Search results for "Symmetry protected topological order"

Signatures of topological phase transitions in Josephson current-phase discontinuities

2016

Topological superconductors differ from topologically trivial ones for the presence of topologically protected zero-energy modes. To date, experimental evidence of topological superconductivity in nanostructures has been mainly obtained by measuring the zero-bias conductance peak via tunneling spectroscopy. Here, we propose an alternative and complementary experimental recipe to detect topological phase transitions in these systems. We show in fact that, for a finite-sized system with broken time-reversal symmetry, discontinuities in the Josephson current-phase relation correspond to the presence of zero-energy modes and to a change in the fermion parity of the groundstate. Such discontinui…

Compact Topological Quantum Groups

1995

Using vector spaces topologies we unify the different models of quantum groups. Duality and reflexivity are built in. The Drinfeld deformation can be extended to the distributions on a simple compact Lie group and dually to the infinitely differentiable functions. The topological quantum double is similarly defined and a uniqueness result is obtained.

Topological Phases in Planar Electrodynamics

2001

This section is meant to be an extension of Chap. 31 on the quantal Berry phases. In particular, we are interested in studying the electromagnetic interaction of particles with a nonzero magnetic moment in \(D = 2 + 1\) dimensions and of translational invariant configurations of \((D = 3 + 1)\)-dimensional charged strings with a nonzero magnetic moment per unit length. The whole discussion is based on our article in Physical Review D44, 1132 (1991).

Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization

2014

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on Projected Entangled Pair States to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation…

Noncompact Topological Quantum Groups

1995

A star-product construction of quantum semisimple real Lie groups is performed for the noncompact case.

Topological field theory

1991

A topological model for Oersted-Amp�re's law

1973

A geometrical description of Oersted-Ampere's law ∮H ds=(4π/c)I can be given in terms of an appropriate topological manifold. More precisely: It will be shown that Oersted-Ampere's law can be related to the topological invariantH 1(S 1), i.e. de Rham's first cohomology group on the differentiable manifoldS 1={(x,y) ∈ ℝ2∶x 2+y 2}