7625841
Topological Hamiltonian as an exact tool for topological invariants.
We propose the concept of 'topological Hamiltonian' for topological insulators and superconductors in interacting systems. The eigenvalues of the topological Hamiltonian are significantly different from the physical energy spectra, but we show that the topological Hamiltonian contains the information of gapless surface states, therefore it is an exact tool for topological invariants.
925818
Topological order parameters for interacting topological insulators.
We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time-reversal invariant topological insulator, and it can be experimentally measured through the topological magneto-electric effect. This topological order parameter can be applied to both interacting and disordered systems, and used for determining their phase diagrams.
119270278
Strongly correlated topological superconductors and topological phase transitions via Green's function
We propose several topological order parameters expressed in terms of Green's function at zero frequency for topological superconductors, which generalizes the previous work for interacting insulators. The coefficient in topological field theory is expressed in terms of zero frequency Green's function. We also study topological phase transition beyond noninteracting limit in this zero frequency Green's function approach.
17728532
The Off-Nuclear Starbursts in NGC 4038/4039 (The Antennae Galaxies)
Imaging of the Antennae galaxies (NGC 4038/4039) with the Infrared Array Camera (IRAC) aboard the Spitzer Space Telescope reveals large concentrations of star-forming activity away from both nuclei of the two merging galaxies. These images confirm earlier findings based on Infrared Space Observatory (ISO) data with lower angular resolution. The short-wavelength emission shows numerous compact sources identified as stellar clusters. At the longer wavelengths, bright, more amorphous and filamentary features correlate well with the known distributions of denser gas, warm dust, and H II regions. There are also fainter, more diffuse components at all wavelengths that permeate the entire region and extend into the two tidal tails. Nonstellar dust emission dominates the 5.8 and 8.0 μm images, accounting for as much as 79% of the light at 5.8 μm and 95% at 8 μm, averaged over the entire galaxy. Assuming that the nonstellar emission traces star formation, the IRAC data provide a view into the total underlying star-forming activities unaffected by obscuration. Using the flux ratio of nonstellar to stellar emission as a guide, we map the local star formation rate in the Antennae and compare that to similar measurements in both normal and infrared-luminous galaxies. This rate in the active regions is found to be as high as those seen in starburst and some ultraluminous infrared galaxies on a "per unit mass" basis. The two galactic centers actually have lower star-forming rates than the off-nuclear regions despite the presence of abundant dense gas and dust, suggesting that the latter is a necessary but not sufficient condition for ongoing star formation.
120394115
Manipulation of Majorana fermions by point-like gate voltage in the Vortex state of a topological superconductor
A vortex in a topological superconductor induces two Majorana fermions (MFs), one in the core and the other at the sample edge. Here we demonstrate that edge MFs can be transported and braided by turning gate voltages on and off at the point-like constriction junctions between samples. The controllable high mobility of edge MFs is due to the topological property, namely an edge MF appears when the sample perimeter includes odd vorticity, and disappears for even vorticity. As shown explicitly by solving the time-dependent Bogoliubov-de Gennes equation, disturbance to the quantum coherence of MFs during braiding is negligibly small in this scheme due to the point-like application of the gate voltage. The present work bridges for the first time the fundamental topological features of edge MFs and their adiabatic dynamics which is important for performing topological quantum computation.
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.
118596683
Fractional quantum Hall effect in topological insulators: The role of Zeeman effect
We study the role of Zeeman effect in fractional quantum Hall effect (FQHE) on the surface of topological insulators (TIs). We show that the effective pseudopotentials of the Coulomb interaction are reformed due to Zeeman effect, which are quite different from those in graphene. By exactly diagonalizing the many-body Hamiltonian in the sphere geometry, we find that the ground state energies and the excitation gaps at $\nu$=1/3 FQHE between the $n$=$\pm1$ Landau levels (LLs) render asymmetry, and the FQHE state at the $n$=1 LL is more robust than that at $n$=-1 LL since the excitation gap at $n$=1 LL is larger than that at $n$=-1 LL.
121348798
Scaling theory of the Hall coefficient near the metal-insulator transition, a renormalization-group approach
Abstract We investigate the critical properties of the Hall conduxtivity in weak magetic fields near the disorder driven metal-insulator transition. We derive an effective lagrangian governing the interactions of the diffusive modes in the presence of time-reversal and particle-hole symmetry breaking and identify a new operator relevant to the scaling behavior of the weak-field Hall conductivity. A Wilson-Polyakov renormalization-group analysis is carried out and the flow equations are obtained near two dimensions. We show that the perturbative behavior of the Hall conductivity in the weakly localized regime, in two dimensions, is not simply related to the critical behavior of the Hall conductivity, due to the role played by a new scaling variable. Solving the renormalization-group equations close to the zero-field fixed point, our theory predicts that the Hall number vanishes at the mobility edge with an exponent g = 1 in agreement with several experimental observations. We clarify the connection between the field-theoretic approach and the conventional perturbative approach and elucidate why perturbation in the disorder, which is valid in the weak localization regime fails to predict the correct critical behavior.