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