Electronic mechanism of critical temperature variation in RBa_2Cu_3O_(7− δ)

We have performed systematic studies of the trend of the critical temperature T_c due to both Madelung site potential difference between in-plane oxygen and copper sites ΔV_M and interlayer effect in the optimally doped 123 superconductors RBa_2Cu_3O_(7−δ). ΔV_M is found to decrease with the increase of the trivalent rare-earth ionic radius r_(R^(3^+)). This change enhances the next-nearest-neighbor hopping integral t′, which results in the experimentally observed increase of T_c with r_(R^(3^+)). The coherent interlayer single-particle hopping t_⊥ has a more profound effect than t′ on the nearly linear trend of T_c as a function of r_(R^(3^+)). These results reveal the importance of the electronic origin of the rare-earth ionic size effect on T_c in this family

Small protein number effects in stochastic models of autoregulated bursty gene expression

A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large such that fluctuations in protein numbers due to reversible protein-promoter binding can be ignored. Here we derive an alternative model that takes into account these fluctuations and hence can be used to study low protein number effects. The exact steady-state protein number distributions is derived as a sum of Gaussian hypergeometric functions. We use the theory to study how promoter switching rates and the type of feedback influence the size of protein noise and noise-induced bistability. Furthermore we show that our model predictions for the protein number distribution are significantly different from those of Kumar et al. when the protein mean is small, gene switching is fast, and protein binding is faster than unbinding.Comment: 30 pages, 10 figure

Gapped spin liquid with Z2\mathbb{Z}_2-topological order for kagome Heisenberg model

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the $\mathbb{Z}_2$-topological order (or toric code type), which has a long correlation length $\xi\sim 10$ unit cell length. We justify that the TRG method can handle very large systems with over thousands of spins. Such a long $\xi$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than 10 unit cell length. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.Comment: 10 pages, 7 figure