Polaronic effects on the energy spectrum of two anyons in a parabolic quantum dot

Abstract

Polaronic effects, arising from the electron--longitudinal-optic-phonon interaction, on low-lying spectrum for a system of two-interacting anyons confined in a two-dimensional parabolic quantum dot geometry and subjected to an external uniform magnetic field are investigated. The analysis is based on a synthesis of the Fr\"ohlich polaron model from the nonrelativistic quantum field theory through Wilczek's arguments from anyon theory. In this synthesis, anyons, being composed of electrons and point magnetic flux tubes attached to them, are treated as quasiparticles such that each of which not only interacts with others by a Coulomb interaction and statistical gauge field but also interacts with longitudinal optic phonons. In studying the polaronic effects on a two-anyon system in a two-dimensional parabolic quantum dot, first we pictured such a system by writing the anyonic version of the Fr\"ohlich Hamiltonian in the fermionic representation and, then, to handle the electron-phonon interaction part of the relevant Hamiltonian, employed a variational procedure based on two successive unitary transformations called Lee-Low-Pines and Huybrechts transformation. Furthermore, to check the consistency of our model, we have performed some checks including whether the well-known results previously obtained in the literature are covered in the absence of electron-electron and electron-phonon interactions. We observe that these two basic interactions cause non-negligible combined effects on the spectrum of two noninteracting anyons, exhibiting quite an unusual picture as compared to those of the usual noninteracting counterparts.