Reduced Density Matrices in Quantum Physics and Role of Fermionic Exchange Symmetry

Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels


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Duncan Haldane talks about Quantum Geometry, Exclusion Statistics, and the Geometry of "Flux Attachment" in 2D Landau levels. The degenerate partially-filled 2D Landau level is a remarkable environment in which kinetic energy is replaced by "quantum geometry" (or an uncertainty principle) that quantises the space occupied by the electrons quite differently from the atomic-scale quantisation by a periodic arrangement of atoms. In this arena, when the short-range part of the Coulomb interaction dominates, it can lead to "flux attachment", where a particle (or cluster of particles) exclusively occupies a quantised region of space. This principle underlies both the incompressible fractional quantum Hall fluids an the composite fermion Fermi liquid states that occur in such systems.
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Reduced Density Matrices in Quantum Physics and Role of Fermionic Exchange SymmetryBy Oxford University