# Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect

@inproceedings{Zeng2021ChernNM, title={Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect}, author={Tian-Sheng Zeng and W. Zhu}, year={2021} }

While the internal structure of Abelian topological order is well understood, how to characterize the non-Abelian topological order is an outstanding issue. We propose a distinctive scheme based on the many-body Chern number matrix to characterize non-Abelian multicomponent fractional quantum Hall states. As a concrete example, we study the many-body ground state of two-component bosons at the filling faction ν = 4/3 in topological flat band models. Utilizing density-matrix renormalization…

## One Citation

Integer quantum Hall effect of two-component hardcore bosons in topological triangular lattice

- Physics
- 2022

We study the many-body ground states of two-component hardcore bosons in topological triangular lattice models. Utilizing exact diagonalization and density-matrix renormalization group calculations,…

## References

SHOWING 1-10 OF 56 REFERENCES

Non-abelian quantum Hall effect in topological flat bands.

- PhysicsPhysical review letters
- 2012

Significant numerical evidence is found of a stable ν=1 bosonic non-abelian quantum Hall effect in lattice models with topological flat bands with characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap.

Quantum spin-Hall effect and topologically invariant Chern numbers.

- PhysicsPhysical review letters
- 2006

It is shown that the topology of the band insulator can be characterized by a 2 x 2 matrix of first Chern integers, and the nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM).

Bridge between Abelian and non-Abelian fractional quantum Hall states.

- Physics, MathematicsPhysical review letters
- 2008

Numerical calculations corroborate the picture that K-component Halperin wave functions may be a common basis for both Abelian and non-Abelian trial wave functions in the study of one-component quantum Hall systems.

NEW CLASS OF NON-ABELIAN SPIN-SINGLET QUANTUM HALL STATES

- Physics
- 1999

We present a new class of non-abelian spin-singlet quantum Hall states, generalizing Halperin's abelian spin-singlet states and the Read-Rezayi non-abelian quantum Hall states for spin-polarized…

Classification of Abelian quantum Hall states and matrix formulation of topological fluids.

- PhysicsPhysical review. B, Condensed matter
- 1992

It is shown that under certain mild assumptions the generalized hierarchy construction exhausts all possible Abelian fractional quantum Hall states and identifies and determines the topological quantity known as the shift.

Possible non-Abelian Moore-Read state in double-layer bosonic fractional quantum Hall system

- Physics
- 2015

Identifying and understanding interacting systems that can host non-Abelian topological phases with fractionalized quasiparticles have attracted intense attentions in the past twenty years.…

SU (N ) fractional quantum Hall effect in topological flat bands

- Physics
- 2017

We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group…

K -matrices for non-Abelian quantum Hall states

- Physics
- 2000

Two fundamental aspects of so-called non-abelian quantum Hall states (the $q$-pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-abelian…

Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU(
N
) symmetry

- PhysicsPhysical Review B
- 2019

We study the many-body ground states of SU($N$) symmetric hardcore bosons on the topological flat-band model by using controlled numerical calculations. By introducing strong intracomponent and…

Non-Abelian statistics in the fractional quantum Hall states.

- Mathematics, PhysicsPhysical review letters
- 1991

The Fractional Quantum Hall states with non-Abelian statistics are studied and it is argued that the topological orders and the associated properties are robust against any kinds of small perturbations.