Minimal effective model and possible high-TcT_{c} mechanism for superconductivity of La3_{3}Ni2_{2}O7_{7} under high pressure

The recent discovery of high-$T_{c}$ superconductivity in bilayer nickelate La$_{3}$Ni$_{2}$O$_{7}$ under high pressure has stimulated great interest concerning its pairing mechanism. We argue that the weak coupling model from the almost fully-filled $d_{z^{2}}$ bonding band cannot give rise to its high $T_{c}$, and thus propose a strong coupling model based on local inter-layer spin singlets of Ni-$d_{z^{2}}$ electrons due to their strong on-site Coulomb repulsion. This leads to a minimal effective model that contains local pairing of $d_{z^{2}}$ electrons and a considerable hybridization with near quarter-filled itinerant $d_{x^{2}-y^{2}}$ electrons on nearest-neighbor sites. The strong coupling between two components provides a composite scenario to achieve high-$T_{c}$ superconductivity. Our theory highlights the importance of the bilayer structure of superconducting La$_{3}$Ni$_{2}$O$_{7}$ and points out a potential route for the exploration of more high-$T_{c}$ superconductors.Comment: 6 pages, 3 figure

Negative entanglement measure for bipartite separable mixed states

We define a negative entanglement measure for separable states which shows that how much entanglement one should compensate the unentangled state at least for changing it into an entangled state. For two-qubit systems and some special classes of states in higher-dimensional systems, the explicit formula and the lower bounds for the negative entanglement measure have been presented, and it always vanishes for bipartite separable pure states. The negative entanglement measure can be used as a useful quantity to describe the entanglement dynamics and the quantum phase transition. In the transverse Ising model, the first derivatives of negative entanglement measure diverge on approaching the critical value of the quantum phase transition, although these two-site reduced density matrices have no entanglement at all. In the 1D Bose-Hubbard model, the NEM as a function of $t/U$ changes from zero to negative on approaching the critical point of quantum phase transition.Comment: 6 pages, 3 figure