Self-consistent renormalization of Chern-Simons term and correlations in system of anyons

Francesco Mancarella

Lucjan Jacak, Piotr Sitko, Konrad Wieczorek +1 more

This chapter addresses the quantum theory of many-body systems with Chern–Simons field in order to describe the change of statistics in two-dimensional systems. The random phase approximation is used for an anyon gas. Within this approach the correlation energy of an anyon gas is found. The Hartree–Fock approximation for Chern–Simons systems and diagram analysis for a gas of anyons for self-consistent Hartree and Hartree–Fock approximations is also given.

Théotime Girardot, Jinyeop Lee

We study the time evolution of an initial product state in a system of almost-bosonic-extended-anyons in the large-particle limit. We show that the dynamics of this system can be well approximated, in finite time, by a product state evolving under the effective Chern--Simons--Schrödinger equation. Furthermore, we provide a convergence rate for the approximation in terms of the radius $R = (\log N)^{\frac{1}{2}+\varepsilon}$ of the extended anyons. These results establish a rigorous connection between the microscopic dynamics of almost-bosonic-anyon gases and the emergent macroscopic behavior described by the Chern--Simons--Schrödinger equation.

D Eliezer, Gordon Walter Semenoff

C. R. Hägen

Abstract It is pointed out that Chern-Simons field theories do not always allow an interpretation in terms of anyons even in the nonrelativistic limit. Significantly, when the two approaches are found to differ the former is the one which is compatible with established physical principles. Thus the role left for the anyon is that of a very special subcase of Chern-Simons theories in the limit in which relativistic and spin considerations become irrelevant.