14055947
Classification of symmetric polynomials of infinite variables: Construction of Abelian and non-Abelian quantum Hall states
Classification of complex wave functions of infinite variables is an important problem since it is related to the classification of possible quantum states of matter. In this paper, we propose a way to classify symmetric polynomials of infinite variables using the pattern of zeros of the polynomials. Such a classification leads to a construction of a class of simple non-Abelian quantum Hall states which are closely related to parafermion conformal field theories.
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.
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.
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.
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.
17172847
Topological graph polynomials and quantum field theory Part I: heat kernel theories
We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first paper we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial, and how the new polynomials of noncommutative quantum field theory are particular versions of the Bollob\'as-Riordan polynomials.
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.
16232368
A SEARCH FOR FALLBACK DISKS IN FOUR YOUNG SUPERNOVA REMNANTS
We report on our search for the optical/infrared counterparts to the central compact objects in four young supernova remnants: Pup A, PKS 1209−52, RCW 103, and Cas A. The X-ray point sources in these supernova remnants are excellent targets for probing the existence of supernova fallback disks, since irradiation of a disk by a central X-ray source should lead to an infrared excess. We used ground-based optical and near-infrared imaging and Spitzer Space Telescope mid-infrared imaging to search for optical/infrared counterparts at the X-ray point source positions measured by the Chandra X-Ray Observatory. We did not detect any counterparts, and hence find no evidence for fallback disks around any of these sources. In PKS 1209−52, we are able to exclude a nearby optical/infrared candidate counterpart. In RCW 103, a blend of 3 faint stars at the X-ray source position prevents us from deriving useful limits. For the other targets, the upper limits on the infrared/X-ray flux ratio are as deep as (1.0–1.7)×10 −4 . Comparing these limits to the ratio of ≈ 6 × 10 −5 measured for 4U 0142+61 (a young pulsar recently found with an X-ray irradiated dust disk), we conclude that the non-detection of any disks around young neutron stars studied here are consistent with their relatively low X-ray luminosities, although we note that a similar dust disk around the neutron star in Pup A should be detectable by deeper infrared observations. Subject headings: ISM: individual (Puppis A, PKS 1209−52, RCW 103, Cassiopeia A) — supernova remnants — X-rays: stars — stars: neutron
303237
Discovery of Pulsations in the X-Ray Transient 4U 1901+03
We describe observations of the 2003 outburst of the hard-spectrum X-ray transient 4U 1901+03 with the Rossi X-Ray Timing Explorer (RXTE). The outburst was first detected in 2003 February by the All-Sky Monitor and reached a peak 2.5-25 keV flux of 8 × 10-9 ergs cm-2 s-1 (around 240 mcrab). The only other known outburst occurred 32.2 yr earlier, likely the longest currently known recurrence time for any X-ray transient. Proportional Counter Array (PCA) observations over the 5 month duration of the 2003 outburst revealed a 2.763 s pulsar in a 22.58 days orbit. The detection of pulsations down to a flux of 3 × 10-11 ergs cm-2 s-1 (2.5-25 keV), along with the inferred long-term accretion rate of 8.1 × 10-11 M☉ yr-1 (assuming a distance of 10 kpc), suggests that the surface magnetic field strength is below ~5 × 1011 G. The corresponding cyclotron energy is thus below 4 keV, consistent with the nondetection of resonance features at high energies. Although we could not unambiguously identify the optical counterpart, the lack of a bright IR candidate within the 1' RXTE error circle rules out a supergiant mass donor. The neutron star in 4U 1901+03 probably accretes from the wind of a main-sequence OB star, like most other high-mass binary X-ray pulsars. The almost circular orbit (e = 0.036) confirms the system's membership in a growing class of wide, low-eccentricity systems in which the neutron stars may have received much smaller kicks as a result of their natal supernova explosions.
118954426
Calculation of the quark condensate through Schwinger-Dyson equation
In this letter, we clarify the algebra expression for calculating the quark condensate based on the non-perturbative quark propagator calculated through Schwinger-Dyson equation. The quark condensates, which characterize the low energy QCD vacuum, should not get a divergent quantity at large energy scale; the re-normalization group evolution behaviour at large energy scale therefore should be interpreted as "smeared collective effects" for it contains both perturbative and non-perturbative parts. 
We prefer the integral expression and get a quantity which is both convergent and scale dependent.