We study a homogeneous two-component dipolar Fermi gas with 1D spin-orbit coupling (SOC) at zero temperature and find that the system undergoes a transition from the paramagnetic phase to the ferromagnetic phase under suitable dipolar interaction constant λ d, SOC constant λ SOC and contact interaction constant λ s. This phase transition can be of either 1st order or 2nd order, depending on the parameters. Near the 2nd-order phase transition, the system is partially magnetized in the ferromagnetic phase. With SOC, the ferromagnetic phase can even exist in the absence of the contact interaction. The increase in dipolar interaction, SOC strength, and contact interaction are all helpful to stabilize the ferromagnetic state. The critical dipolar interaction strength at the phase transition can be reduced by the increase in SOC strength or contact interaction. Phase diagrams of these systems are obtained.

We study the ferromagnetic transition of a two-component homogeneous dipolar Fermi gas with 1D spin–orbit coupling (SOC) at finite temperature. The ferromagnetic transition temperature is obtained as functions of dipolar constant λ d, spin–orbit coupling constant λ SOC and contact interaction constant λ s. It increases monotonically with these three parameters. In the ferromagnetic phase, the Fermi surfaces of different components can be deformed differently. The phase diagrams at finite temperature are obtained.

Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still remains a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in parity–time ( PT )-symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also non-Hermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3s) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT -broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform toward the investigation of the higher-order EPs and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.

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