Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2001.06635 · Physical review. B./Physical review. B

Non-Abelian fractional Chern insulator in disk geometry

Ai‐Lei He, Wei-Wei Luo, Hong Yao, Yi-Fei Wang

Published Apr 21, 2020• 9 citations
arXivHTMLPDF

Abstract

Non-Abelian (NA) fractional topological states with quasiparticles obeying NA braiding statistics have attracted intensive attention for both their fundamental nature and the prospect for topological quantum computation. To date, there are many models proposed to realize the NA fractional topological states, such as the well-known Moore-Read quantum Hall states and the non-Abelian fractional Chern insulators (NA-FCIs). Here, we investigate the NA-FCI in disk geometry with three-body hard-core bosons loaded into a topological flat band. This stable $\ensuremath{\nu}=1$ bosonic NA-FCI is characterized by edge excitations and the ground-state angular momentum. Based on the generalized Pauli principle and the Jack polynomials, we successfully construct a trial wave function for the NA-FCI. Moreover, a $\ensuremath{\nu}=1/2$ Abelian FCI state emerges with the increase of the on-site interaction and it can be identified with the help of the trial wave function as well. Our findings not only lead to an optimal wave function for the NA-FCI, but also directly provide an effective approach for future researches on paired topological states.

DOI
10.1103/physrevb.101.165127

Related papers

Wave functions for fractional Chern insulators in disk geometry

Ai-Lei He, Wei-Wei Luo, Yi-Fei Wang +1 more

Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands. These systems exhibit similar fractionalization phenomena to the conventional fractional quantum Hall (FQH) systems. Using the mapping relationship between the FQH states and the FCI/FQAH states, we construct the many-body wave functions of the fermionic FCI/FQAH states in disk geometry with the aid of the generalized Pauli principle (GPP) and Jack polynomials. Compared with the ground state by the exact diagonalization method, the wave-function overlap is higher than 0.97, even when the Hilbert space dimension is as large as 3 × 10 6 . We also use the GPP and the Jack polynomials to construct edge excitations for the fermionic FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems reproduce the prediction of the chiral Luttinger liquid theory, complementing the exact diagonalization results with larger lattice sizes and more particles.

arXiv:1509.01760•New Journal of Physics•Dec 7, 2015•21 citations

Non-Abelian fractional Chern insulators from long-range interactions

Zhao Liu, Emil J. Bergholtz, Eliot Kapit

The recent theoretical discovery of fractional Chern insulators (FCIs) has provided an important new way to realize topologically ordered states in lattice models. In earlier works, on-site and nearest-neighbor Hubbard-like interactions have been used extensively to stabilize Abelian FCIs in systems with nearly flat, topologically nontrivial bands. However, attempts to use two-body interactions to stabilize non-Abelian FCIs, where the ground state in the presence of impurities can be massively degenerate and manipulated through anyon braiding, have proven very difficult in uniform lattice systems. Here, we study the remarkable effect of long-range interactions in a lattice model that possesses an exactly flat lowest band with a unit Chern number. When spinless bosons with two-body long-range interactions partially fill the lowest Chern band, we find convincing evidence of gapped, bosonic Read-Rezayi (RR) phases with non-Abelian anyon statistics. We characterize these states through studying topological degeneracies, the overlap between the ground states of two-body interactions and the exact RR ground states of three- and four-body interactions, and state counting in the particle-cut entanglement spectrum. Moreover, we demonstrate how an approximate lattice form of Haldane's pseudopotentials, analogous to that in the continuum, can be used as an efficient guiding principle in the search for lattice models with stable non-Abelian phases.

arXiv:1309.4106•Physical Review B•Nov 1, 2013•51 citations

Edge excitations in fractional Chern insulators

Wei-Wei Luo, Wen-Chao Chen, Yi-Fei Wang +1 more

Recent theoretical papers have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role in obtaining a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagome-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.

arXiv:1304.4338•Physical Review B•Oct 29, 2013•23 citations

Non-Abelian Quantum Hall Effect in Topological Flat Bands

Yi-Fei Wang, Hong Yao, Zheng‐Cheng Gu +2 more

Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.

arXiv:1110.4980•Physical Review Letters•Mar 21, 2012•124 citations

Role of the defect-core orbital in fractional Chern insulators

Ai‐Lei He

Fractional Chern insulator (FCI) states have been proposed in singular lattices with arbitrary $n$-fold rotational symmetry. Particles occupy non-defect-core orbitals in previously reported FCIs. However, the role of defect-core orbitals in the singular-lattice FCI states has seldom been discussed. In this paper, we report a series of singular-lattice FCI states with one particle occupying the defect-core orbital. This singular-lattice FCI state can be identified with the aid of the edge excitations, the angular momentum of the ground state (GS), and the optimal trial wave functions. Edge excitations and GS angular momentum are obtained using exact diagonalization. Optimal trial wave functions are constructed on the basis of the generalized Pauli principle, the Jack polynomials, and single-particle states. The present FCI state is identified as a $\ensuremath{\nu}=1/2$ FCI with high values of wave function overlap, where one particle occupies the low-energy defect-core orbital. Our studies reveal the intriguing interplay between the singular-lattice FCI and the defect-core orbital and provide an effective approach for future researches on FCIs with various defects or disorders.

