12401003
A class of P,T-invariant topological phases of interacting electrons
We describe a class of parity- and time-reversal-invariant topological states of matter which can arise in correlated electron systems in 2+1-dimensions. These states are characterized by particle-like excitations exhibiting exotic braiding statistics. P and T invariance are maintained by a doubling of the low-energy degrees of freedom which occurs naturally without doubling the underlying microscopic degrees of freedom. The simplest examples have been the subject of considerable interest as proposed mechanisms for high-Tc superconductivity. One is the doubled version of the chiral spin liquid. The chiral spin liquid gives rise to anyon superconductivity at finite doping and the corresponding field theory is U ð1Þ Chern–Simons theory at coupling constant m ¼ 2. The doubled theory is two copies of this theory, one with m ¼ 2 the other with m ¼� 2. The second example corresponds to Z2 gauge theory, which describes a scenario for spin-charge separation. Our main concern, with an eye towards applications to quantum computation, are richer models which support non-Abelian statistics. All of these models, richer or poorer, lie in a tightly organized discrete family indexed by the Baraha numbers, 2 cosðp=ðk þ 2ÞÞ, for positive integer k. The physical inference is that a material manifesting the Z2 gauge theory or a doubled chiral spin liquid might be easily altered to one capable of universal quantum computation. These phases of matter have a field-theoretic description in terms of gauge theories which, in their infrared limits, are topological field theories. We motivate these gauge theories using a parton model or slave-fermion construction and show how they can be solved exactly. The structure of the resulting Hilbert spaces can be understood in purely combinatorial terms. The highly constrained nature of this combinatorial construction,
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.
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.
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.
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.
204935313
Analysis of hadronic coupling constants $G_{B_c^*B_c\Upsilon}$, $G_{B_c^*B_c J/\psi}$, $G_{B_cB_c\Upsilon}$ and $G_{B_cB_c J/\psi}$ with QCD sum rules
In this article, we study momentum dependence of the hadronic coupling constants $G_{B_c^* B_c \Upsilon}$, $G_{B_c^* B_c J/\psi}$, $G_{B_c B_c \Upsilon}$ and $G_{B_c B_c J/\psi}$ with the off-shell $\Upsilon$ and $J/\psi$ using the three-point QCD sum rules. Then we fit the hadronic coupling constants into analytical functions and extrapolate them into deep time-like regions to obtain the on-shell values 
$ G_{B_c^*B_c\Upsilon}(q^2=M_{\Upsilon}^2)$, $ G_{B_c^*B_c J/\psi}(q^2=M_{J/\psi}^2)$, $ G_{B_cB_c\Upsilon}(q^2=M_{\Upsilon}^2)$ and $ G_{B_cB_c J/\psi}(q^2=M_{J/\psi}^2)$ for the first time. Those hadronic coupling constants can be taken as basic input parameters in phenomenological analysis.
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.
124633288
Beam dynamics simulation of HEBT for the SSC-linac injector
The SSC-linac (a new injector for the Separated Sector Cyclotron) is being designed in the HIRFL (Heavy Ion Research Facility in Lanzhou) system to accelerate 238U34+ from 3.72 keV/u to 1.008 MeV/u. As a part of the SSC-linac injector, the HEBT (high energy beam transport) has been designed by using the TRACE-3D code and simulated by the 3D PIC (particle-in-cell) Track code. The total length of the HEBT is about 12 meters and a beam line of about 6 meters are shared with the exiting beam line of the HIRFL system. The simulation results show that the particles can be delivered efficiently in the HEBT and the particles at the exit of the HEBT well match the acceptance of the SSC for further acceleration. The dispersion is eliminated absolutely in the HEBT. The space-charge effect calculated by the Track code is inconspicuous. According to the simulation, more than 60 percent of the particles from the ion source can be transported into the acceptance of the SSC.
119282064
Topological field theory and thermal responses of interacting topological superconductors
We investigate the three-dimensional, time-reversal invariant topological superconductors with generic interaction by their response to external fields. The first description is a gravitational topological field theory, which gives a $Z_2$ classification of topological superconductors, and predicts a half-quantized thermal Hall effect on the surface. The second description introduces an s-wave proximity pairing field on the surface, and the associated topological defects give an integer $Z$ classification of the topological superconductors.
122884461
On the composition laws of Beltrami-Liouville theories and 2D quantum gravity☆
Abstract We present the composition laws or cocycle conditions of the Liouville theory and Beltrami-Liouville theory as well as the quantum gravity in two dimensions. We show that for the 2D gravity, their special cases give rise to the composition laws of Polyakov's light-cone action and that of the geometric action of the Virasoro group. By means of the composition laws, we give the gravitational Ward identities and a relation between the actions of the Liouville theory and the topological gravity and find that the principal action of the 2D topological gravity is a coboundary which should obey a cocylce condition in the Liouville complex.