Fermionic spinon theory of square lattice spin liquids near the N\'eel state

Quantum fluctuations of the N\'eel state of the square lattice antiferromagnet are usually described by a $\mathbb{CP}^1$ theory of bosonic spinons coupled to a U(1) gauge field, and with a global SU(2) spin rotation symmetry. Such a theory also has a confining phase with valence bond solid (VBS) order, and upon including spin-singlet charge 2 Higgs fields, deconfined phases with $\mathbb{Z}_2$ topological order possibly intertwined with discrete broken global symmetries. We present dual theories of the same phases starting from a mean-field theory of fermionic spinons moving in $\pi$-flux in each square lattice plaquette. Fluctuations about this $\pi$-flux state are described by 2+1 dimensional quantum chromodynamics (QCD$_3$) with a SU(2) gauge group and $N_f=2$ flavors of massless Dirac fermions. It has recently been argued by Wang et al. (arXiv:1703.02426) that this QCD$_3$ theory describes the N\'eel-VBS quantum phase transition. We introduce adjoint Higgs fields in QCD$_3$, and obtain fermionic dual descriptions of the phases with $\mathbb{Z}_2$ topological order obtained earlier using the bosonic $\mathbb{CP}^1$ theory. We also present a fermionic spinon derivation of the monopole Berry phases in the U(1) gauge theory of the VBS state. The global phase diagram of these phases contains multi-critical points, and our results imply new boson-fermion dualities between critical gauge theories of these points.Comment: Version 2: 32 pages, 3 figures, 12 tables; fixed typos, merged figure

Deconfined Quantum Critical Point on the Triangular Lattice

We first propose a topological term that captures the "intertwinement" between the standard "$\sqrt{3} \times \sqrt{3}$" antiferromagnetic order (or the so-called 120$^\circ$ state) and the "$\sqrt{12}\times \sqrt{12}$" valence solid bond (VBS) order for spin-1/2 systems on a triangular lattice. Then using a controlled renormalization group calculation, we demonstrate that there exists an unfine-tuned direct continuous deconfined quantum critical point (dQCP) between the two ordered phases mentioned above. This dQCP is described by the $N_f = 4$ quantum electrodynamics (QED) with an emergent PSU(4)=SU(4)/$Z_4$ symmetry only at the critical point. The topological term aforementioned is also naturally derived from the $N_f = 4$ QED. We also point out that physics around this dQCP is analogous to the boundary of a $3d$ bosonic symmetry protected topological state with on-site symmetries only

Innovations in energy and climate policy: lessons from Vermont

We ask in this article: how can planners and policymakers replicate Vermont’s energy and climate policies? We begin by explaining the research methods utilized for this article—mainly research interviews with a pool of experts, coupled with a targeted literature review. We then analyze the success of Vermont energy policy across four areas: energy efficiency, renewable energy, the smart grid, and energy governance. The following sections first explain how Vermont accomplished these successes, next identify a number of remaining barriers and elements of Vermont’s approach that may not be replicable, and finally present the article’s conclusions

Provincialising MacDiarmid:Decolonisation and Scottish literary history

Examines the development of MacDiarmid's aesthetic and political views, in light of decolonial theory and criticism, as showing the 'inexorable and exigent doubling of Scotland with Empire', arguing that though MacDiarmid has been central to the construction of a postcolonial Scottish literary history, free from historical anxiety, a decolonial approach unsettles the narrative of Scotttish exceptionalism and challenges the political romanticism associated with the aesthetic construction of the national, endorsed by MacDiarmid and continued by recent cultural and literary histories [Ed.]