Correlated two-dimensional (2D) layers exhibit varies quantum phases, e.g. unconventional superconductor^{[1, 2]}, quantum spin liquids^{[3, 4]}, Mott and charge-transfer (CT) insulators^[5-7], charge-density ware (CDW)^{[8, 9]} and Wigner crystals^[10-12], have been emerging in correlated systems. The understanding of correlated electronic systems and the phase transitions between those quantum states is very important.