A Quantum Impurity Model for Anyons

Yakaboylu, Enderalp; Ghazaryan, Areg; Lundholm, Douglas; Rougerie, Nicolas; Lemeshko, Mikhail; Seiringer, Robert

doi:10.48550/arxiv.1912.07890

Cited by 3 publications

(12 citation statements)

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“…Furthermore, the authors provide numerical evidence of the formation of localised density profiles identified as anyons. We also find references [150,151] to be similar in spirit to our scheme. There, when identical impurities are introduced in a planar bosonic bath, Frölich polarons are identified as anyons, which play a similar role to our localised density profiles.…”

Section: Discussionmentioning

confidence: 59%

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Synthetic Flux Attachment

Valentí-Rojas,

Westerberg,

Öhberg

2020

Preprint

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Topological field theories emerge at low energy in strongly-correlated condensed matter systems and appear in the context of planar gravity. In particular, the study of Chern-Simons terms gives rise to the concept of flux attachment when the gauge field is coupled to matter, yielding flux-charge composites. Here we investigate the generation of flux attachment in a Bose-Einstein condensate in the presence of non-linear synthetic gauge potentials. In doing so, we identify the U(1) Chern-Simons gauge field as a singular density-dependent gauge potential, which in turn can be expressed as a Berry connection. We envisage a proof-of-concept scheme where the artificial gauge field is perturbatively induced by an effective light-matter detuning created by interparticle interactions. At a mean field level, we recover the action of a "charged" superfluid minimally coupled to both a background and a Chern-Simons gauge field. Remarkably, a localised density perturbation in combination with a non-linear gauge potential gives rise to a bosonic fractional quantum Hall effect, displaying anyonic vortices.

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Section: Discussionmentioning

confidence: 59%

“…We also thank K. Hazzard for drawing our attention to Refs. [150,151]. G. V-R. acknowledges financial support from EPSRC CM-CDT Grant No.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Synthetic Flux Attachment

Valentí-Rojas,

Westerberg,

Öhberg

2020

Preprint

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“…Several authors have theoretically addressed the quantum mechanics of mobile impurities immersed in FQH fluids and have written effective Hamiltonians for the motion of the resulting charge-flux-tube complexes [37][38][39][40][41][42][43]. Most such treatments were however based on heuristic models of the binding mechanism: while this was sufficient to get an accurate answer for the synthetic charge and the fractional statistics, it did not provide a quantitative prediction for the mass of the anyonic molecule: this is in fact determined by the bare mass of the impurity, supplemented by a correction due to the inertia of the FQH quasi-holes.…”

Section: The Born-oppenheimer Approximationmentioning

confidence: 99%

“…An interferometric scheme to measure fractional charges by binding a mobile impurity to quasi-particles was proposed in [40]. Alternative models where heavy particles may acquire fractional statistics by interacting with phonons in the presence of strong magnetic fields and/or fast rotation were proposed in [41,42]. The transport properties of impurities embedded in a Fermi gas in a (integer) Chern-insulating state were recently studied in [43].…”

Section: Introductionmentioning

confidence: 99%

Anyonic Molecules in Atomic Fractional Quantum Hall Liquids: A Quantitative Probe of Fractional Charge and Anyonic Statistics

2020

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We study the quantum dynamics of massive impurities embedded in a strongly interacting twodimensional atomic gas driven into the fractional quantum Hall (FQH) regime under the effect of a synthetic magnetic field. For suitable values of the atom-impurity interaction strength, each impurity can capture one or more quasi-hole excitations of the FQH liquid, forming a bound molecular state with novel physical properties. An effective Hamiltonian for such molecules is derived within the Born-Oppenheimer approximation, which provides renormalized values for the effective mass, charge and statistics of such anyonic molecules by combining the finite mass of the impurity and the fractional charge and anyonic statistics of the quasi-holes. The anyonic statistics is shown to provide a long-range Aharonov-Bohm-like interaction between molecules. The resulting relative phase of the direct and exchange scattering channels can be thus extracted from the angular position of the interference fringes in the scattering cross section of a pair of colliding molecules. Different configurations providing direct and quantitative insight on the fractional charge and the anyonic statistics of quasi-hole excitations in FQH liquids are highlighted for both cold atoms and photonic systems.

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“…For instance, it has been recently shown in Refs. [19,20] how these quasiparticles emerge from impurities in standard condensed matter systems. Nevertheless, all these works focus on the particles moving on the two-dimensional plane, i.e., on R 2 .…”

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confidence: 99%