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Topological origin of zero-energy edge states in particle-hole symmetric systems.
A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians and provides a unified framework to discuss zero- energy edge modes for several systems such as fully gapped superconductor, two-dimensional d-wave superconductors, and graphite ribbons. Expand
Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin)Expand
Quantized Berry Phases as a Local Order Parameter of a Quantum Liquid(Condensed matter: structure and mechanical and thermal properties)
We propose the use of quantized Berry phases as a local topological order parameter of a gapped quantum liquid in any dimension that is invariant under some antiunitary operation. The BerryExpand
Quantum Spin Hall Effect in Three Dimensional Materials: Lattice Computation of Z2 Topological Invariants and Its Application to Bi and Sb
We derive an efficient formula for Z 2 topological invariants characterizing the quantum spin Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numericalExpand
Entanglement entropy and the Berry phase in the solid state
The entanglement entropy (von Neumann entropy) has been used to characterize the complexity of many-body ground states in strongly correlated systems. In this paper, we try to establish a connectionExpand
Exactly Solvable Model of Correlated Lattice Electrons in Any Dimensions
We present an exactly solvable Hamiltonian which consists of nearest neighbor hopping and long-range interaction. The ground state and the thermodynamic quantities are analytically obtained in anyExpand
Manipulation of Dirac Cones in Mechanical Graphene
The vibration spectrum of mechanical graphene is characterized by Dirac cones serving as sources of topological nontriviality, and it is found that the spectrum has dramatic dependence on the spring tension at equilibrium as a natural control parameter. Expand
Topological aspects of the quantum spin-Hall effect in graphene: Z2 topological order and spin Chern number
For generic time-reversal-invariant systems with spin-orbit couplings, we clarify a close relationship between the ${\mathrm{Z}}_{2}$ topological order and the spin Chern number (SChN) in the quantumExpand
Topological analysis of the quantum Hall effect in graphene: Dirac-Fermi transition across van Hove singularities and edge versus bulk quantum numbers
Inspired by a recent discovery of a peculiar integer quantum Hall effect (QHE) in graphene, we study QHE on a honeycomb lattice in terms of the topological quantum number, with two interests. First,Expand
Exceptional rings protected by emergent symmetry for mechanical systems
We propose mechanical systems, described by Newton's equation of motion, as suited platforms for symmetry protection of non-Hermitian degeneracies. We point out that in contrast to other systems withExpand