Bosonization approach to the edge reconstruction of two-dimensional electron systems in a quantum dot

We consider edge reconstruction of electrons in a two-dimensional harmonic trap under a strong magnetic field. In this system the edge reconstruction occurs as a result of competition between electron-electron interaction and confining potential. We develop a bosonization scheme for two-dimensional electron systems. With this method we obtain the excitation spectrum and demonstrate that the edge reconstruction occurs when magnetic field reaches a critical value. We also show that the edge reconstruction depends on the number of electrons. We calculate the third-order terms of bosons in Hamiltonian and examine the effect of those terms with a perturbation theory.