Low energy effective interaction of XXZ spin interaction in the two-dimensional quantum dot

We investigate the low-energy behavior of the two-dimensional quantum dot. By using the renormalization group analysis with the random matrix theory, we examine the role of anisotropy of the electron-electron interaction and demonstrate the induced instabilities in the universal Hamiltonian. As a result, it is found that anisotropy in general gives rise to four additional phases (eight phases as total), and in certain regions, the anisotropy becomes amplified at low temperature.