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

An experience of modularity through design

We aim to utilise the experiences of a marine industry-based design team to determine the need for research into a modular design methodology in an industrial environment. In order to achieve this we couple the outcome of a current design project with the findings of a recent literature survey with the objectives of firstly, clarifying why a methodology is required and, secondly, defining the key elements which the methodology would have to realise or address. The potential benefits of modularity have long been recognised in the shipbuilding industry. Many shipbuilders adopt a 'module' approach to ship construction whereby the ship structure is separated into a number of large structural 'blocks' to ease manufacture and manoeuvrability during construction. However, as understanding of the capabilities of modularity as a design tool develops there is increased interest in capitalising on the differing life phase benefits of modularity such as reduced design costs and time, increased ease of maintenance, upgrade, re-use, redesign and standardisation across individual products and product families. This is especially pertinent in naval shipbuilding where the maintenance of a class of ship requires that all previously designed ships in that class must be of similar outfitting and must be able to interface with the new ship, in terms of propulsion, weapons, communications and electronics, and thus often require some form of retrofit. Therefore, many shipbuilders are moving from viewing modularity as a purely 'manufacturing' principle to a design centred principle. However, as noted by Chang and Ward 'none of the design theories or tools in the mechanical world serves as an articulate procedure for designers to follow in practising modular design'. Thus, despite the identification of a need to introduce modular principles at an earlier stage than detail design and construction, there is little aid in the form of tools, techniques and methodologies for designers in practice