30 research outputs found
Spin-Charge Separation in the Model: Magnetic and Transport Anomalies
A real spin-charge separation scheme is found based on a saddle-point state
of the model. In the one-dimensional (1D) case, such a saddle-point
reproduces the correct asymptotic correlations at the strong-coupling
fixed-point of the model. In the two-dimensional (2D) case, the transverse
gauge field confining spinon and holon is shown to be gapped at {\em finite
doping} so that a spin-charge deconfinement is obtained for its first time in
2D. The gap in the gauge fluctuation disappears at half-filling limit, where a
long-range antiferromagnetic order is recovered at zero temperature and spinons
become confined. The most interesting features of spin dynamics and transport
are exhibited at finite doping where exotic {\em residual} couplings between
spin and charge degrees of freedom lead to systematic anomalies with regard to
a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic
fluctuation with a small, doping-dependent energy scale is found, which is
characterized in momentum space by a Gaussian peak at (, ) with
a doping-dependent width (, is the doping
concentration). This commensurate magnetic fluctuation contributes a
non-Korringa behavior for the NMR spin-lattice relaxation rate. There also
exits a characteristic temperature scale below which a pseudogap behavior
appears in the spin dynamics. Furthermore, an incommensurate magnetic
fluctuation is also obtained at a {\em finite} energy regime. In transport, a
strong short-range phase interference leads to an effective holon Lagrangian
which can give rise to a series of interesting phenomena including linear-
resistivity and Hall-angle. We discuss the striking similarities of these
theoretical features with those found in the high- cuprates and give aComment: 70 pages, RevTex, hard copies of 7 figures available upon request;
minor revisions in the text and references have been made; To be published in
July 1 issue of Phys. Rev. B52, (1995
A New Linear Algorithm for Intersecting Convex Polygons
An algorithm is presented that computes the intersection of two convex polygons in linear time. The algorithm is fundamentally different from the only known linear algorithms for this problem, due to Shamos and to Hoey. These algorithms depend on a division of the plane into either angular sectors (Shamos) or parallel slabs (Hoey), and are mildly complex. The authors'algorithm searches for the intersection points of the polygons by advancing a single pointer around each polygon, and is very easy to progra