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Topological entanglement entropy provides a robust measure for detecting the long-range entanglement that characterizes quantum ground states displaying topological order. A new method for calculating this entropy isolates minimally entangled states from the ground states of a topological phase—offering a reliable test for identifying topological spin liquids.

It was recently demonstrated that particular materials with non-trivial electronic band structure support quasiparticle excitations described by the relativistic Weyl equation. Here, the authors explore how an analogous magnonic band structure may exist in breathing pyrochlore antiferromagnets.

The structure of domain walls is of interest to the antiferromagnetic spintronics. Here the authors find an additional contribution to the Hall conductivity tensor and a transverse magnetization generated by domain walls in Mn3Sn and report that the sign of this contribution depends on the prior history of the sample.

At absolute zero temperature, exotic phases of matter can be found near a quantum critical point. If geometric frustration is also present, as happens in columbite, the extra quantum fluctuations lead to five distinct states of matter.

Mott insulators are driven by strong Coulomb repulsion and topological insulators by strong spin–orbit coupling. Although these effects are normally in competition, in some cases the Coulomb interaction can enhance the effects of spin–orbit coupling. Together these interactions could lead to gapless spin-only excitations on the surface of a strongly correlated insulator.

The latest advances in our understanding of correlated electron systems have implications that range from fundamental physics such as string theory to novel applications including the manipulation and retrieval of electron spin.

Quantum spin liquids are exotic states of matter first predicted more than 40 years ago. An inorganic material has properties consistent with these predictions, revealing details about the nature of quantum matter. See Letter p.559

Magnetostriction refers to the contraction or expansion of the crystal lattice of a magnetic material when a magnetic field is applied. Here, Meng et al show that Mn₃Sn, a noncollinear antiferromagnet, hosts a large linear magnetostriction, which is driven by the field induced in-plane rotation of spins.

A combination of strong spin–orbit coupling and electronic correlations in pyrochlore iridates produces a quantum insulator–metal transition that can be induced by applying a magnetic field along specific crystalline axes.

Spin liquids are predicted to emerge in materials that combine strong electronic correlations with geometric frustration. Evidence has now been found for a spin liquid state in the triangular-lattice material NaRuO₂.

The interplay between superconductivity that might break time-reversal symmetry and charge order is a key issue in kagome materials. Now, optical measurements show that spatial and time-reversal symmetries are broken at the onset of charge order.

Some materials can display magnetic order despite having spin-singlet ground state on individual magnetic sites. This arises due to exchange interactions mixing excited crystal electric field states. Here, Gao et al study and example of such a system, Ni₂Mo₃O₈, and find that crystal electric field states in both the paramagnetic and antiferromagnetic states exhibit dispersive excitations.

A study reveals a temperature-dependent cascade of different symmetry-broken electronic states in the kagome superconductor CsV₃Sb₅, and highlights intriguing parallels between vanadium-based kagome metals and materials exhibiting similar electronic phases.

The phenomenon of many-body localization gives rise to entirely new phases of quantum matter when it is driven away from equilibrium. A numerical study now shows that one of these phases—the discrete time crystal—can also occur in a classical spin chain.

At zero magnetic field, the triangular-lattice antiferromagnet NaYbO₂ shows the absence of long-range magnetic order down to 50 mK, consistent with quantum spin liquid behaviour. An external field renders the system a collinear ordered phase.

Oscillations of the order parameter amplitude in magnetically ordered materials provide condensed matter analogues of the Higgs boson but in most cases they are unstable. Dally et al. show that the quasi-one-dimensional magnet α-Na_0.9MnO₂ supports stable amplitude excitations.

The identification of superconductivity and strong interactions in twisted bilayer 2D materials prompted many questions about the interplay of these phenomena. This Perspective presents the status of the field and the urgent issues for future study.

The precise nature of the charge-density-wave state in kagome superconductors remains unclear. Now, local spectroscopy shows that rotational symmetry in real space is broken, with one direction being distinct from the other two.

Materials hosting magnetic rare-earth ions sitting on a two-dimensional triangular lattices are ideal candidates to realize spin liquid states. In this work, the authors synthesize a high-quality single crystal sample of an erbium based triangular lattice compound, that exhibits a mixture of ferromagnetic and antiferromagnetic behaviour.