Exclusion bounds for extended anyons

Abstract

We introduce a rigorous approach to the many-body spectral theory of extended anyons, i.e. quantum particles confined to two dimensions that interact via attached magnetic fluxes of finite extent. Our main results are many-body magnetic Hardy inequalities and local exclusion principles for these particles, leading to estimates for the ground-state energy of the anyon gas over the full range of the parameters. This brings out further non-trivial aspects in the dependence on the anyonic statistics parameter, and also gives improvements in the ideal (non-extended) case.

Accepted and final version. 51 pages 7 figures

References in corpus (7)

• Many-Body Physics with Ultracold Gases
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons and the quantum Hall effect - a pedagogical review
• Emergence of fractional statistics for tracer particles in a Laughlin liquid
• Many-anyon trial states
• Gaussian potentials facilitate access to quantum Hall states in rotating Bose gases
• Local density approximation for the almost-bosonic anyon gas

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• A Quantum Impurity Model for Anyons
• Average Field Approximation for Almost Bosonic Anyons in a Magnetic Field
• Local Density Approximation for Almost-Bosonic Anyons
• Lieb-Robinson bounds, the spectral flow, and stability of the spectral gap for lattice fermion systems
• Fermionic behavior of ideal anyons
• Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics
• Semiclassical limit for almost fermionic anyons
• Properties of 2D anyon gas
• A Lieb-Thirring inequality for extended anyons
• Exchange and exclusion in the non-abelian anyon gas
• The Lieb-Thirring inequality for interacting systems in strong-coupling limit
• The six blinds and the elephant or an interdisciplinary selection of measurement features
• 2D magnetic stability