753418
On Picture (2+1)-TQFTs
The goal of the paper is an exposition of the simplest $(2+1)$-TQFTs in a sense following a pictorial approach. In the end, we fell short on details in the later sections where new results are stated and proofs are outlined. Comments are welcome and should be sent to the 4th author.
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.
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.
197437557
Construction of 2-dimensional Grosse-Wulkenhaar Model
In this paper we construct the noncommutative Grosse-Wulkenhaar model on 2-dimensional Moyal plane with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense.
119218814
Infrared Observations of the Millisecond Pulsar Binary J1023+0038: Evidence for the Short-term Nature of Its Interacting Phase in 2000-2001
We report our multi-band infrared (IR) imaging of the transitional millisecond pulsar system J1023+0038, a rare pulsar binary known to have an accretion disk in 2000-2001. The observations were carried out with ground-based and space telescopes from near-IR to far-IRwavelengths. We detected the source in near-IR JH bands and Spitzer 3.6 and 4.5 mu m mid-IR channels. Combined with the previously reported optical spectrum of the source, the IR emission is found to arise from the companion star, with no excess emission detected in the wavelength range. Because our near-IR fluxes are nearly equal to those obtained by the 2MASS all-sky survey in 2000 February, the result indicates that the binary did not contain the accretion disk at the time, whose existence would have raised the near-IR fluxes to twice larger values. Our observations have thus established the short-term nature of the interacting phase seen in 2000-2001: the accretion disk existed for at most 2.5 yr. The binary was not detected by the WISE all-sky survey carried out in 2010 at its 12 and 22 mu m bands and our Herschel far-IR imaging at 70 and 160 mu m. Depending on the assumed properties of the dust, the resulting flux upper limits provide a constraint of <3 x 10(22)-3 x 10(25) g on the mass of the dust grains that possibly exist as the remnants of the previously seen accretion disk.
121280592
The exchange algebra for Liouville field on Riemann surfaces with h>1 genus
We consider the classical Liouville field theory on the Riemann surface with h>1 genus. In terms of the uniformization theorem of the Riemann surface, we show explicitly the classical exchange algebra (CEA) for the chiral components of the Liouville field. We find that this classical exchange algebra is just the same as that on a Riemann sphere with 2h punctures.
119625166
Construction of the Noncommutative Rank I Bergman Domain
In this paper we present a harmonic oscillator realization of the most degenerate discrete series representations of the SU(2,1) group and the deformation quantization of the coset space \(D = SU(2,1)/U(2)\) with the method of coherent state quantization. This short article is based on a talk given at the 9-th International Workshop, Varna “Lie Theory and Its Applications in Physics” (LT-9).
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.