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

  title={Topological Phases of One-Dimensional Fermions: An Entanglement Point of View},
  author={Ari M. Turner and F. Pollmann and Erez Berg},
  journal={Physical Review B},
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 L. Fidkowski and A. Kitaev [Phys. Rev. B 81, 134509 (2010)], we find that in the presence of interactions there… 

Figures and Tables from this paper

Topological phases of fermions in one dimension
In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of one-dimensional systems. We focus on the
Theory and classification of interacting integer topological phases in two dimensions: A Chern-Simons approach
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e. with a unique ground state on closed manifolds and no fractional excitations).
Classification of Interacting Topological Floquet Phases in One Dimension
Periodic driving of a quantum system can enable new topological phases with no analog in static systems. In this paper we systematically classify one-dimensional topological and symmetry-protected
Quantum phases and topological properties of interacting fermions in one-dimensional superlattices
The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter
Bipartite charge fluctuations in one-dimensional Z 2 superconductors and insulators
Bipartite charge fluctuations (BCFs) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to
Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke
Quenched dynamics and spin-charge separation in an interacting topological lattice
We analyze the static and dynamical properties of a one-dimensional topological lattice, the fermionic Su-Schrieffer-Heeger model, in the presence of on-site interactions. Based on a study of charge
Topology and Edge Modes in Quantum Critical Chains.
It is shown that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases and can be stable in the presence of interactions and disorder.
Gapless Topological Phases and Symmetry-Enriched Quantum Criticality
We introduce topological invariants for critical bosonic and fermionic chains. More generally, the symmetry properties of operators in the low-energy conformal field theory (CFT) provide discrete
Asymptotic Correlations in Gapped and Critical Topological Phases of 1D Quantum Systems
Topological phases protected by symmetry can occur in gapped and—surprisingly—in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is


arXiv : 1008 . 3745 ( 2010 ) . 20 A
  • 2010
Why then is it possible to make half-integer spins out of integer spins in a spin chain? The point is that operators cannot transform in a "fractional way
    arXiv : 0912 . 0028 ( 2009 ) . 22 L . Fidkowski
    • Phys . Rev . Lett .
    • 2001