Topological phase transitions driven by gauge fields in an exactly solvable model

We demonstrate the existence of a new topologically ordered phase in Kitaev's honeycomb lattice model. This new phase appears due to the presence of a vortex lattice and it supports chiral Abelian anyons. We characterize the phase by its low-energy behavior that is described by a distinct number of Dirac fermions. We identify two physically distinct types of topological phase transitions and obtain analytically the critical behavior of the extended phase space. The Fermi surface evolution associated with the transitions is shown to be due to the Dirac fermions coupling to chiral gauge fields. Finally, we describe how the new phase can be understood in terms of interactions between the anyonic vortices.Comment: 5 pages, 5 figures, published versio

Seeing Majorana fermions in time-of-flight images of spinless fermions coupled by s-wave pairing

The Chern number, nu, as a topological invariant that identifies the winding of the ground state in the particle-hole space, is a definitive theoretical signature that determines whether a given superconducting system can support Majorana zero modes. Here we show that such a winding can be faithfully identified for any superconducting system (p-wave or s-wave with spin-orbit coupling) through a set of time-of-flight measurements, making it a diagnostic tool also in actual cold atom experiments. As an application, we specialize the measurement scheme for a chiral topological model of spinless fermions. The proposed model only requires the experimentally accessible s-wave pairing and staggered tunnelling that mimics spin-orbit coupling. By adiabatically connecting this model to Kitaev's honeycomb lattice model, we show that it gives rise to nu = \pm 1 phases, where vortices bind Majorana fermions, and nu=\pm 2 phases that emerge as the unique collective state of such vortices. Hence, the preparation of these phases and the detection of their Chern numbers provide an unambiguous signature for the presence of Majorana modes. Finally, we demonstrate that our detection procedure is resilient against most inaccuracies in experimental control parameters as well as finite temperature.Comment: 9+4 pages, 11 figures, expanded versio

Non-Abelian statistics as a Berry phase in exactly solvable models

We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasiparticles, the resulting Berry phase provides a direct demonstration of their non-Abelian statistics. We apply this technique to Kitaev's honeycomb lattice model and explicitly demonstrate the existence of non-Abelian Ising anyons confirming the previous conjectures. Finally, we present the manipulations needed to transport and detect the statistics of these quasiparticles in the laboratory. Various physically realistic system sizes are considered and exact predictions for such experiments are provided.Comment: 10 pages, 3 figures. To appear in New Journal of Physic

Using auxiliary data to model nonresponse bias The challenge of knowing too much about nonrespondents rather than too little?

The ADDResponse project (www.addresponse.org) explores the potential for using auxiliary data from multiple sources to understand and correct for nonresponse bias in general social surveys in the UK. Data from the census and other administrative sources together with consumer profiling data and geographic information about local neighbourhoods have been matched to data from Round 6 of the European Social Survey in the UK.1 Preliminary bivariate analysis suggests that a large number of these variables may be associated with response propensity and worthy of further investigation. Here we discuss some of the preliminary steps we have taken to try and identify the most likely candidates for nonresponse adjustment and compare the results from propensity models employing theory-driven vs. automated variable selection

Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost

Topographic and electronic contrast of the graphene moir\'e on Ir(111) probed by scanning tunneling microscopy and non-contact atomic force microscopy

Epitaxial graphene grown on transition metal surfaces typically exhibits a moir\'e pattern due to the lattice mismatch between graphene and the underlying metal surface. We use both scanning tunneling microscopy (STM) and atomic force microscopy (AFM) experiments to probe the electronic and topographic contrast of the graphene moir\'e on the Ir(111) surface. While STM topography is influenced by the local density of states close to the Fermi energy and the local tunneling barrier height, AFM is capable of yielding the 'true' surface topography once the background force arising from the van der Waals (vdW) interaction between the tip and the substrate is taken into account. We observe a moir\'e corrugation of 35$\pm$10 pm, where the graphene-Ir(111) distance is the smallest in the areas where the graphene honeycomb is atop the underlying iridium atoms and larger on the fcc or hcp threefold hollow sites.Comment: revised versio

Using geographically weighted regression to explore spatial variation in survey data

Nonresponse can undermine the quality of social survey data. Understanding who does/does not respond to surveys is important for those involved in the collection and analysis of these data. Levels of nonresponse are known to vary geographically. However, there has been little consideration of how the predictors of survey nonresponse might vary geographically within countries. This study examines the possibility of spatial variation in response behavior using regional interactions and geographically weighted regression. Our results suggest that there is geographical variation in response behavior. Relying on “one size fits all” global models in nonresponse modelling might, therefore, be insufficient

Diagnosing Topological Edge States via Entanglement Monogamy

Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this Letter, we propose an alternative approach to assessing topologically induced edge states in free and interacting fermionic systems. We do so by focussing on the fermionic covariance matrix. This matrix is often tractable either analytically or numerically, and it precisely captures the relevant correlations of the system. By invoking the concept of monogamy of entanglement, we show that highly entangled states supported across a system bipartition are largely disentangled from the rest of the system, thus, usually appearing as gapless edge states. We then define an entanglement qualifier that identifies the presence of topological edge states based purely on correlations present in the ground states. We demonstrate the versatility of this qualifier by applying it to various free and interacting fermionic topological systems

Informing Non-Response Bias Model Creation in Social Surveys with Visualisation

Through an ongoing process of co-design and co-discovery we are developing and using visualization to explore large amounts of auxiliary data from unfamiliar sources to understand non-response bias in social surveys. We present auxiliary data in their geographical contexts and show how this can complement traditional data analysis and provide a more comprehensive understanding of the data. This is helping select variables for non-response modelling. These processes are not just limited to non-response analysis, but have potential to be used in wider quantitative analysis in social science