119634202
On enriching the Levin–Wen model with symmetry
Symmetry protected (SPT) and symmetry enriched topological (SET) phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Levin?Wen (LW) model for spin/boson systems is an important rigorously solvable model for studying 2D topological phases. The input data for the LW model is a unitary fusion category, but the same model also works for unitary multi-fusion categories. In this paper, we provide the details for this extension of the LW model, and show that the extended LW model is a natural playground for the theoretical study of SPT and SET phases of matter.
54954168
From String Nets to Nonabelions
We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for the system to be in the DFib (Doubled Fibonacci) topological phase, that is, be described at low energy by an SO(3)3 × SO(3)3 doubled Chern-Simons theory, with the appropriate non-abelian statistics governing the braiding of the low-lying quasiparticle excitations (nonabelions). Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.
125952499
Representations of the loop braid group
119138174
On Metaplectic Modular Categories and Their Applications
For non-abelian simple objects in a unitary modular category, the density of their braid group representations, the #P-hard evaluation of their associated link invariants, and the BQP-completeness of their anyonic quantum computing models are closely related. We systematically study such properties of the non-abelian simple objects in the metaplectic modular categories SO(m)2 for an odd integer m ≥ 3. The simple objects with quantum dimensions $${\sqrt{m}}$$m have finite image braid group representations, and their link invariants are classically efficient to evaluate. We also provide classically efficient simulations of their braid group representations. These simulations of the braid group representations can be regarded as qudit generalizations of the Knill–Gottesmann theorem for the qubit case. The simple objects of dimension 2 give us a surprising result: while their braid group representations have finite images and are efficiently simulable classically after a generalized localization, their link invariants are #P-hard to evaluate exactly. We sharpen the #P-hardness by showing that any sufficiently accurate approximation of their associated link invariants is already #P-hard.
18058928
Density of the SO(3) TQFT Representation of Mapping Class Groups
We show that for an odd prime r>3 and an integer g>1, in the projective representation given by the SO(3) Witten-Reshitikhin-Turaev theory at an rth root of unity, the image of the mapping class group of a surface of genus g is dense.
19017470
Topological properties of Abelian and non-Abelian quantum Hall states classified using patterns of zeros
It has been shown that different Abelian and non-Abelian fractional quantum Hall states can be characterized by patterns of zeros described by sequences of integers ${{S}_{a}}$. In this paper, we will show how to use the data ${{S}_{a}}$ to calculate various topological properties of the corresponding fraction quantum Hall state, such as the number of possible quasiparticle types and their quantum numbers, as well as the actions of the quasiparticle tunneling and modular transformations on the degenerate ground states on torus.
197485150
Searching for New Topological Types of Majorana Fermions from Boundary-bulk Correspondence of Topological Insulators/Superconductors
Majorana fermions (MFs) are particles that are their own anti-particles and may satisfy non-Abelian statistics. For the past ten years, a kind of MFs have been theoretically predicted in one-dimensional superconducting models without the time-reversal symmetry (TRS), which has recently intrigued a huge experimental interest to search for this type of exotic particles. Here we report our theoretical discoveries, including (i) a general and quantitative relation between topological stabilities of Fermi surfaces (FSs) and topological insulators(TIs)/superconductors(TSCs) is rigorously established; (ii) based on (i), we find four topologically distinct types of MFs in fermionic systems that have at least the particle-hole symmetry (PHS); (iii) apart from the existing one type, three new types of topologically nontrivial gapless edge-modes (MFs) are revealed for the first time in one dimensional finite systems with both TP and (iv) all kinds of candidate models that potentially have MFs are presented, opening a wider door for searching MFs experimentally.
54015576
Analysis of the Radiative Decays Among the Charmonium States
In this article, we study the radiative decays among the charmonium states with the heavy quark effective theory, and make predictions for the ratios among the radiative decay widths of an special multiplet to another multiplet. The predictions can be confronted with the experimental data in the future and put additional constraints in identifying the X, Y, Z charmonium-like mesons.
119172158
Construction of the noncommutative complex ball
We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space D = SU(m, 1)/U(m), with the method of coherent state quantization. In the commutative limit, we obtain the standard manifold. We also consider a quantum field theory model on the noncommutative manifold.
119548246
Subarcsecond Resolution Mid-Infrared Observations of Super Star Clusters in the Antennae (NGC 4038/4039)*
We present ground-based subarcsecond mid-infrared imaging and spectroscopy of young super star clusters in the overlap region of the merging galaxies NGC 4038/4039 (the Antennae) obtained with the VLT Imager and Spectrometer for mid-InfraRed (VISIR). With its unprecedented spatial resolution, VISIR begins for the first time to resolve the H II/photodissociation region complexes around the star-forming regions. In the N-band spectra of two young star clusters, unexpectedly low polycyclic aromatic hydrocarbon (PAH) emission is observed, compared to what is seen with the Infrared Space Observatory and with the Spitzer Space Telescope. We conclude that a large fraction of the PAH emission cannot be directly associated with the super star clusters but originates from an extended region of at least 215 pc radius around the clusters. In the distribution of [Ne II] 12.81 μm emission, a highly obscured cluster is discovered that does not have an optical or near-infrared counterpart.
119270278
Strongly correlated topological superconductors and topological phase transitions via Green's function
We propose several topological order parameters expressed in terms of Green's function at zero frequency for topological superconductors, which generalizes the previous work for interacting insulators. The coefficient in topological field theory is expressed in terms of zero frequency Green's function. We also study topological phase transition beyond noninteracting limit in this zero frequency Green's function approach.