Evidence of spin liquid with hard-core bosons in a square lattice

We show that laser assisted hopping of hard core bosons in a square optical lattice can be described by an antiferromagnetic $J_{1}$-$J_{2}$ XY model with tunable ratio of $J_{2}/J_{1}$. We numerically investigate the phase diagram of the $J_{1}$-$J_{2}$ XY model using both the tensor network algorithm for infinite systems and the exact diagonalization for small clusters and find strong evidence that in the intermediate region around $$, there is a spin liquid phase with vanishing magnetization and valence bond orders, which interconnects the Neel state on the $J_{2}\ll J_{1}$ side and the stripe antiferromagnetic phase on the $$ side. This finding opens up the possibility of studying the exotic spin liquid phase in a realistic experimental system using ultracold atoms in an optical lattice.Comment: 5 pages, 5 figure

Supersolid and charge density-wave states from anisotropic interaction in an optical lattice

We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well controlled numerical method based on the tensor network algorithm, we calculate phase diagram of the resultant effective Hamiltonian in a two-dimensional square lattice - an anisotropic Hubbard model of hard-core bosons with attractive interaction in one direction and repulsive interaction in the other direction. Besides the conventional superfluid and the Mott insulator states, we find the striped and the checkerboard charge density wave states and the supersolid phase that interconnect the superfluid and the striped solid states. The transition to the supersolid phase has a mechanism different from the case of the soft-core Bose Hubbard model.Comment: 5 pages, 5 figures

MObile Technology for Improved Family Planning: update to randomised controlled trial protocol.

BACKGROUND: This update outlines changes to the MObile Technology for Improved Family Planning study statistical analysis plan and plans for long-term follow-up. These changes result from obtaining additional funding and the decision to restrict the primary analysis to participants with available follow-up data. The changes were agreed prior to finalising the statistical analysis plan and sealing the dataset. METHODS/DESIGN: The primary analysis will now be restricted to subjects with data on the primary outcome at 4-month follow-up. The extreme-case scenario, where all those lost to follow-up are counted as non-adherent, will be used in a sensitivity analysis. In addition to the secondary outcomes outlined in the protocol, we will assess the effect of the intervention on long-acting contraception (implant, intra-uterine device and permanent methods).To assess the long-term effect of the intervention, we plan to conduct additional 12-month follow-up by telephone self-report for all the primary and secondary outcomes used at 4 months. All participants provided informed consent for this additional follow-up when recruited to the trial. Outcome measures and analysis at 12 months will be similar to those at the 4-month follow-up. The primary outcomes of the trial will be the use of an effective modern contraceptive method at 4 months and at 12 months post-abortion. Secondary outcomes will include long-acting contraception use, self-reported pregnancy, repeat abortion and contraception use over the 12-month post-abortion period. DISCUSSION: Restricting the primary analysis to those with follow-up data is the standard approach for trial analysis and will facilitate comparison with other trials of interventions designed to increase contraception uptake or use. Undertaking 12-month trial follow-up will allow us to evaluate the long-term effect of the intervention. TRIAL REGISTRATION: ClinicalTrials.gov NCT01823861

Iterative solution of perturbation equations

Iterative solution of perturbation equation