is comparable with neutrons in cooling the excited proton-rich nuclei, in particular for the channels with $\alpha$ and proton evaporation. The production cross section increases with the mass asymmetry of colliding systems because of the decrease of the inner fusion barrier. The channels with pure neutron evaporation depend on the isotopic targets. But it is different for the channels with charged particles and more sensitive to the odd-even effect.Comment: 15 pages, 10 figures. arXiv admin note: text overlap with arXiv:0803.1117, arXiv:0707.258