Anyon Superconductivity and Off-Diagonal Long-Range Order

Abstract

§ 1. Introduction to fractional statistics Particles obeying fractional statistics 1 l-Sl can, in two space dimensions form an exotic quantum fluid which can condense into a new type of superconductor. 4 l The simplest realization of a fractional statistics particle or 'anyon' consists of an ordinary boson (or fermion) bound to a magnetic flux tube (oriented perpendicular to the 2D plane) as shown in Fig. 1.If one anyon is dragged adiabatically around another in a closed counterclockwise path, the quantum state acquires an extra (Berry's) phase due to the Aharanov-Bohm effect If we call this phase factor exp(i28) then adiabatic counterclockwise exchange of two particles will yield an extra phase exp(i8). Hence 8 (whose value is determined by the particle charge and the strength of the flux tube) is called the statistics angle. If 8 = 7r and the original particles were bosons, the composite particles are fermions since they yield a minus sign up exchange. There are no quantization conditions which constrain the strength of the flux tube and hence 8 is continuously adjustable. Systems for which 8/Jr is fractional are said to obey fractional statistics. We shall be particularly concerned here with the special case of 'semions' which have 8/Jr=1/2.The Hamiltonian for a system of N non-relativistic anyons is at Ernst Mayr

Superconductivity in a system of interacting spinful semions

“…To investigate the presence of ODLRO for these systems, we now define the two-body reduced density matrix as [34,36]…”

“…This mean field theory produces algebraic ODLRO in the 2body reduced density matrix [33,34]. There also exists an exactly solvable model of spinful semions beyond the mean field description, which exhibits (not just algebraic) ODLRO [35,36]. In this paper, we revisit this problem by developing a method to construct the Hubbard model of anyons.…”

Dependence of critical exponents on θ parameter in anyon lattice model

“…We consider this problem important because of the existence of the phase state found in Ref. [22], in which the two-body density matrix does not depend on distance between particles at large distances.…”