From Quantum Rabi Model To Jaynes–Cummings Model: Symmetry‐Breaking Quantum Phase Transitions, Symmetry‐Protected Topological Transitions and Multicriticality. Issue 1 (7th November 2021) - Ying, Zu‐Jian
Abstract: The ground state and excitation gap are studied for the anisotropic quantum Rabi model (QRM) which connects the fundamental QRM and the Jaynes–Cummings model (JCM). While conventionally the ground state has a second‐order quantum phase transition in the low frequency limit, turning on finite frequencies sheds a novel light on the phase diagram to illuminate a fine structure of first‐order transition series. It is found that the conventional quantum phase transition is accompanied with a hidden symmetry breaking, whereas the emerging series transitions are topological transitions without symmetry breaking. The topological structure of the wave function provides a novel universality classification in bridging the QRM and the JCM among the diversity that arises from finite frequencies. The aspect of topological transitions provides a renewed insight for the role of the counter‐rotating interaction. Moreover, it is shown that the conventionally established tricritical point is actually a pentacritical or hexacritical point and following this multicritical point emerges a series of quadruple points. Besides the emerging multicriticality and reformed universality, the result demonstrates that a single‐qubit system can even exhibit analogs of topological phase transitions which traditionally occur in condensed matter. Abstract : A fine‐structure phase diagram is illuminated for anisotropic quantum Rabi model with a finding of series transitions, multicriticality and quadruple points emerging beyond the conventional picture. The emerging transitions are found to be topological transitions. The topological feature of the ground‐state wave function provides a new universality classification reformed among the diversity in the breaking down of the conventional universality.