119198764
Metaplectic Anyons, Majorana Zero Modes, and their Computational Power
We introduce and study a class of anyon models that are a natural generalization of Ising anyons and Majorana fermion zero modes. These models combine an Ising anyon sector with a sector associated with $SO(m)_2$ Chern-Simons theory. We show how they can arise in a simple scenario for electron fractionalization and give a complete account of their quasiparticles types, fusion rules, and braiding. We show that the image of the braid group is finite for a collection of $2n$ fundamental quasiparticles and is a proper subgroup of the metaplectic representation of $Sp(2n-2,\mathbb{F}_m)\ltimes H(2n-2,\mathbb{F}_m)$, where $Sp(2n-2,\mathbb{F}_m)$ is the symplectic group over the finite field $\mathbb{F}_m$ and $H(2n-2,\mathbb{F}_m)$ is the extra special group (also called the $(2n-1)$-dimensional Heisenberg group) over $\mathbb{F}_m$. Moreover, the braiding of fundamental quasiparticles can be efficiently simulated classically. However, computing the result of braiding a certain type of composite quasiparticle is $# P$-hard, although it is not universal for quantum computation because it has a finite braid group image. This a rare example of a topological phase that is not universal for quantum computation through braiding but nevertheless has $# P$-hard link invariants. We argue that our models are closely related to recent analyses finding non-Abelian anyonic properties for defects in quantum Hall systems, generalizing Majorana zero modes in quasi-1D systems.
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.
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.
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.
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.
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.
34602223
Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid.
We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.
119184301
The Zb(10610) and Zb(10650) as axial-vector tetraquark states in the QCD sum rules
Abstract In this article, we study the axial-vector mesons Z b ( 10 610 ) and Z b ( 10 650 ) with the C γ μ – C γ 5 type and C γ μ – C γ ν type interpolating currents, respectively, by carrying out the operator product expansion to the vacuum condensates up to dimension 10. In calculations, we explore the energy scale dependence of the QCD spectral densities of the hidden bottom tetraquark states in detail for the first time, and suggest a formula μ = M X / Y / Z 2 − ( 2 M b ) 2 with the effective mass M b = 5.13 GeV to determine the energy scales. The numerical results favor assigning the Z b ( 10 610 ) and Z b ( 10 650 ) as the C γ μ – C γ 5 type and C γ μ – C γ ν type hidden bottom tetraquark states, respectively. We obtain the mass of the J PC = 1 + + hidden bottom tetraquark state as a byproduct, which can be compared to the experimental data in the futures. Furthermore, we study the strong decays Z b ± ( 10 610 ) → ϒ π ± , η b ρ ± with the three-point QCD sum rules, the decay widths also support assigning the Z b ( 10 610 ) as the C γ μ – C γ 5 type hidden bottom tetraquark state.
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.
118555545
Analysis of the Light-Flavor Scalar and Axial-Vector Diquark States with QCD Sum Rules
In this article, we study the light-flavor scalar and axial-vector diquark states in the vacuum and in the nuclear matter using the QCD sum rules in a systematic way, and make reasonable predictions for their masses in the vacuum and in the nuclear matter.
125029705
Development of an advanced electropolishing setup for multicell high gradient niobium cavities