Structuring the set of incompressible quantum Hall fluids Original Research Article

A classification of incompressible quantum Hall fluids in terms of integral lattices and arithmetical invariants thereof is proposed. This classification enables us to characterize the plateau values of the Hall conductivity σH in the interval (0,1] (in units where e2/h = 1) corresponding to “stable” incompressible quantum Hall fluids. A bijection, called shift map, between classes of stable incompressible quantum Hall fluids corresponding to plateaux of σH in the intervals [1(2p + 1), 1(2p − 1)) and [1(2q + 1), 1(2q − 1)), respectively, is constructed, with p,q=1,2,3,(…), p ≠ q.