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Abstract We overview the concept of dynamical phase transitions (DPTs) in isolated quantum systems quenched out of equilibrium. We focus on non-equilibrium transitions characterized by an order parameter, which features qualitatively distinct temporal behavior on the two sides of a certain dynamical critical point. DPTs are currently mostly understood as long-lived prethermal phenomena in a regime where inelastic collisions are incapable to thermalize the system. The latter enables the dynamics to substain phases that explicitly break detailed balance and therefore cannot be encompassed by traditional thermodynamics. Our presentation covers both cold atoms as well as condensed matter systems. We revisit a broad plethora of platforms exhibiting pre-thermal DPTs, which become theoretically tractable in a certain limit, such as for a large number of particles, large number of order parameter components, or large spatial dimension. The systems we explore include, among others, quantum magnets with collective interactions, ϕ 4 quantum field theories, and Fermi–Hubbard models. A section dedicated to experimental explorations of DPTs in condensed matter and AMO systems connects this large variety of theoretical models. 

Magnetic topological semimetals allow for an effective control of the topological electronic states by tuning the spin configuration. Among them, Weyl nodal line semimetals are thought to have the greatest tunability, yet they are the least studied experimentally due to the scarcity of material candidates. Here, using a combination of angle-resolved photoemission spectroscopy and quantum oscillation measurements, together with density functional theory calculations, we identify the square-net compound EuGa₄as a magnetic Weyl nodal ring semimetal, in which the line nodes form closed rings near the Fermi level. The Weyl nodal ring states show distinct Landau quantization with clear spin splitting upon application of a magnetic field. At 2 K in a field of 14 T, the transverse magnetoresistance of EuGa₄exceeds 200,000%, which is more than two orders of magnitude larger than that of other known magnetic topological semimetals. Our theoretical model suggests that the non-saturating magnetoresistance up to 40 T arises as a consequence of the nodal ring state.