Soft self-assembly of Weyl materials for light and sound

Soft materials can self-assemble into highly structured phases which replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound. Here, we present a bottom-up approach based on self-assembly to engineer three-dimensional photonic and phononic crystals with topologically protected Weyl points. In addition to angular and frequency selectivity of their bulk optical response, Weyl materials are endowed with topological surface states, which allows for the existence of one-way channels even in the presence of time-reversal invariance. Using a combination of group-theoretical methods and numerical simulations, we identify the general symmetry constraints that a self-assembled structure has to satisfy in order to host Weyl points, and describe how to achieve such constraints using a symmetry-driven pipeline for self-assembled material design and discovery. We illustrate our general approach using block copolymer self-assembly as a model system.Comment: published version, SI are available as ancillary files, code and data are available on Zenodo at https://doi.org/10.5281/zenodo.1182581, PNAS (2018

Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents

We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z2-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Delta_sigma=0.518154(15), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.Comment: 55 pages, many figures; v2 - refs and comments added, to appear in a special issue of J.Stat.Phys. in memory of Kenneth Wilso

Geometric free energy of toric AdS4/CFT3 models

We study the supersymmetric free energy of three dimensional Chern-Simons-matter theories holographically dual to AdS$_4$ times toric Sasaki-Einstein seven-manifolds. In the large $N$ limit, we argue that the square of the free energy can be written as a quartic polynomial of trial R-charges. The coefficients of the polynomial are determined geometrically from the toric diagrams. We present the coefficients of the quartic polynomial explicitly for generic toric diagrams with up to 6 vertices, and some particular diagrams with 8 vertices. Decomposing the trial R-charges into mesonic and baryonic variables, and eliminating the baryonic ones, we show that the quartic polynomial reproduces the inverse of the Martelli-Sparks-Yau volume function. On the gravity side, we explore the possibility of using the same quartic polynomial as the prepotential in the AdS gauged supergravity. Comparing Kaluza-Klein gravity and gauged supergravity descriptions, we find perfect agreement in the mesonic sector but some discrepancy in the baryonic sector.Comment: 39 pages, 21 figures; v2. references added, minor improvement

Bootstrapping Mixed Correlators in the 3D Ising Model

We study the conformal bootstrap for systems of correlators involving non-identical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a $\mathbb{Z}_2$ global symmetry. For the leading $\mathbb{Z}_2$-odd operator $\sigma$ and $\mathbb{Z}_2$-even operator $\epsilon$, we obtain numerical constraints on the allowed dimensions $(\Delta_\sigma, \Delta_\epsilon)$ assuming that $\sigma$ and $\epsilon$ are the only relevant scalars in the theory. These constraints yield a small closed region in $(\Delta_\sigma, \Delta_\epsilon)$ space compatible with the known values in the 3D Ising CFT.Comment: 39 pages, 6 figure

Stress-Minimizing Orthogonal Layout of Data Flow Diagrams with Ports

We present a fundamentally different approach to orthogonal layout of data flow diagrams with ports. This is based on extending constrained stress majorization to cater for ports and flow layout. Because we are minimizing stress we are able to better display global structure, as measured by several criteria such as stress, edge-length variance, and aspect ratio. Compared to the layered approach, our layouts tend to exhibit symmetries, and eliminate inter-layer whitespace, making the diagrams more compact

Higgs Sector in Extensions of the MSSM

Extensions of the Minimal Supersymmetric Standard Model (MSSM) with additional singlet scalar fields solve the important mu-parameter fine tuning problem of the MSSM. We compute and compare the neutral Higgs boson mass spectra, including one-loop corrections, of the following MSSM extensions: Next-to-Minimal Supersymmetric Standard Model (NMSSM), the nearly-Minimal Supersymmetric Standard Model (nMSSM), and the U(1)'-extended Minimal Supersymmetric Standard Model (UMSSM) by performing scans over model parameters. We find that the Secluded U(1)'-extended Minimal Supersymmetric Standard Model (sMSSM) is identical to the nMSSM if three of the additional scalars decouple. The dominant part of the one-loop corrections are model-independent since the singlet field does not couple to MSSM particles other than the Higgs doublets. Thus, model-dependent parameters enter the masses only at tree-level. We apply constraints from LEP bounds on the Standard Model and MSSM Higgs boson masses and the MSSM chargino mass, the invisible Z decay width, and the Z-Z' mixing angle. Some extended models permit a Higgs boson with mass substantially below the SM LEP limit or above theoretical limits in the MSSM. Ways to differentiate the models via masses, couplings, decays and production of the Higgs bosons are discussed.Comment: 65 pages, 15 figures. Figure replaced and typos corrected. Version to appear in Phys. Rev.

Robust determination of maximally-localized Wannier functions

We propose an algorithm to determine Maximally Localized Wannier Functions (MLWFs). This algorithm, based on recent theoretical developments, does not require any physical input such as initial guesses for the Wannier functions, unlike popular schemes based on the projection method. We discuss how the projection method can fail on fine grids when the initial guesses are too far from MLWFs. We demonstrate that our algorithm is able to find localized Wannier functions through tests on two-dimensional systems, simplified models of semiconductors, and realistic DFT systems by interfacing with the Wannier90 code. We also test our algorithm on the Haldane and Kane-Mele models to examine how it fails in the presence of topological obstructions

Fixed parameter tractability of crossing minimization of almost-trees

We investigate exact crossing minimization for graphs that differ from trees by a small number of additional edges, for several variants of the crossing minimization problem. In particular, we provide fixed parameter tractable algorithms for the 1-page book crossing number, the 2-page book crossing number, and the minimum number of crossed edges in 1-page and 2-page book drawings.Comment: Graph Drawing 201