Some New Results Concerning the Primal-Dual Path-Following Interior Point Algorithm for Linear Programming

The Primal-Dual (PD) path-following interior point algorithm for solving Linear Programming (LP) problems is considered. Firstly, we investigate its convergence and complexity properties when a new long-step linesearch procedure suggested by M. J. D.Powell is employed. Assuming that a primal-dual strictly feasible starting point is available and that the centring parameters are bounded away from zero, we show that the duality gap of the iterates tends to zero, thereby proving that the limit points of the sequence of iterates are solutions of the {LP} problem. Further, we consider whether the limit points of the sequence of iterates generated by some long-step variants of the {PD} algorithm coincide with the analytic centre of the primal-dual solution set of the problem. Because of the difficulty of the analysis involved, we restrict attention to the case when the standard form of the {LP} problem has one equality constraint and multiple solutions. We find that, when the centring parameters are bounded away from zero, the sequence of iterates does converge to the analytic centre. When the centring parameters tend to zero asymptotically at the same rate as the duality gap of the iterates, however, we show that in exact arithmetic the sequence of iterates may have other limit points in the solution set.\ud \ud The author was supported through grant GR/S34472 from the Engineering and Physical Sciences Research Council of the U

Slater to Mott crossover in the metal to insulator transition of Nd2Ir2O7

We present an angle-resolved photoemission study of the electronic structure of the three-dimensional pyrochlore iridate Nd2Ir2O7 through its magnetic metal-insulator transition. Our data reveal that metallic Nd2Ir2O7 has a quadratic band, touching the Fermi level at the Gamma point, similarly to that of Pr2Ir2O7. The Fermi node state is, therefore, a common feature of the metallic phase of the pyrochlore iridates. Upon cooling below the transition temperature, this compound exhibits a gap opening with an energy shift of quasiparticle peaks like a band gap insulator. The quasiparticle peaks are strongly suppressed, however, with further decrease of temperature, and eventually vanish at the lowest temperature, leaving a non-dispersive flat band lacking long-lived electrons. We thereby identify a remarkable crossover from Slater to Mott insulators with decreasing temperature. These observations explain the puzzling absence of Weyl points in this material, despite its proximity to the zero temperature metal-insulator transition

Doping dependence of the vortex glass and sublimation transitions in the high-TcT_{c} superconductor La2−x_{2-x}Srx_{x}CuO4_{4} as determined from macroscopic measurements

Magnetization and ac-susceptibility measurements are used to characterize the mixed phase of the high-temperature cuprate superconductor La$_{2-x}$Sr$_{x}$CuO$_{4}$ over a large range of doping (0.075 $\leq x\leq$ 0.20). The first order vortex lattice phase transition line $H_{FOT}(T)$, the upper critical field $H_{c2}(T)$ and the second peak $H_{sp}(T)$ have been investigated up to high magnetic fields (8 Tesla applied perpendicular to the $CuO_2$ planes). Our results reveal a strong doping dependence of the magnetic phase diagram, which can mainly be explained by the increasing anisotropy with underdoping. Within our interpretation, the first order vortex lattice phase transition is due to the sublimation (rather than melting) of the vortex lattice into a gas of pancake vortices, whereas the second peak is related to the transition to a more disordered vortex glass state.Comment: 7 pages, 5 figure