Quantum impurity model for anyons

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

doi:10.1103/physrevb.102.144109

Cited by 17 publications

(16 citation statements)

References 118 publications

(154 reference statements)

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“…We also note that the treatment in [25,31] differs from the one discussed in Refs. [21,22]: the flux tube in the latter is self-induced by an emergent (external) gauge field within the classical Fröhlich-Bogoliubov theory (which is a particular instance of the standard Maxwell electrodynamics), while in our case the flux attachment is a primary constraint built upon the microscopic Lagrangian description of the coupled systemenvironment complex (see A for further details on the microscopic Lagrangian). The consequences of this property at the microscopic level are better illustrated in terms of the imaginary-time path integral formalism, which has played a major role in the description of Brownian systems [29,30].…”

Section: Flux-carrying Brownian Particlesmentioning

confidence: 99%

“…The retarded self-energy in the real time domain is given by Eq. (22). To show the latter we begin with the frequency-dependent Fourier transforms of the dynamical susceptibilities, which can be computed from the back imaginary-time Fourier transforms (4), ( 10) and ( 11) via the analytic continuation [26], e.g.…”

Section: Appendix A: Nonequilibrium Generating Functionalmentioning

confidence: 99%

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Statistical physics of flux-carrying Brownian particles

Valido

2020

Annals of Physics

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We develop the kinetic theory of the flux-carrying Brownian motion recently introduced in the context of open quantum systems. This model constitutes an effective description of two-dimensional dissipative particles violating both time-reversal and parity that is consistent with standard thermodynamics. By making use of an appropriate Breit-Wigner approximation, we derive the general form of its quantum kinetic equation for weak system-environment coupling. This encompasses the well-known Kramers equation of conventional Brownian motion as a particular instance. The influence of the underlying chiral symmetry is essentially twofold: the anomalous diffusive tensor picks up antisymmtretic components, and the drift term has an additional contribution which plays the role of an environmental torque acting upon the system particles. These yield an unconventional fluid dynamics that is absent in the standard (two-dimensional) Brownian motion subject to an external magnetic field or an active torque. For instance, the quantum single-particle system displays a dissipationless vortex flow in sharp contrast with ordinary diffusive fluids. We also provide preliminary results concerning the relevant hydrodynamics quantities, including the fluid vorticity and the vorticity flux, for the dilute scenario near thermal equilibrium. In particular, the flux-carrying effects manifest as vorticity sources in the Kelvin's circulation equation. Conversely, the energy kinetic density remains unchanged and the usual Boyle's law is recovered up to a reformulation of the kinetic temperature.

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Section: Flux-carrying Brownian Particlesmentioning

confidence: 99%

Section: Appendix A: Nonequilibrium Generating Functionalmentioning

confidence: 99%

Statistical physics of flux-carrying Brownian particles

Valido

2020

Annals of Physics

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“…They have been conjectured [2,42,53] to be relevant for the fractional quantum Hall effect (see [24,30,28] for review). They could also be simulated in certain cold atoms systems with synthetic gauge fields [17,10,61,63,64,12].…”

Section: Model and Main Resultsmentioning

confidence: 99%

Semiclassical Limit for Almost Fermionic Anyons

Girardot

Rougerie

2021

Commun. Math. Phys.

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In two-dimensional space there are possibilities for quantum statistics continuously interpolating between the bosonic and the fermionic one. Quasi-particles obeying such statistics can be described as ordinary bosons and fermions with magnetic interactions. We study a limit situation where the statistics/magnetic interaction is seen as a "perturbation from the fermionic end". We vindicate a mean-field approximation, proving that the ground state of a gas of anyons is described to leading order by a semi-classical, Vlasov-like, energy functional. The ground state of the latter displays anyonic behavior in its momentum distribution. Our proof is based on coherent states, Husimi functions, the Diaconis-Freedman theorem and a quantitative version of a semi-classical Pauli pinciple.

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“…The full Hamiltonian (3) acts on an appropriate dense domain in the tensor product Hilbert space of the impurities L 2 sym/asym (S 2 × S 2 ), where L 2 sym (S 2 × S 2 ) is the bosonic Hilbert space and L 2 asym (S 2 × S 2 ) the fermionic one, with the Fock space F L 2 S 2 of the bath. Following the analysis for impurity problems in the planar case [25], the statistics gauge field emerges from H angulon,Ω , by restricting it to the ground state of its pure many-…”

Section: Emerging Gauge Field From the Angulon Hamiltonianmentioning

confidence: 99%

“…This opens up a whole new domain of quantum statistics known as intermediate or fractional statistics. Even though the realization of anyons in experimentally feasible systems has been subject of recent research [18][19][20][21][22][23][24][25], all these works concern particles moving on the Euclidean plane R 2 , or a subset thereof. However, since the statistical behaviour of anyons depends on the topology, and even more importantly on the geometry and symmetry, of the underlying space, investigations on curved spaces can demonstrate novel properties of quantum statistics [2,[26][27][28][29][30][31][32] (see also graph geometries [33,34]).…”

Section: Introductionmentioning

confidence: 99%

Emergence of Anyons on the Two-Sphere in Molecular Impurities

Morris

Lemeshko

Lundholm

et al. 2021

Atoms

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Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle.

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Quantum impurity model for anyons

Cited by 17 publications

References 118 publications

Statistical physics of flux-carrying Brownian particles

Statistical physics of flux-carrying Brownian particles

Semiclassical Limit for Almost Fermionic Anyons

Emergence of Anyons on the Two-Sphere in Molecular Impurities

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