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Quantum phase transition of two-mode Bose-Einstein condensates with an entanglement order parameter

The ground state entanglement of the two-mode Bose-Einstein Condensates varies with the coupling strength. We show that this is a kind of quantum phase transitions, if the von Neumann entropy of the entanglement measurement is viewed as the order parameter. The critical point lies in the small coupling regime, the Fock regime, and the critical behavior is polynomial. The susceptibility of this order parameter diverges with increasing system sizes, so it’s a continuous phase transition. The nite-size scaling is done with the datas of various system sizes falling into a single curve. This kind of quantum phase transitions is driven by the derivative of the quantum uctuation with respect to the external eld, in contrast to the quantum phase transitions of thermal order parameters, which is driven by the quantum uctuations.