Physical review. B./Physical review. B•Mar 22, 2021•8 citations

Fractional quantum Hall effect in topological flat bands with Chern number two

Yi-Fei Wang, Hong Yao, Chang-De Gong +1 more

Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number $C=1$. Here we study hard-core bosons and interacting fermions in a three-band triangular-lattice model with the lowest topological flat band of Chern number $C=2$. We find convincing numerical evidence of bosonic fractional quantum Hall effect at the $\ensuremath{\nu}=1/3$ filling characterized by threefold quasidegeneracy of ground states on a torus, a fractional Chern number for each ground state, a robust spectrum gap, and a gap in quasihole excitation spectrum. We also observe numerical evidence of a robust fermionic fractional quantum Hall effect for spinless fermions at the $\ensuremath{\nu}=1/5$ filling with short-range interactions.

arXiv:1204.1697•Physical Review B•Nov 5, 2012•166 citations
Non-Abelian (NA) fractional topological states with quasiparticles obeying NA braiding statistics have attracted intensive attention for both their fundamental nature and the prospect for topological quantum computation. To date, there are many models proposed to realize the NA fractional topological states, such as the well-known Moore-Read quantum Hall states and the non-Abelian fractional Chern insulators (NA-FCIs). Here, we investigate the NA-FCI in disk geometry with three-body hard-core bosons loaded into a topological flat band. This stable \ensuremathν=1\ensuremath{\nu}=1\ensuremathν=1 bosonic NA-FCI is characterized by edge excitations and the ground-state angular momentum. Based on the generalized Pauli principle and the Jack polynomials, we successfully construct a trial wave function for the NA-FCI. Moreover, a \ensuremathν=1/2\ensuremath{\nu}=1/2\ensuremathν=1/2 Abelian FCI state emerges with the increase of the on-site interaction and it can be identified with the help of the trial wave function as well. Our findings not only lead to an optimal wave function for the NA-FCI, but also directly provide an effective approach for future researches on paired topological states.
Recently, fractional Chern insulators (FCIs), also called fractional quantum anomalous Hall (FQAH) states, have been theoretically established in lattice systems with topological flat bands. These systems exhibit similar fractionalization phenomena to the conventional fractional quantum Hall (FQH) systems. Using the mapping relationship between the FQH states and the FCI/FQAH states, we construct the many-body wave functions of the fermionic FCI/FQAH states in disk geometry with the aid of the generalized Pauli principle (GPP) and Jack polynomials. Compared with the ground state by the exact diagonalization method, the wave-function overlap is higher than 0.97, even when the Hilbert space dimension is as large as 3 × 10 6 . We also use the GPP and the Jack polynomials to construct edge excitations for the fermionic FCI/FQAH states. The quasi-degeneracy sequences of fermionic FCI/FQAH systems reproduce the prediction of the chiral Luttinger liquid theory, complementing the exact diagonalization results with larger lattice sizes and more particles.
The recent theoretical discovery of fractional Chern insulators (FCIs) has provided an important new way to realize topologically ordered states in lattice models. In earlier works, on-site and nearest-neighbor Hubbard-like interactions have been used extensively to stabilize Abelian FCIs in systems with nearly flat, topologically nontrivial bands. However, attempts to use two-body interactions to stabilize non-Abelian FCIs, where the ground state in the presence of impurities can be massively degenerate and manipulated through anyon braiding, have proven very difficult in uniform lattice systems. Here, we study the remarkable effect of long-range interactions in a lattice model that possesses an exactly flat lowest band with a unit Chern number. When spinless bosons with two-body long-range interactions partially fill the lowest Chern band, we find convincing evidence of gapped, bosonic Read-Rezayi (RR) phases with non-Abelian anyon statistics. We characterize these states through studying topological degeneracies, the overlap between the ground states of two-body interactions and the exact RR ground states of three- and four-body interactions, and state counting in the particle-cut entanglement spectrum. Moreover, we demonstrate how an approximate lattice form of Haldane's pseudopotentials, analogous to that in the continuum, can be used as an efficient guiding principle in the search for lattice models with stable non-Abelian phases.
Recent theoretical papers have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role in obtaining a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagome-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.
Inspired by the recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-abelian quantum Hall effect in lattice models with topological flat bands. Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a topological flat band, we find convincing numerical evidence of a stable ν=1 bosonic non-abelian quantum Hall effect, with the characteristic threefold quasidegeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower-energy sector satisfying the same counting rule as the Moore-Read pfaffian state.
Fractional Chern insulator (FCI) states have been proposed in singular lattices with arbitrary nnn-fold rotational symmetry. Particles occupy non-defect-core orbitals in previously reported FCIs. However, the role of defect-core orbitals in the singular-lattice FCI states has seldom been discussed. In this paper, we report a series of singular-lattice FCI states with one particle occupying the defect-core orbital. This singular-lattice FCI state can be identified with the aid of the edge excitations, the angular momentum of the ground state (GS), and the optimal trial wave functions. Edge excitations and GS angular momentum are obtained using exact diagonalization. Optimal trial wave functions are constructed on the basis of the generalized Pauli principle, the Jack polynomials, and single-particle states. The present FCI state is identified as a $\ensuremath{\nu}=1/2$ FCI with high values of wave function overlap, where one particle occupies the low-energy defect-core orbital. Our studies reveal the intriguing interplay between the singular-lattice FCI and the defect-core orbital and provide an effective approach for future researches on FCIs with various defects or disorders.
Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number C=1C=1C=1. Here we study hard-core bosons and interacting fermions in a three-band triangular-lattice model with the lowest topological flat band of Chern number C=2C=2C=2. We find convincing numerical evidence of bosonic fractional quantum Hall effect at the $\ensuremath{\nu}=1/3$ filling characterized by threefold quasidegeneracy of ground states on a torus, a fractional Chern number for each ground state, a robust spectrum gap, and a gap in quasihole excitation spectrum. We also observe numerical evidence of a robust fermionic fractional quantum Hall effect for spinless fermions at the $\ensuremath{\nu}=1/5$ filling with short-range interactions.