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.