We present constraints on weakly interacting massive particles (WIMP)-nucleus scattering from the 2013 data of the Large Underground Xenon dark matter experiment, including 1.4×104  kg day of search exposure. This new analysis incorporates several advances: single-photon calibration at the scintillation wavelength, improved event-reconstruction algorithms, a revised background model including events originating on the detector walls in an enlarged fiducial volume, and new calibrations from decays of an injected tritium β source and from kinematically constrained nuclear recoils down to 1.1 keV. Sensitivity, especially to low-mass WIMPs, is enhanced compared to our previous results which modeled the signal only above a 3 keV minimum energy. Under standard dark matter halo assumptions and in the mass range above 4  GeV c−2, these new results give the most stringent direct limits on the spin-independent WIMP-nucleon cross section. The 90% C.L. upper limit has a minimum of 0.6 zb at 33  GeV c−2 WIMP mass.