We have developed a matrix model for FQH states at filling factor \nu_{ k_1k_2} going beyond the Laughlin theory. To illustrate our idea, we have considered an FQH system of a finite number N=(N_{ 1}+N_{ 2}) of electrons with filling factor \nu_{ k_{ 1}k_{ 2}} = \nu_{ p_{ 1}p_{ 2}}=\frac{ p_{ 2}}{ p_{ 1}p_{ 2}-1}; p_{ 1} is an odd integer and p_{ 2} is an even integer. The \nu_{ p_{ 1}p_{ 2}} series corresponds just to the level two of the Haldane hierarchy; it recovers the Laughlin series \nu_{ p_{ 1}} =\frac{ 1}{ p_{ 1}} by going to the limit p_{ 2} large and contains several observable FQH states such as \nu = 2/3, 2/5, >....
Categories: hep-th cond-mat