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Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We focus on describing the topological semimetal, a three-dimensional phase of
Entanglement spectrum of a topological phase in one dimension
We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of
Quasiparticle statistics and braiding from ground state entanglement
Topologically ordered phases are gapped states, defined by the properties of excitations when taken around one another. Here we demonstrate a method to extract the statistics and braiding of
Symmetry protection of topological phases in one-dimensional quantum spin systems
We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-S Haldane phase is a topologically nontrivial
Topological mechanics of gyroscopic metamaterials
This work presents an experimental and theoretical study of an active metamaterial—composed of coupled gyroscopes on a lattice—that breaks time-reversal symmetry and presents a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice.
Entanglement Entropy of Gapped Phases and Topological Order in Three dimensions
We discuss entanglement entropy of gapped ground states in different dimensions, obtained on partitioning space into two regions. For trivial phases without topological order, we argue that the
Detection of symmetry-protected topological phases in one dimension
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped symmetric phases in one-dimensional (1D) systems can be completely
Quantized response and topology of magnetic insulators with inversion symmetry
We study three-dimensional insulators with inversion symmetry in which other point group symmetries, such as time reversal, are generically absent. We find that certain information about such
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