Average Field Approximation for Almost Bosonic Anyons in a Magnetic Field

Abstract

We study the ground state of a large number N of 2D anyons in an external magnetic field. We consider a scaling limit where the statistics parameter $\alpha$ tends to zero when N tends to infinity which allows the statistics to be seen as a "perturbation from the bosonic end". Our model is that of bosons in a magnetic field and interacting through long-range magnetic potential generated by magnetic charges carried by each particle, smeared over discs of radius R. Our method allows to take R tends to not too fast at the same time as N tends to infinity. We use the information theoretic version of the de Finetti theorem of Brand{ã}o and Harrow to justify the so-called "average field approximation": the particles behave like independent, identically distributed bosons interacting via a self-consistent magnetic field.

arXiv commentarXiv admin note: text overlap with arXiv:1505.05982, arXiv:1901.09561 by other authors

References in corpus (10)

• Aharonov-Bohm Effect with $\delta$--type Interaction
• Emergence of fractional statistics for tracer particles in a Laughlin liquid
• Hardy and Lieb-Thirring inequalities for anyons
• Many Particle Hardy-Inequalities
• Quantum de Finetti theorem under fully-one-way adaptive measurements
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Cited by in corpus (10)

• A Quantum Impurity Model for Anyons
• The condensation of a trapped dilute Bose gas with three-body interactions
• Magnetic Perturbations of Anyonic and Aharonov-Bohm Schrödinger Operators
• Kohn-Sham Density Functional Theory of Abelian Anyons
• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
• Schrödinger operators with multiple Aharonov-Bohm fluxes
• Semiclassical limit for almost fermionic anyons
• Properties of 2D anyon gas
• A Lieb-Thirring inequality for extended anyons
• 2D magnetic stability