Symmetry-Protected Topological Orders in Interacting Bosonic Systems

@article{Chen2012SymmetryProtectedTO,
  title={Symmetry-Protected Topological Orders in Interacting Bosonic Systems},
  author={Xie Chen and Zheng-Cheng Gu and Zhengxin Liu and Xiao-Gang Wen},
  journal={Science},
  year={2012},
  volume={338},
  pages={1604 - 1606}
}
Symmetry Semantics Topological insulators (TIs) are characterized by boundary states that are protected by time-reversal symmetry. A systematic study of this, and other symmetry-protected states, is possible in noninteracting systems, but complications arise when interactions are present. Chen et al. (p. 1604; see the Perspective by Qi) used group cohomology theory to predict symmetry-protected phases of interacting bosons. The analysis enabled the generalization of a known result in one… 
Symmetry-protected topological phases from decorated domain walls.
TLDR
It is shown that symmetry-protected topological phases are realized when these domain walls are decorated, that is, are themselves symmetries in one lower dimension, both for unitary Z2 and anti-unitary time reversal symmetry.
Higher-order symmetry-protected topological states for interacting bosons and fermions
Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces,
Interacting edge states of fermionic symmetry-protected topological phases in two dimensions
Recently, it has been found that there exist symmetry-protected topological phases of fermions, which have no realizations in non-interacting fermionic systems or bosonic models. We study the edge
Physics of symmetry protected topological phases involving higher symmetries and its applications
We discuss physical constructions and the boundary properties of various symmetry-protected topological phases that involve 1-form symmetries from one spatial dimension to four spatial dimensions
Classification of Interacting Electronic Topological Insulators in Three Dimensions
TLDR
It is proved that these eight phases form a complete list of all possible interacting topological insulators and discuss their experimental signatures.
Anomalous Symmetry Protected Topological States in Interacting Fermion Systems.
TLDR
The essential idea that there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system is demonstrated and the layer structure and systematical construction of ASPT states in interacting fermion systems in 2D with a total symmetry G_{f}=G_{b}×Z_{2}^{f}.
Observation of symmetry-protected topological band with ultracold fermions
TLDR
This work reports the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and studies quench dynamics between topologically distinct regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology.
Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases
Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered
Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
We generalize Laughlin's flux insertion argument, originally discussed in the context of the quantum Hall effect, to topological phases protected by non-on-site unitary symmetries, in particular by
Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
We study glide protected topological (GSPT) phases of interacting bosons and fermions in three spatial dimensions with certain on-site symmetries. They are crystalline SPT phases, which are
...
...

References

SHOWING 1-10 OF 33 REFERENCES
Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations
Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected
Periodic table for topological insulators and superconductors
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a
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
Classification of gapped symmetric phases in one-dimensional spin systems
Quantum many-body systems divide into a variety of phases with very different physical properties. The questions of what kinds of phases exist and how to identify them seem hard, especially for
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
Classification of topological insulators and superconductors in three spatial dimensions
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial
Topological Orders in Rigid States
We study a new kind of ordering — topological order — in rigid states (the states with no local gapless excitations). We concentrate on characterization of the different topological orders. As an
Braiding statistics approach to symmetry-protected topological phases
We construct a 2D quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected topological phase."
Classifying quantum phases using matrix product states and projected entangled pair states
We give a classification of gapped quantum phases of one-dimensional systems in the framework of matrix product states (MPS) and their associated parent Hamiltonians, for systems with unique as well
Topological insulators and superconductors: Tenfold way and dimensional hierarchy
It has recently been shown that in every spatial dimension there exist precisely five distinct classes of topological insulators or superconductors. Within a given class, the different topological
...
...