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

Exploring the total Galactic extinction with SDSS BHB stars

Aims: We used 12,530 photometrically-selected blue horizontal branch (BHB) stars from the Sloan Digital Sky Survey (SDSS) to estimate the total extinction of the Milky Way at the high Galactic latitudes, $R_V$ and $A_V$ in each line of sight. Methods: A Bayesian method was developed to estimate the reddening values in the given lines of sight. Based on the most likely values of reddening in multiple colors, we were able to derive the values of $R_V$ and $A_V$. Results: We selected 94 zero-reddened BHB stars from seven globular clusters as the template. The reddening in the four SDSS colors for the northern Galactic cap were estimated by comparing the field BHB stars with the template stars. The accuracy of this estimation is around 0.01\,mag for most lines of sight. We also obtained $$ to be around 2.40$\pm1.05$ and $A_V$ map within an uncertainty of 0.1\,mag. The results, including reddening values in the four SDSS colors, $A_V$, and $R_V$ in each line of sight, are released on line. In this work, we employ an up-to-date parallel technique on GPU card to overcome time-consuming computations. We plan to release online the C++ CUDA code used for this analysis. Conclusions: The extinction map derived from BHB stars is highly consistent with that from Schlegel, Finkbeiner & Davis(1998). The derived $R_V$ is around 2.40$\pm1.05$. The contamination probably makes the $R_V$ be larger.Comment: 16 pages, 13 figures, 4 tables, accepted for publication in A&