Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models

String-net models allow us to systematically construct and classify 2+1D topologically ordered states which can have gapped boundaries. We can use a simple ideal string-net wavefunction, which is described by a set of F-matrices [or more precisely, a unitary fusion category (UFC)], to study all the universal properties of such a topological order. In this paper, we describe a finite computational method -- Q-algebra approach, that allows us to compute the non-Abelian statistics of the topological excitations [or more precisely, the unitary modular tensor category (UMTC)], from the string-net wavefunction (or the UFC). We discuss several examples, including the topological phases described by twisted gauge theory (i.e., twisted quantum double $D^\alpha(G)$). Our result can also be viewed from an angle of holographic bulk-boundary relation. The 1+1D anomalous topological orders, that can appear as edges of 2+1D topological states, are classified by UFCs which describe the fusion of quasiparticles in 1+1D. The 1+1D anomalous edge topological order uniquely determines the 2+1D bulk topological order (which are classified by UMTC). Our method allows us to compute this bulk topological order (i.e., the UMTC) from the anomalous edge topological order (i.e., the UFC).Comment: 32 pages, 8 figures, reference updated, some refinement

Phonon anharmonicity of rutile TiO_2 studied by Raman spectrometry and molecular dynamics simulations

Raman spectra of rutile titanium dioxide (TiO_2) were measured at temperatures from 100 to 1150 K. Each Raman mode showed unique changes with temperature. Beyond the volume-dependent quasiharmonicity, the explicit anharmonicity was large. A new method was developed to fit the thermal broadenings and shifts of Raman peaks with a full calculation of the kinematics of three-phonon and four-phonon processes, allowing the cubic and quartic components of the anharmonicity to be identified for each Raman mode. A dominant role of phonon-phonon kinematics on phonon shifts and broadenings is reported. Force-field molecular dynamics calculations with the Fourier-transformed velocity autocorrelation method were also used to perform a quantitative study of anharmonic effects, successfully accounting for the anomalous phonon anharmonicity of the B_1_(g) mode

A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons

Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while in 2+1D bosonic systems the topological orders are classified by a pair: a modular tensor category and a chiral central charge. In this paper, we propose a partial classification of topological orders for 3+1D bosonic systems: If all the point-like excitations are bosons, then such topological orders are classified by unitary pointed fusion 2-categories, which are one-to-one labeled by a finite group $G$ and its group 4-cocycle $\omega_4 \in \mathcal H^4[G;U(1)]$ up to group automorphisms. Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.Comment: An important new result "Untwisted sector of dimension reduction is the Drinfeld center of E" is added in Sec. IIIC; other minor refinements and improvements; 23 pages, 10 figure

Deficiency of NOX1 or NOX4 Prevents Liver Inflammation and Fibrosis in Mice through Inhibition of Hepatic Stellate Cell Activation.

Reactive oxygen species (ROS) produced by nicotinamide adenine dinucleotide phosphate oxidase (NOX) play a key role in liver injury and fibrosis. Previous studies demonstrated that GKT137831, a dual NOX1/4 inhibitor, attenuated liver fibrosis in mice as well as pro-fibrotic genes in hepatic stellate cells (HSCs) as well as hepatocyte apoptosis. The effect of NOX1 and NOX4 deficiency in liver fibrosis is unclear, and has never been directly compared. HSCs are the primary myofibroblasts in the pathogenesis of liver fibrosis. Therefore, we aimed to determine the role of NOX1 and NOX4 in liver fibrosis, and investigated whether NOX1 and NOX4 signaling mediates liver fibrosis by regulating HSC activation. Mice were treated with carbon tetrachloride (CCl4) to induce liver fibrosis. Deficiency of either NOX1 or NOX4 attenuates liver injury, inflammation, and fibrosis after CCl4 compared to wild-type mice. NOX1 or NOX4 deficiency reduced lipid peroxidation and ROS production in mice with liver fibrosis. NOX1 and NOX4 deficiency are approximately equally effective in preventing liver injury in the mice. The NOX1/4 dual inhibitor GKT137831 suppressed ROS production as well as inflammatory and proliferative genes induced by lipopolysaccharide (LPS), platelet-derived growth factor (PDGF), or sonic hedgehog (Shh) in primary mouse HSCs. Furthermore, the mRNAs of proliferative and pro-fibrotic genes were downregulated in NOX1 and NOX4 knock-out activated HSCs (cultured on plastic for 5 days). Finally, NOX1 and NOX4 protein levels were increased in human livers with cirrhosis compared with normal controls. Thus, NOX1 and NOX4 signaling mediates the pathogenesis of liver fibrosis, including the direct activation of HSC

Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy

Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological orders. Our criteria also determine which 2+1D topological orders must have gapless edge modes, namely which 1+1D global gravitational anomalies ensure gaplessness. Furthermore, we introduce a new mathematical object, the tunneling matrix $\mathcal W$, whose entries are the fusion-space dimensions $\mathcal W_{ia}$, to label different types of gapped domain walls. By studying many examples, we find evidence that the tunneling matrices are powerful quantities to classify different types of gapped domain walls. Since a gapped boundary is a gapped domain wall between a bulk topological order and the vacuum, regarded as the trivial topological order, our theory of gapped domain walls inclusively contains the theory of gapped boundaries. In addition, we derive a topological ground state degeneracy formula, applied to arbitrary orientable spatial 2-manifolds with gapped domain walls, including closed 2-manifolds and open 2-manifolds with gapped boundaries.Comment: 5+9 pages, 3 figures, updated references, fixed typos and refinements, added proof for equivalence to Lagrangian subgroups in Abelian case

Advanced Post-Processing Techniques of Molecular Dynamics Simulations in Studying Strong Anharmonic Thermodynamics of Solids

While the vibrational thermodynamics of materials with small anharmonicity at low temperatures has been understood well based on the harmonic phonons approximation; at high temperatures, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermal expansion, thermodynamic stability, heat capacity, optical properties, thermal transport and other nonlinear properties ofmaterials. To date the anharmonic lattice dynamics is poorly understood despite its great importance, andmost studies on lattice dynamics still rely on the harmonic or quasiharmonicmodels. With recent developement of computational models, the anharmonic information can be extracted from the atomic trajectories of molecular dynamics simulations. For example, the vibrational energy spectra, the effective potential energy surface and the phonon-phonon interaction channels can be derived from these trajectories which appear stochastic. These inter-dependent methods are adopted to successfully uncover the strong anharmonic phenomena while the traditional harmonic models fail dramatically, e.g., the negative thermal expansion of cuprite and the high temperature thermal stability of rutile