Exactly soluble model of boundary degeneracy.

@article{Ganeshan2017ExactlySM,
  title={Exactly soluble model of boundary degeneracy.},
  author={Sriram Ganeshan and Alexey V. Gorshkov and Victor Gurarie and Victor M. Galitski},
  journal={Physical review. B},
  year={2017},
  volume={95}
}
We investigate the topological degeneracy that can be realized in Abelian fractional quantum spin Hall states with multiply connected gapped boundaries. Such a topological degeneracy (also dubbed as "boundary degeneracy") does not require superconducting proximity effect and can be created by simply applying a depletion gate to the quantum spin Hall material and using a generic spin-mixing term (e.g., due to backscattering) to gap out the edge modes. We construct an exactly soluble microscopic… 

Figures and Topics from this paper

Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
We present a detailed microscopic investigation of fractional quantum Hall states with gapped boundaries in a coupled bilayer lattice model featuring holes whose counterpropagating chiral edge states
Topological Quantum Computation with Gapped Boundaries
This paper studies fault-tolerant quantum computation with gapped boundaries. We first introduce gapped boundaries of Kitaev's quantum double models for Dijkgraaf-Witten theories using their
Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
We present an exactly solvable lattice Hamiltonian to realize gapped boundaries of Kitaev’s quantum double models for Dijkgraaf-Witten theories. We classify the elementary excitations on the
From coupled wires to coupled layers: Model with three-dimensional fractional excitations
We propose a systematic approach to constructing microscopic models with fractional excitations in three-dimensional (3D) space. Building blocks are quantum wires described by the (1+1)-dimensional
Topological quantum computation with gapped boundaries and boundary defects
We survey some recent work on topological quantum computation with gapped boundaries and boundary defects and list some open problems.

References

SHOWING 1-10 OF 35 REFERENCES
Boundary degeneracy of topological order
We introduce the concept of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary degeneracy provides richer
Experimental Proposal to Detect Topological Ground State Degeneracy
One of the most profound features of topologically ordered states of matter, such as the fractional quantum Hall (FQH) states, is that they possess topology-dependent ground state degeneracies that
Ground-state degeneracy of topological phases on open surfaces.
TLDR
It is proposed that gapped boundary conditions of the surface are in one-to-one correspondence with the sets of condensates, each being able to completely break the phase, and generalized pumping may find applications in quantum control of anyons, eventually realizing topological quantum computation.
Ground-state degeneracy for Abelian anyons in the presence of gapped boundaries
Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well defined and can be computed using methods of topological quantum
Charge 2e/3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States.
TLDR
It is demonstrated that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode, and the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state.
Topological Nematic States and Non-Abelian Lattice Dislocations
An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall (FQH) states in simple lattice models without a large external magnetic field. A
Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
We study the superconducting proximity effect on the helical edge states of time-reversal-symmetric fractional topological insulators(FTI). The Cooper pairing of electrons results in many-particle
Fractional topological superconductor with fractionalized Majorana fermions
In this paper, we introduce a two-dimensional fractional topological superconductor (FTSC) as a strongly correlated topological state which can be achieved by inducing superconductivity into an
Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors
Realizing fractional Chern insulators in dipolar spin systems.
TLDR
This work predicts that the ν = 1/2 fractional Chern insulator arises naturally in a two-dimensional array of driven, dipolar-interacting spins and presents a detailed experimental blueprint for its realization and demonstrates that the implementation is consistent with near-term capabilities.
...
1
2
3
4
...