Non-Abelian fractional Chern insulators from long-range interactions

Liu, Zhao; Bergholtz, Emil J.; Kapit, Eliot

doi:10.1103/physrevb.88.205101

Cited by 37 publications

(58 citation statements)

References 81 publications

(105 reference statements)

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“…Parent Hamiltonians of the states in the lattice limit were derived using analytical tools from CFT and in some cases it was shown that these states could be stabilized by local Hamiltonians in one and two dimensions. The Hamiltonians derived in the present paper are not expected [31] to be of the fractional Chern insulator type, but since the models can be constructed on arbitrary lattices, it would be of interest to check whether Moore-Read states obtained in fractional Chern insulators [17,[20][21][22][23][24] are close to the states we introduce. Moreover it has been possible using tools from CFT to write lattice wave functions for localized quasiholes of Laughlin states and to derive their parent Hamiltonians [56] and we expect that a similar procedure can be applied to the states we have introduced to obtain quasiholes of Moore-Read states as well as their parent Hamiltonians.…”

Section: Resultsmentioning

confidence: 89%

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Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

et al. 2015

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We introduce a family of strongly-correlated spin wave functions on arbitrary spin-1 2 and spin-1 lattices in one and two dimensions. These states are lattice analogues of Moore-Read states of particles at filling fraction q 1 , which are non-Abelian fractional quantum Hall states in 2D. One parameter enables us to perform an interpolation between the continuum limit, where the states become continuum Moore-Read states of bosons (odd q) and fermions (even q), and the lattice limit. We show numerical evidence that the topological entanglement entropy stays the same along the interpolation for some of the states we introduce in 2D, which suggests that the topological properties of the lattice states are the same as in the continuum, while the 1D states are critical states. We then derive exact parent Hamiltonians for these states on lattices of arbitrary size. By deforming these parent Hamiltonians, we construct local Hamiltonians that stabilize some of the states we introduce in 1D and in 2D.

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Section: Resultsmentioning

confidence: 89%

“…In the first approach, one tries to mimic electrons in a magnetic field by replacing the fractionally filled Landau level by a nearly flat fractionally filled Chern band and adding local interactions [15][16][17][18][19]. Non-Abelian FQH states where found in such lattice models with topological flat bands [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

et al. 2015

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“…Possible extensions of this work include other FCI states, and in particular those hosting non-Abelian QHs [88][89][90][91][92]. State E/t Ψ0 -9.865430303 Ψ1 -9.860769293 Ψ2 -9.828784649 TABLE IV.…”

Section: Discussionmentioning

confidence: 99%

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

Macaluso

Comparin

Umucalılar

et al. 2020

Phys. Rev. Research

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We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling ν = 1/2, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For this purpose we employ a Tree Tensor Network technique, which allows us to study systems with up to N = 18 particles on a 16 × 16 lattice and experiencing an additional harmonic confinement. First, we observe the quantization of the quasihole charge at fractional values and its robustness against the shape and strength of the impurity potentials used to create and localize such excitations. Then, we numerically characterize quasihole anyonic statistics by applying a discretized version of the relation connecting the statistics of quasiholes in the lowest Landau level to the depletions they create in the density profile [E. Macaluso et al., arxiv:1903.03011]. Our results give a direct proof of the anyonic statistics for quasiholes of fractional Chern insulators, starting from a realistic Hamiltonian. Moreover, they provide strong indications that this property can be experimentally probed through local density measurements, making our scheme readily applicable in state-of-the-art experiments with ultracold atoms and superconducting qubits.arXiv:1910.05222v1 [cond-mat.quant-gas]

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“…with integer k ≥ 1 [32]. In this setup, the ground state without defects is two copies of model Z k Read-Rezayi (RR) states on the lattice, residing in the lowest 2φL x L y exactly degenerate eigenstates of H 0 with filling fraction ν = N b /(2φL x L y ) = k/2 [33,34]. Adding M pairs of defects effectively deforms the topology to a single g = M + 1 surface but should not change ν in the thermodynamic limit.…”

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confidence: 99%

Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States

Liu¹,

Möller²,

Bergholtz³

2017

Phys. Rev. Lett.

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We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects. Introduction. Extrinsic defects embedded in topologically ordered phases of matter [1-5] may acquire exotic properties [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Genons [11,12], named after their ability to effectively increase the genus of space thus enhancing the topological degeneracy, are particularly intriguing representatives of this idea and can be visualized as twist defects at the ends of branch cuts connecting separate "world sheets" of different components in the host system. Importantly, the linkage of genons to the topology of space and the underlying topological order establishes them as powerful tools to overcome the long-standing challenge of accessing topological orders on surfaces with tunable genus. It also imparts them with nontrivial quantum dimensions and braiding statistics that are significantly different from those of intrinsic quasiparticles of the host system [12], thus enabling fault tolerant topological quantum computation [23,24] even in Abelian host states without this capability and extending our knowledge of topological order. However, while the beautiful idea of genons is based on topological field theory [11,12] and corroborated by complicated exactly solvable models [6,10,16], its actual relevance to realistic microscopic models has remained open.

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Non-Abelian fractional Chern insulators from long-range interactions

Cited by 37 publications

References 81 publications

Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

Exact parent Hamiltonians of bosonic and fermionic Moore–Read states on lattices and local models

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States

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