Some Aspects of Anyon Thermodynamics and Chern-Simons Theory

Ya.I. Kogan, Dmitri V. Khveshchenko

A. A. Belov, Andrey Morozov

Abstract Chern–Simons theory in application to the quantum computing is actively developing at the present. However, most discussed are the questions of using materials with known parameters and building corresponding quantum gates and algorithms. In this paper we discuss opposite problem of finding Chern–Simons level k in the unknown material. For this purpose, we use the previously derived braiding rules for Chern–Simons $$SU(2)_k$$ S U ( 2 ) k anyons. Using certain operations (turnarounds) on three anyons, one can measure probabilities of annihilation of pairs of anyons, which depend on the parameter of the theory. Therefore, Chern–Simons level k can be found from such an experiment. It is implied that anyons additionally possess certain properties which are required for topological quantum computations.

Shiing-Shen Chern, C. W. Chu, C. S. Ting

Diptiman Sen

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.

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.