Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

Manna, Sourav; Wildeboer, Julia; Sierra, Germȧn; Nielsen, Anne E. B.

doi:10.1103/physrevb.98.165147

Cited by 13 publications

(13 citation statements)

References 51 publications

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“…We exploit the results obtained in Ref. 20 for quasiholes in the states (let us denote the state as |Ψ qh α with qh standing for quasiholes) and derive the parent Hamiltonian for our cases (|Ψ α ). We have the number of particles for |Ψ qh α as M qh = (η qh N − k p qh k )/q and the number of particles for |Ψ α as M = (ηN − k p k )/q.…”

Section: Parent Hamiltoniansmentioning

confidence: 99%

Quasielectrons in lattice Moore-Read models

2019

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Moore-Read states can be expressed as conformal blocks of the underlying rational conformal field theory, which provides a well explored description for the insertion of quasiholes. It is known, however, that quasielectrons are more difficult to describe in continuous systems, since the natural guess for how to construct them leads to a singularity. In this work, we show that the singularity problem does not arise for lattice Moore-Read states. This allows us to construct Moore-Read Pfaffian states on lattices for filling fraction 5/2 with both quasiholes and quasielectrons in a simple way. We investigate the density profile, charge, size and braiding properties of the anyons by means of Monte Carlo simulations. Further we derive an exact few-body parent Hamiltonian for the states. Finally, we compare our results to the density profile, charge and shape of anyons in the Kapit-Mueller model by means of exact diagonalization. arXiv:1810.12288v2 [cond-mat.str-el]

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Section: Parent Hamiltoniansmentioning

confidence: 99%

Quasielectrons in lattice Moore-Read models

2019

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“…Finally, let us remark that for some values of η, it is possible to derive a parent Hamiltonian for single Moore-Read [54,56] or Laughlin [57] lattice quantum Hall states. However, it is not straightforward to extend these calculations to the case when the system is described by two different CFTs.…”

Section: A the Construction Of The Wavefunctionmentioning

confidence: 99%

“…It can be shown [56] that, assuming the conformal blocks are orthogonal or there is just one, we can express the Berry phase (29) solely using the normalization constant…”

Section: Anyon Statisticsmentioning

confidence: 99%

Model wave functions for interfaces between lattice Laughlin states

Jaworowski

Nielsen

2020

Phys. Rev. B

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We use conformal field theory to construct model wavefunctions for an interface between lattice versions of a bosonic ν = 1/2 Laughlin state and a fermionic ν = 5/2 Moore-Read state. The properties of the resulting model state, such as particle density, correlation function and Rényi entanglement entropy are then studied using the Monte Carlo approach. Moreover, we construct the wavefunctions also for localized anyonic excitations (quasiparticles and quasiholes). We study their density profile, charge and statistics. We show that, similarly to the Laughlin-Laughlin case studied earlier, some anyons (the Laughlin Abelian ones) can cross the interface, while others (the non-Abelian ones) lose their anyonic character in such a process. Also, we argue that, under an assumption of local particle exchange, multiple interfaces give rise to a topological degeneracy, which can be interpreted as originating from Majorana zero modes.

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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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Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

Cited by 13 publications

References 51 publications

Quasielectrons in lattice Moore-Read models

Quasielectrons in lattice Moore-Read models

Model wave functions for interfaces between lattice Laughlin states

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

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