125952499
Representations of the loop braid group
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.
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.
119278662
Symmetry, Defects, and Gauging of Topological Phases
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the topological symmetry group, which characterizes the symmetry of the emergent topological quantum numbers of a topological phase $\mathcal{C}$, and we describe its relation with the microscopic symmetry of the underlying physical system. We derive a general framework to classify symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter $\mathcal{C}$ with symmetry group $G$. The algebraic theory of the defects, known as a $G$-crossed braided tensor category $\mathcal{C}_{G}^{\times}$, allows one to compute many properties, such as the number of topologically distinct types of defects associated with each group element, their fusion rules, quantum dimensions, zero modes, braiding exchange transformations, a generalized Verlinde formula for the defects, and modular transformations of the $G$-crossed extensions of topological phases. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic $G$-defects are turned into deconfined quasiparticle excitations, which results in a different topological phase $\mathcal{C}/G$. A number of instructive and/or physically relevant examples are studied in detail.
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.
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.
59247128
Quantum field theory on quantized Bergman domain
We present an oscillator realization of discrete series representations of group SU(2, 2). We give formulas for the coherent state star-product quantization of a Bergman domain D. A formulation of a (regularized) noncommutative scalar field on a quantized D is given.
123937746
INTRINSIC LOOP REGULARIZATION AND RENORMALIZATION IN QED
We show how to regularize and renormalize the QED at the one-loop order by means of the intrinsic loop regularization method proposed by the authors. All the results are the same as those derived by means of other regularization methods.
16126253
The X-ray position and optical counterpart of the accretion-powered millisecond pulsar XTE J1814-338
We report the precise optical and X-ray localization of the 3.2 ms accretion-powered X-ray pulsar XTE J1814-338 with data from the Chandra X-Ray Observatory as well as optical observations conducted during the 2003 June discovery outburst. Optical imaging of the field during the outburst of this soft X-ray transient reveals an R = 18 star at the X-ray position. This star is absent (R > 20) from an archival 1989 image of the field and brightened during the 2003 outburst, and we therefore identify it as the optical counterpart of XTE J1814-338. The best source position derived from optical astrometry is R.A. = 18h13m3904, decl. = -33°46'223 (J2000). The featureless X-ray spectrum of the pulsar in outburst is best fit by an absorbed power law (with photon index γ = 1.41 ± 0.06) plus blackbody (with kT = 0.95 ± 0.13 keV) model, where the blackbody component contributes approximately 10% of the source flux. The optical broadband spectrum shows evidence for an excess of infrared emission with respect to an X-ray heated accretion disk model, suggesting a significant contribution from the secondary or from a synchrotron-emitting region. A follow-up observation performed when XTE J1814-338 was in quiescence reveals no counterpart to a limiting magnitude of R = 23.3. This suggests that the secondary is an M3 V or later-type star and therefore very unlikely to be responsible for the soft excess, making synchrotron emission a more reasonable candidate.
17015371
Analysis of the X(1576) as a tetraquark state with the QCD sum rules
In this letter, we take the point of view that the X(1576) be tetraquark state which consists of a scalar-diquark and an anti-scalar-diquark in relative P -wave, and calculate its mass in the framework of the QCD sum rules approach. The numerical value of the mass mX = (1.66±0.14)GeV is consistent with the experimental data, there may be some tetraquark component in the vector meson X(1576). PACS numbers: 12.38.Lg; 12.39.Mk
118394396
Analysis of strong decays of the charmed mesons $D_J(2580), D^*_J(2650), D_J(2740), D^*_J(2760), D_J(3000), D^*_J(3000)$
In this article, we tentatively identify the charmed mesons $D_J(2580)$, $D_J^*(2650)$, $D_J(2740)$, $D^*_J(2760)$, $D_J(3000)$, $D_J^*(3000)$ observed by the LHCb collaboration according to their spin, parity and masses, then study their strong decays to the ground state charmed mesons plus light pseudoscalar mesons with the heavy meson effective theory in the leading order approximation, and obtain explicit expressions of the decay widths. The ratios among the decay widths can be used to confirm or reject the assignments of the newly observed charmed mesons. The strong coupling constants in the decay widths can be fitted to the experimental data in the future at the LHCb, BESIII, KEK-B and $\rm{\bar{P}ANDA}$.