20940257
Universal quantum computation with weakly integral anyons
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as the Fibonacci anyon is theoretically a possibility, accessible anyons with current technology all belong to a class that is called weakly integral—anyons whose squared quantum dimensions are integers. We analyze the computational power of the first non-abelian anyon system with only integral quantum dimensions—$$D(S_3)$$D(S3), the quantum double of $$S_3$$S3. Since all anyons in $$D(S_3)$$D(S3) have finite images of braid group representations, they cannot be universal for quantum computation by braiding alone. Based on our knowledge of the images of the braid group representations, we set up three qutrit computational models. Supplementing braidings with some measurements and ancillary states, we find a universal gate set for each model.
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.
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.
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.
54896614
Galois conjugates of topological phases
Galois conjugation relates unitary conformal field theories and topological quantum field theories (TQFTs) to their nonunitary counterparts. Here we investigate Galois conjugates of quantum double models, such as the Levin-Wen model. While these Galois-conjugated Hamiltonians are typically non-Hermitian, we find that their ground-state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground-state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such nonunitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this, we rigorously prove that no local change of basis can transform the ground states of the Galois-conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasilocal Hamiltonians. A similar statement holds for many other nonunitary TQFTs. One consequence is that these nonunitary TQFTs do not describe physical realizations of topological phases. In particular, this implies that the ``Gaffnian'' wave function can not be the ground state of a gapped fractional quantum Hall state.
11394439
Identifying topological order by entanglement entropy
Topological entanglement entropy provides a robust measure for detecting the long-range entanglement that characterizes quantum ground states displaying topological order. A new method for calculating this entropy isolates minimally entangled states from the ground states of a topological phase—offering a reliable test for identifying topological spin liquids.
55540815
Abelian and non-Abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect
We study the quantum anomalous Hall effect described by a class of two-component Haldane models on square lattices. We show that the latter can be transformed into a pseudospin triplet p + ip-wave paired superfluid. In the long wavelength limit, the ground-statewave function is described by Halperin's ( 1,1,-1) state of neutral fermions analogous to the double-layer quantum Hall effect. The vortex excitations are charge e/2 Abelian anyons which carry a neutral Dirac fermion zero mode. The superconducting proximity effect induces "tunneling" between "layers" which leads to topological phase transitions whereby the Dirac fermion zero mode fractionalizes and Majorana fermions emerge in the edge states. The charge e/2 vortex excitation carrying a Majorana zero mode is a non-Abelian anyon. The proximity effect can also drive a conventional insulator into a quantum anomalous Hall effect state with a Majorana edge mode and the non-Abelian vortex excitations.
99565521
Study of the psi(2S) decay to p anti-p pi+ pi- (pi0)
11569124
Spitzer Mid-Infrared Imaging of Nearby Ultraluminous Infrared Galaxies
We have observed 14 nearby (z < 0.16) Ultraluminous Infrared Galaxies (ULIRGs) with Spitzer at 3.6-24μm. The underlying host galaxies are well-detected, in addition to the luminous nuclear cores. While the spatial resolution of Spitzer is poor, the great sensitivity of the data reveals the underlying galaxy merger remnant, and provides the first look at off-nuclear mid-infrared activity.
16797551
Analysis of the $B\to a_1(1260)$ form-factors with light-cone QCD sum rules
In this article, we calculate the $B\to a_1(1260)$ form-factors $V_1(q^2)$, $V_2(q^2)$, $V_3(q^2)$ and $A(q^2)$ with the $B$-meson light-cone QCD sum rules. Those form-factors are basic parameters in studying the exclusive non-leptonic two-body decays $B\to AP$ and semi-leptonic decays $B\to A l \nu_l$, $B\to A \bar{l}l$. Our numerical results are consistent with the values from the (light-cone) QCD sum rules. The main uncertainty comes from the parameter $\omega_0$ (or $\lambda_B$), which determines the shapes of the two-particle and three-particle light-cone distribution amplitudes of the $B$ meson, it is of great importance to refine this parameter.
124095561
THE QUANTUM R-MATRIX VIA CANONICAL QUANTIZATION IN THE LIOUVILLE THEORY
Starting from the classical Liouville theory, we study its quantum theory through canonical quantization. We find that if the Poisson bracket relations between two vectors are dominated by the classical r-matrix in the classical case, their quantum analogue is replaced by the exchange relations dominated by the quantum R-matrix. The quantum group structure in the quantum Liouville theory is studied and the central charge of the quantum Liouville theory is also obtained.