Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Antiferromagnetic materials could represent the future of spintronic applications thanks to the numerous interesting features they combine: they are robust against perturbation due to magnetic fields, produce no stray fields, display ultrafast dynamics, and are capable of generating large magnetotransport effects. Intense research efforts over the past decade have been invested in unraveling spin transport properties in antiferromagnetic materials. Whether spin transport can be used to drive the antiferromagnetic order and how subsequent variations can be detected are some of the thrilling challenges currently being addressed. Antiferromagnetic spintronics started out with studies on spin transfer and has undergone a definite revival in the last few years with the publication of pioneering articles on the use of spin-orbit interactions in antiferromagnets. This paradigm shift offers possibilities for radically new concepts for spin manipulation in electronics. Central to these endeavors are the need for predictive models, relevant disruptive materials, and new experimental designs. This paper reviews the most prominent spintronic effects described based on theoretical and experimental analysis of antiferromagnetic materials. It also details some of the remaining bottlenecks and suggests possible avenues for future research. This review covers both spin-transfer-related effects, such as spin-transfer torque, spin penetration length, domain-wall motion, and "magnetization" dynamics, and spin-orbit related phenomena, such as (tunnel) anisotropic magnetoresistance, spin Hall, and inverse spin galvanic effects. Effects related to spin caloritronics, such as the spin Seebeck effect, are linked to the transport of magnons in antiferromagnets. The propagation of spin waves and spin superfluids in antiferromagnets is also covered.

A large number of experimental discoveries especially in the heavy quarkonium sector that did not meet the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy. Among various explanations of the internal structure of these excitations, hadronic molecules, being analogs of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty. Experimental evidence of various candidates of hadronic molecules and methods of identifying such structures are reviewed. Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules and are discussed in both the continuum and finite volumes. Also pertinent lattice QCD results are presented. Further, the production mechanisms and decays of hadronic molecules are discussed and comments are given on the reliability of certain assertions often made in the literature.

Atomically thin materials such as graphene and monolayer transition metal dichalcogenides (TMDs) exhibit remarkable physical properties resulting from their reduced dimensionality and crystal symmetry. The family of semiconducting transition metal dichalcogenides is an especially promising platform for fundamental studies of two-dimensional (2D) systems, with potential applications in optoelectronics and valleytronics due to their direct band gap in the monolayer limit and highly efficient light-matter coupling. A crystal lattice with broken inversion symmetry combined with strong spin-orbit interactions leads to a unique combination of the spin and valley degrees of freedom. In addition, the 2D character of the monolayers and weak dielectric screening from the environment yield a significant enhancement of the Coulomb interaction. The resulting formation of bound electron-hole pairs, or excitons, dominates the optical and spin properties of the material. Here recent progress in understanding of the excitonic properties in monolayer TMDs is reviewed and future challenges are laid out. Discussed are the consequences of the strong direct and exchange Coulomb interaction, exciton light-matter coupling, and influence of finite carrier and electron-hole pair densities on the exciton properties in TMDs. Finally, the impact on valley polarization is described and the tuning of the energies and polarization observed in applied electric and magnetic fields is summarized.

Quantum chromodynamics (QCD), the generally accepted theory for strong interactions, describes the interactions between quarks and gluons. The strongly interacting particles that are seen in nature are hadrons, which are composites of quarks and gluons. Since QCD is a strongly coupled theory at distance scales that are characteristic of observable hadrons, there are no rigorous, first-principle methods to derive the spectrum and properties of the hadrons from the QCD Lagrangian, except for lattice QCD simulations that are not yet able to cope with all aspects of complex and short-lived states. Instead, a variety of "QCD inspired" phenomenological models have been proposed. Common features of these models are predictions for the existence of hadrons with substructures that are more complex than the standard quark-antiquark mesons and the three-quark baryons of the original quark model that provides a concise description of most of the low-mass hadrons. Recently, an assortment of candidates for nonstandard multiquark mesons, meson-gluon hybrids, and pentaquark baryons that contain heavy (charm or bottom) quarks has been discovered. Here the experimental evidence for these states is reviewed and some general comparisons of their measured properties with standard quark model expectations and predictions of various models for nonstandard hadrons are made. The conclusion is that the spectroscopy of all but the simplest hadrons is not yet understood.

This article reviews recent developments in tests of fundamental physics using atoms and molecules, including the subjects of parity violation, searches for permanent electric dipole moments, tests of the CPT theorem and Lorentz symmetry, searches for spatiotemporal variation of fundamental constants, tests of quantum electrodynamics, tests of general relativity and the equivalence principle, searches for dark matter, dark energy, and extra forces, and tests of the spin-statistics theorem. Key results are presented in the context of potential new physics and in the broader context of similar investigations in other fields. Ongoing and future experiments of the next decade are discussed.

