Many-anyon trial states

Abstract

The problem of bounding the (abelian) many-anyon ground-state energy from above, with a dependence on the statistics parameter which matches that of currently available lower bounds, is reduced to studying the correlation functions of Moore-Read (Pfaffian) and Read-Rezayi type clustering states.Comment: 26 pages, 5 figures. Various improvements; added figures and reference

Fermionic behavior of ideal anyons

“…In particular, it is not known whether it depends smoothly, or even continuously, on . We refer to [ 1 , 2 , 20 , 21 , 25 ] for further discussion on the -dependence of the ground-state energy.…”

Quantum impurity model for anyons

“…Rigorous upper and lower bounds on the exact ground-state energy were established in Refs. [66][67][68][69][70][71]. Another approach has been to first regularize the Hamiltonian (5) by making the fluxes extended [72][73][74][75], and in this situation an exact averagefield theory and a corresponding Thomas-Fermi theory may be derived in the almost-bosonic limit α ∼ N −1 → 0 [28,[76][77][78][79].…”

Anyonic quasiparticles of hardcore anyons

“…One can obtain the exact ground-state basis for such a continuum many-anyon Hamiltonian, which is entirely confined to the lowest Landau level [16][17][18]. A recent work has introduced variational ansätze for the ground state of the above Hamiltonian [19,20]. One such ansatz was shown to be the same as the Read-Rezayi state [21].…”