Peculiar Quantum Phase Transitions and Hidden Supersymmetry in a Lipkin-Meshkov-Glick Model

In this paper we theoretically report an unconventional quantum phase transition of a simple Lipkin-Meshkov-Glick model: an interacting collective spin system without external magnetic field. It is shown that this model with integer-spin can exhibit a first-order quantum phase transition between different disordered phases, and more intriguingly, possesses a hidden supersymmetry at the critical point. However, for half-integer spin we predict another first-order quantum phase transition between two different long-range-ordered phases with a vanishing energy gap, which is induced by the destructive topological quantum interference between the intanton and anti-instanton tunneling paths and accompanies spontaneously breaking of supersymmetry at the same critical point. We also show that, when the total spin-value varies from half-integer to integer this model can exhibit an abrupt variation of Berry phase from π to zero. (physics of elementary particles and fields)