This study is started from a photon-magnon model with a competition effect of the level attraction and repulsion, its Hermiticity is mainly decided by a phase-dependent and asymmetric coupling factor, namelyφ = 0 for Hermitian andϕ=πfor non-Hermitian. Then an extensional study predicts the quantum critical behaviors using an Hermitian and even no-Hermitian photon-spins model with an additional second-order drive. The numerical results firstly indicate that this coupling phaseφcan function the protective effect on quantum phase transitions (QPTs), and the new tricritical points can not only be modulated by this nonlinear drive, but also be influenced by the dissipation and the collective decoherence. Secondly, this competition effect can also induce a reversal of the value of order parameters between the positive and negative. This study can also bring more important results of QPTs toward the issue of symmetry breaking and non-Hermiticity.
Keywords: competition effect; non-Hermitian Hamiltonian; quantum phase transitions; systemic symmetry breaking.
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