Adiabatic quantum computing (AQC) started as an approach to solving optimization problems and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. This review gives an account of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. Several variants are presented of the adiabatic theorem, the cornerstone of AQC, and examples are given of explicit AQC algorithms that exhibit a quantum speedup. An overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory is given. Considerable space is devoted to stoquastic AQC, the setting of most AQC work to date, where obstructions to success and their possible resolutions are discussed.

Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well-developed techniques for trapping, controlling, and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold, and ultracold gases of neutral atoms. Moreover, atoms can strongly couple to external forces and fields, which makes them ideal for ultraprecise sensing and time keeping. All these factors call for generating nonclassical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.

Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.

Quantum-enhanced measurements exploit quantum mechanical effects for increasing the sensitivity of measurements of certain physical parameters and have great potential for both fundamental science and concrete applications. Most of the research has so far focused on using highly entangled states, which are, however, difficult to produce and to stabilize for a large number of constituents. In the following alternative mechanisms are reviewed, notably the use of more general quantum correlations such as quantum discord, identical particles, or nontrivial Hamiltonians; the estimation of thermodynamical parameters or parameters characterizing nonequilibrium states; and the use of quantum phase transitions. Both theoretically achievable enhancements and enhanced sensitivities not primarily based on entanglement that have already been demonstrated experimentally and indicate some possible future research directions are described.

The vast majority of hadrons observed in nature are not stable under the strong interaction; rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy nonperturbative region, and in addition many probes of the limits of the electroweak sector of the standard model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter hadrons, so a complete approach to QCD is required. Presently, lattice QCD is the only available tool that provides the required nonperturbative evaluation of hadron observables. This article reviews progress in the study of few-hadron reactions in which resonances and bound states appear using lattice QCD techniques. The leading approach is described that takes advantage of the periodic finite spatial volume used in lattice QCD calculations to extract scattering amplitudes from the discrete spectrum of QCD eigenstates in a box. An explanation is given of how from explicit lattice QCD calculations one can rigorously garner information about a variety of resonance properties, including their masses, widths, decay couplings, and form factors. The challenges which currently limit the field are discussed along with the steps being taken to resolve them.

Although dark matter is a central element of modern cosmology, the history of how it became accepted as part of the dominant paradigm is often ignored or condensed into an anecdotal account focused around the work of a few pioneering scientists. The aim of this review is to provide a broader historical perspective on the observational discoveries and the theoretical arguments that led the scientific community to adopt dark matter as an essential part of the standard cosmological model.

Pressure has long been recognized as a fundamental thermodynamic variable but its application was previously limited by the available pressure vessels and probes. The development of megabar diamond anvil cells and a battery of associated in-laboratory and synchrotron techniques at the turn of the century have opened a vast new window of opportunities. With the addition of the pressure dimension, we are facing a new world with an order of magnitude more materials to be discovered than all that have been explored at ambient pressure. Pressure drastically and categorically alters all elastic, electronic, magnetic, structural, and chemical properties, and pushes materials across conventional barriers between insulators and superconductors, amorphous and crystalline solids, ionic and covalent compounds, vigorously reactive and inert chemicals, etc. In the process, it reveals surprising high-pressure physics and chemistry and creates novel materials. This reviewdescribes the principles and methodology used to reach ultrahigh static pressure: the in situ probes, the physical phenomena to be investigated, the long-pursued goals, the surprising discoveries, and the vast potential opportunities. Exciting examples include the quest for metallic hydrogen, the record-breaking superconducting temperature of 203 K in HnS, the complication of "free-electron gas" alkali metals, the magnetic collapse in 3d transition elements, the pressure-induced superconductivity from topological insulators, the novel stoichiometry in simple compounds, the interaction of nanoscience, the accomplishment of 750 GPa pressure, etc. These highlights are the integral results of technological achievements, specific measurements, and theoretical advancement; therefore, the same highlightswill appear in different sections corresponding to these different aspects. Overall, this review demonstrates that high-pressure research is a new dimension in condensed-matter physics.

