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Topological insulators exhibit unidirectional flow of robust electric charge at the edge of the system. Two recent experiments have observed these chiral edge modes in exceptionally controllable settings of ultracold atoms.

Approximate notions of quantum error-correcting codes hold wide importance across quantum information and physics, but are not cohesively understood. Now, general rigorous connections established between approximate quantum error correction and quantum circuit complexity reveal a ‘complexity phase diagram’ for generalized quantum codes — and create a new unifying lens on complex quantum systems.

Dimensionality tuning can control fluctuations and induce complex phase diagrams with multiple orders and transitions among them. Now, experiments demonstrate intertwined vestigial order in the two- to three-dimensional crossover region in a van der Waals magnet.

The mechanism behind the ultrafast insulator-to-metal transition in Mott materials is still not well understood. Now, it is shown that this phase transition propagates along the pathway of a photoinduced compressive strain wave in prototypical V₂O₃.

By measuring terahertz photon echoes, multidimensional spectroscopy demonstrates that interlayer tunnelling in a cuprate superconductor remains largely unaffected by electronic disorder, even near the phase transition.

The collective behaviour of quantum gases strongly depends on the confining dimensionality. Its role in the emergence of a phase transition in a quantum gas of photons has now been explored using a new trapping technique, transitioning from 2D to 1D.

The Fisher information imposes a fundamental limit on the precision with which an unknown parameter can be estimated from noisy data, as Dorian Bouchet explains.

PhD students can face many challenges, such as a lack of confidence in their newly acquired skills or the uncertainty about which career path to choose. We highlight some ways to empower students in their doctoral journey.

How cells manage the internal energetic budget to drive mechanical and chemical dynamics is still an open question. Now it is shown that the allocation of energy depends on the distance from thermodynamic equilibrium.

Kondo physics has been observed in moiré bilayers, but the expected magnetic transitions have not been reported. Now, a metal–insulator transition with ferromagnetic order that develops at nearly the same time is reported in a moiré bilayer.

Edge modes are a key feature of topological materials, but their propagation is difficult to directly observe in condensed matter systems. The controlled injection and propagation of chiral edge modes has now been shown in a rotating ultracold gas.

The dimensionality of a many-body system strongly impacts its physical behaviour. Now, a crossover from 1D to 2D has been observed in the Bose–Einstein condensate of a photon gas.

Approximate—rather than exact—quantum error correction is a useful but relatively unexplored idea in quantum computing and many-body physics. A theoretical framework has now been established based on connections with quantum circuit complexity.

Optical near-field microscopy has facilitated our understanding of nanophotonics. This Perspective explores the opportunities that near-field studies of terahertz fields provide for ultrafast phase transitions in condensed matter systems.

Magnetic phases that are stabilized by quantum fluctuations in low dimensions are rare. A thickness-dependent crossover from three-dimensional antiferromagnetism to a two-dimensional vestigial nematic state that is driven by fluctuations has now been observed.

Understanding the mechanism of bacterial cell division is important in both fundamental and applied biology. Now, researchers have investigated the self-organization of cytoskeletal filaments and the role nematic ordering plays in cell division.

The Kibble–Zurek mechanism is a key framework for describing the dynamics of continuous phase transitions. Recent experiments with ultracold gases, employing alternative methods to create a superfluid, highlight its universality.