Journal
PHYSICAL REVIEW B
Volume 104, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.104.035133
Keywords
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Funding
- ERC AdG NOQIA
- Agencia Estatal de Investigacion [CEX2019-000910-S, FIDEUA PID2019-106901GB-I00/10.13039/501100011033]
- Fundacio Privada Cellex
- Fundacio Mir-Puig
- Generalitat de Catalunya (AGAUR Grant - ERDF Operational Program of Catalonia 2014-2020) [2017 SGR 1341, U16-011424]
- MINECO-EU QUANTERA MAQS (State Research Agency (AEI)) [PCI2019-111828-2/10.13039/501100011033]
- EU Horizon 2020 FET-OPEN OPTOLogic [899794]
- National Science Centre, Poland-Symfonia Grant [2016/20/W/ST4/00314]
- la Caixa Foundation [100010434, LCF/BQ/PI19/11690013, LCF/BQ/DI20/11780033]
- Ministerio de Economia y Competitividad Grant [FIS2017-87534-P]
- ICFO
- MPQ Max-Planck Institute for Quantum Optics - Fundacio Cellex
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The relationship between impurity particles and quasiholes in a system described by the Moore-Read wave function reveals the connection between their angular momentum and the physics of non-Abelian excitations, providing important evidence for proving the non-Abelian nature of the excitations.
Non-Abelian excitations are an interesting feature of many fractional quantum Hall phases, including those phases described by the Moore-Read (or Pfaffian) wave function. However, the detection of the non-Abelian quasiparticles is challenging. Here, we consider a system described by the Moore-Read wave function and assume that impurity particles bind to its quasiholes. Then, the angular momentum of the impurities, reflected also by the impurity density, provides a useful witness of the physics of the non-Abelian excitations. By demanding that the impurities are constrained to the lowest Landau level, we are able to write down the corresponding many-body wave function describing both the Moore-Read liquid and the impurities. Through Monte Carlo sampling, we determine the impurity angular momentum, and we show that it suggests a quantum-statistical parameter alpha = a nu - b + P/2 for the quasiholes, where alpha ranges from 0 for bosons to 1 for fermions. A reasonable agreement with the Monte Carlo results is obtained for a = 1/4, b = 1/8, and P = 0, 1 depending on the parity of the particle number in the Moore-Read liquid. This parity dependence of the angular momentum serves as an unambiguous demonstration of the non-Abelian nature of the excitations. In addition to the studies of excitations in the Moore-Read liquid, we also apply our scheme to Laughlin liquids, for which we focus on interacting bosonic impurities. With this, the impurities themselves form Laughlin states, which allows for a study of hierarchical fractional quantum Hall states.
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