Lower Bounds of Concurrence for Multipartite States

We study the entanglement of multipartite quantum states. Some lower bounds of the multipartite concurrence are reviewed. We further present more effective lower bounds for detecting and qualifying entanglement, by establishing functional relations between the concurrence and the generalized partial transpositions of the multipartite systems.Comment: 13 page

Measuring dark matter-neutrino relative velocity on cosmological scales

We present a new method to measure neutrino masses using the dark matter-neutrino relative velocity. The relative motion between dark matter and neutrinos results in a parity-odd bispectrum which can be measured from cross-correlation of different cosmic fields. This new method is not affected by most systematics which are parity even and not limited by the knowledge of optical depth to the cosmic microwave background. We estimate the detectability of the relative velocity effect and find that the minimal sum of neutrino masses could be detected at high significance with upcoming surveys.Comment: 6 pages, 2 figures, 1 table, published versio

Topological phase transition from nodal to nodeless d-wave superconductivity in electron-doped cuprate superconductors

Unlike the hole-doped cuprates, both nodal and nodeless superconductivity (SC) are observed in the electron-doped cuprates. To understand these two types of SC states, we propose a unified theory by considering the two-dimensional t-J model in proximity to an antiferromagnetic (AF) long-range ordering state. Within the slave-boson mean-field approximation, the d-wave pairing symmetry is still the most energetically favorable even in the presence of the external AF field. In the nodal phase, it is found that the nodes carry vorticity and are protected by the adjoint symmetry of time-reversal and one unit lattice translation. Robust edge modes are obtained, suggesting the nodal d-wave SC being a topological weak-pairing phase. As decreasing the doping concentration or increasing the AF field, the nodes with opposite vorticity annihilate and the nodeless strong-pairing phase emerges. The topological phase transition is characterized by a critical point with anisotropic Bogoliubov quasiparticles, and a universal understanding is thus established for all electron-doped cuprates.Comment: 7 pages, 5 figures; published versio