Topological Phases of One-Dimensional Fermions: An Entanglement Point of View

The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional interacting fermions, focusing on spinless fermions with time-reversal symmetry and particle number parity conservation, using concepts of entanglement. In agreement with an example presented by Fidkowski \emph{et. al.} (Phys. Rev. B 81, 134509 (2010)), we find that in the presence of interactions there are only eight distinct phases, which obey a $\mathbb{Z}_8$ group structure. This is in contrast to the $\mathbb{Z}$ classification in the non-interacting case. Each of these eight phases is characterized by a unique set of bulk invariants, related to the transformation laws of its entanglement (Schmidt) eigenstates under symmetry operations, and has a characteristic degeneracy of its entanglement levels. If translational symmetry is present, the number of distinct phases increases to 16.Comment: 12 pages, 1 figure; journal ref. adde

The Role-Based Performance Scale: Validity Analysis of a Theory-Based Measure

This study introduces a theory-based measure of employee performance (Role Based Performance Scale, RBPS) that is supported with results from a validation study using 10 data sets from six companies. In contrast to traditional, job-related measures of employee performance, we propose an alternative measure of performance based on role theory and identity theory. Because our results support the validity of the scale, we think that the instrument can be used for future research that requires a generalizable measure of performance. The scale demonstrates diagnostic properties that make it useful for practitioners as well as researchers

Topological phases in gapped edges of fractionalized systems

Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator. The low-energy edge degrees of freedom are described by a chain of coupled parafermions. We introduce a classification scheme for the phases that can occur in parafermionic chains. We find that the parafermions support both topological symmetry fractionalized phases as well as phases in which the parafermions condense. In the presence of additional symmetries, the phases form a non-Abelian group. As a concrete example of the classification, we consider the effective edge model for a $\nu= 1/3$ fractional topological insulator for which we calculate the entanglement spectra numerically and show that all possible predicted phases can be realized.Comment: 11 pages, 7 figures, final versio

Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms

We suggest a method to simulate lattice compact Quantum Electrodynamics (cQED) using ultracold atoms in optical lattices, which includes dynamical Dirac fermions in 2+1 dimensions. This allows to test dynamical effects of confinement as well as 2d flux loops deformations and breaking, and to observe Wilson-loop area-law.Comment: Includes supplementary material. Added references, minor modification