Quantum Rabi model (QRM) is fascinating not only because of its broad relevance but also due to its few-body quantum phase transition. In practice, both the bias and the nonlinear coupling in QRM are important controlling parameters in experimental setups. We study the interplay of the bias and the nonlinear interaction with the linear coupling in the ground state which exhibits various patterns of symmetry breaking and different orders of transitions. Several situations of tricriticalities are unveiled in the low-frequency limit and at finite frequencies. We find that the full quantum-mechanical effect leads to transitions, tricriticalities, quadruple points, and a fine structure of spontaneous symmetry breaking, which are much beyond the semiclassical picture. We clarify the underlying mechanisms by analyzing the energy competitions and the essential changeovers of the quantum states, which enables us to extract most analytic phase boundaries.

中文翻译：

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具有偏置和非线性相互作用的量子 Rabi 模型中的对称破缺模式、三临界点和四重点

Quantum Rabi 模型 (QRM) 之所以引人入胜，不仅是因为其广泛的相关性，还因为它的少体量子相变。实际上，QRM 中的偏置和非线性耦合都是实验设置中的重要控制参数。我们研究偏置和非线性相互作用与基态线性耦合的相互作用，基态表现出各种对称破坏模式和不同阶跃迁。在低频极限和有限频率中揭示了几种三临界情况。我们发现完整的量子力学效应会导致跃迁、三临界、四重点和自发对称性破缺的精细结构，这些都远远超出了半经典的图景。