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical mechanics, despite their inherent athermal features. Since then, the statistical mechanics approach for jammed matter-one of the very few generalizations of Gibbs-Boltzmann statistical mechanics to out-of-equilibrium matter-has garnered an extraordinary amount of attention by both theorists and experimentalists. Its importance stems from the fact that jammed states of matter are ubiquitous in nature appearing in a broad range of granular and soft materials such as colloids, emulsions, glasses, and biomatter. Indeed, despite being one of the simplest states of matter-primarily governed by the steric interactions between the constitutive particles-a theoretical understanding based on first principles has proved exceedingly challenging. Here a systematic approach to jammed matter based on the Edwards statistical mechanical ensemble is reviewed. The construction of microcanonical and canonical ensembles based on the volume function, which replaces the Hamiltonian in jammed systems, is discussed. The importance of approximation schemes at various levels is emphasized leading to quantitative predictions for ensemble averaged quantities such as packing fractions and contact force distributions. An overview of the phenomenology of jammed states and experiments, simulations, and theoretical models scrutinizing the strong assumptions underlying Edwards approach is given including recent results suggesting the validity of Edwards ergodic hypothesis for jammed states. A theoretical framework for packings whose constitutive particles range from spherical to nonspherical shapes such as dimers, polymers, ellipsoids, spherocylinders or tetrahedra, hard and soft, frictional, frictionless and adhesive, monodisperse, and polydisperse particles in any dimensions is discussed providing insight into a unifying phase diagram for all jammed matter. Furthermore, the connection between the Edwards ensemble of metastable jammed states and metastability in spin glasses is established. This highlights the fact that the packing problem can be understood as a constraint satisfaction problem for excluded volume and force and torque balance leading to a unifying framework between the Edwards ensemble of equiprobable jammed states and out-of-equilibrium spin glasses.

The advent of visible-infrared laser pulses carrying a substantial fraction of their energy in a single field oscillation cycle has opened a new era in the experimental investigation of ultrafast processes in semiconductors and dielectrics (bulk as well as nanostructured), motivated by the quest for the ultimate frontiers of electron-based signal metrology and processing. Exploring ways to approach those frontiers requires insight into the physics underlying the interaction of strong high-frequency (optical) fields with electrons moving in periodic potentials. This Colloquium aims at providing this insight. Introduction to the foundations of strong-field phenomena defines and compares regimes of field-matter interaction in periodic systems, including (perfect) crystals as well as optical and semiconductor superlattices, followed by a review of recent experimental advances in the study of strong-field dynamics in crystals and nanostructures. Avenues toward measuring and controlling electronic processes up to petahertz frequencies are discussed.

This review examines the tendency of light nuclei to exhibit clustering, where correlations between nucleons result in the formation of precipitates, typically a particles. The observation of clustering dates to the earliest days of the subject, where a particles were the building blocks of some nuclear models. The description of a nucleus in terms of clusters was attractive in terms of simplifying the computationally challenging problem through the reduction of the degrees of freedom. However, more recently it has been possible to develop ab initio methods which seek to build nuclei not from the clusters, but from the individual nucleons with a full account of the Pauli exclusion principle. This review links the development of the subject from the assumption of preformed a particles, through to the development of models which demonstrate the appearance of clustering from the A-nucleon wave function with realistic but effective interactions, to finally first principle approaches using interactions based on chiral effective field theory and the symmetries of quantum chromodynamics. This places the understanding of clustering as a cornerstone of the development of nuclear theory as it attempts to develop a complete understanding of light nuclei from the fundamental strong force.

This Colloquium describes a new paradigm for creating strong quantum interactions of light and matter by way of single atoms and photons in nanoscopic lattices. Beyond the possibilities for quantitative improvements for familiar phenomena in atomic physics and quantum optics, there is a growing research community that is exploring novel quantum phases and phenomena that arise from atom-photon interactions in one- and two-dimensional nanophotonic lattices. Nanophotonic structures offer the intriguing possibility to control atom-photon interactions by engineering the medium properties through which they interact. An important aspect of these new research lines is that they have become possible only by pushing the state-of-the-art capabilities in nanophotonic device fabrication and by the integration of these capabilities into the realm of ultracold atoms. This Colloquium attempts to inform a broad physics community of the emerging opportunities in this new field on both theoretical and experimental fronts. The research is inherently multidisciplinary, spanning the fields of nanophotonics, atomic physics, quantum optics, and condensed matter physics.

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This idea, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest. This renaissance has been possible due to both significant analytical progress in understanding how to set up the bootstrap equations and the development of numerical techniques for finding or constraining their solutions. These developments have led to a number of groundbreaking results, including world-record determinations of critical exponents and correlation function coefficients in the Ising and O(N) models in three dimensions. This article will review these exciting developments for newcomers to the bootstrap, giving an introduction to conformal field theories and the theory of conformal blocks, describing numerical techniques for the bootstrap based on convex optimization, and summarizing in detail their applications to fixed points in three and four dimensions with no or minimal supersymmetry.

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.