Unifying Description of Competing Orders in Two Dimensional Quantum Magnets

Quantum magnets provide the simplest example of strongly interacting quantum matter, yet they continue to resist a comprehensive understanding above one spatial dimension (1D). In 1D, a key ingredient to progress is Luttinger liquid theory which provides a unified description. Here we explore a promising analogous framework in two dimensions, the Dirac spin liquid (DSL), which can be constructed on several different lattices. The DSL is a version of Quantum Electrodynamics ( QED$_3$) with four flavors of Dirac fermions coupled to photons. Importantly, its excitations also include magnetic monopoles that drive confinement. By calculating the complete action of symmetries on monopoles on the square, honeycomb, triangular and kagom\`e lattices, we answer previously open key questions. We find that the stability of the DSL is enhanced on the triangular and kagom\`e lattices as compared to the bipartite (square and honeycomb) lattices. We obtain the universal signatures of the DSL on the triangular and kagom\`e lattices, including those that result from monopole excitations, which serve as a guide to numerics and to experiments on existing materials. Interestingly, the familiar 120 degree magnetic orders on these lattices can be obtained from monopole proliferation. Even when unstable, the Dirac spin liquid unifies multiple ordered states which could help organize the plethora of phases observed in strongly correlated two-dimensional materials.Comment: 13+9 pages, 7 figure

The Innovation and Cultural Value of the Rebirth Motif in Network Fantasy Novels

The writing of rebirth motif in network fantasy novels draws on the cultural connotations inherited from ancient times, and links them closely to the reality and culture of the times in which they are written. This article explores the innovation of the rebirth motif in network fantasy novels from two aspects, the trigger mechanism and the mode of rebirth, and clarifies the transformation of contemporary thinking and cultural values reflected behind it

The Age-Redshift Relationship of Old Passive Galaxies

We use 32 age measurements of passively evolving galaxies as a function of redshift to test and compare the standard model ($\Lambda$CDM) with the $R_{\rm h}=ct$ Universe. We show that the latter fits the data with a reduced $\chi^2_{\rm dof}=0.435$ for a Hubble constant $H_{0}= 67.2_{-4.0}^{+4.5}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$. By comparison, the optimal flat $\Lambda$CDM model, with two free parameters (including $\Omega_{\rm m}=0.12_{-0.11}^{+0.54}$ and $H_{0}=94.3_{-35.8}^{+32.7}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$), fits the age-\emph{z} data with a reduced $\chi^2_{\rm dof}=0.428$. Based solely on their $\chi^2_{\rm dof}$ values, both models appear to account for the data very well, though the optimized $\Lambda$CDM parameters are only marginally consistent with those of the concordance model ($\Omega_{\rm m}=0.27$ and $H_{0}= 70$ km $\rm s^{-1}$ $\rm Mpc^{-1}$). Fitting the age-$z$ data with the latter results in a reduced $\chi^2_{\rm dof}=0.523$. However, because of the different number of free parameters in these models, selection tools, such as the Akaike, Kullback and Bayes Information Criteria, favour $R_{\rm h}=ct$ over $\Lambda$CDM with a likelihood of $\sim 66.5\%-80.5\%$ versus $\sim 19.5\%-33.5\%$. These results are suggestive, though not yet compelling, given the current limited galaxy age-$z$ sample. We carry out Monte Carlo simulations based on these current age measurements to estimate how large the sample would have to be in order to rule out either model at a $\sim 99.7\%$ confidence level. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim 45$ galaxy ages would be sufficient to rule out $R_{\rm h}=ct$ at this level of accuracy, while $\sim 350$ galaxy ages would be required to rule out $\Lambda$CDM if the real Universe were instead $R_{\rm h}=ct$.Comment: 36 pages, 13 figures, 1 table; accepted for publication in The Astronomical Journal. arXiv admin note: text overlap with arXiv:1405.238