We consider theories of gauged quark flavor and identify noninvertible Peccei-Quinn symmetries arising from fractional instantons when the resulting gauge group has nontrivial global structure. Such symmetries exist solely because the standard model has the same number of generations as colors, $N_g=N_c$, which leads to a massless down-type quark solution to the strong $CP$ problem in an ultraviolet $SU(9)$ theory of quark color-flavor unification. We show how the Cabibbo-Kobayashi-Maskawa flavor structure and weak $CP$ violation can be generated without upsetting our solution.

We study the emergence of strong interactions between dissipative coherent structures (pulses) in spatially extended systems. Focusing first on a prototypical model problem from fluid dynamics, that of liquid film flowing down a vertical plane, we show that under certain conditions, a two-pulse system undergoes a transition from a regime of decaying oscillatory dynamics to one with self-sustained oscillations. Intriguingly, such a transition is not governed by the standard Hopf bifurcation. Instead, a novel governing mechanism for transition to oscillatory dynamics is unraveled via a peculiar and atypical Hopf bifurcation in which a complex-conjugate resonance pair crosses the imaginary axis in the complex plane. Prior to crossing the essential spectrum (including at the bifurcation point), this resonance pair does not appear in the standard $L_{\mathbb{C}}^2$-based spectral analysis but reveals itself when appropriate weighted functional spaces are used. We show that such a resonance pair originates from the splitting of a resonance pole of the single-pulse system. While this object is not part of the classical spectrum, it plays a vital role in shaping the system’s dynamics. We further demonstrate that this resonance-pole mechanism extends to a broad range of systems. Specifically, in the generalised Kuramoto-Sivashinsky equation—a model prototype applicable across a wide range of fields from fluid dynamics to geophysics and plasma physics—we observe the same bifurcation and resulting oscillatory pulse interactions. By contrast, in the FitzHugh-Nagumo model—a central model prototype in reaction-diffusion systems—the resonance pole splits into real eigenvalues, and monotonic pulse interactions occur. In addition, we illustrate that the resonance pole may induce oscillatory interactions in three-pulse systems and eventually lead to chaotic dynamics in strongly interacting multipulse systems, which can be quantified in terms of a positive Lyapunov exponent.

Over the past decade, neutrino astronomy has emerged as a new window into the extreme and hidden Universe. Current-generation experiments have detected high-energy neutrinos of astrophysical origin and identified the first sources, opening the field to discovery. Looking ahead, in this Perspective we identify seven major open questions in neutrino astrophysics and particle physics that could lead to transformative discoveries over the next 20 years. These multidisciplinary questions range from understanding the vicinity of a black hole to unveiling the nature of neutrino mass, among other topics. Additionally, we critically review the current experimental capabilities and their limitations and, from there, discuss the interplay between different proposed neutrino telescope technologies and analysis techniques. We firmly believe that achieving the immense discovery potential over the next two decades demands a model of global partnership and specialized, complementary detectors. This collaborative neutrino telescope network will pave the way for a thriving multimessenger era, transforming our understanding of neutrino physics, astrophysics, and the extreme Universe.

Science is founded on the benchmarking of theoretical models against experimental measurements, with the challenge that, for all but the simplest systems, the calculations required for high precision become extremely challenging. ${\mathrm{H}}_2^{+}$ is the simplest stable molecule, and its structure is calculable to high precision. However, studying ${\mathrm{H}}_2^{+}$ experimentally presents significant challenges: Standard control methods such as laser cooling are not applicable due to the long lifetimes of its rotational and vibrational states. Here, we solve this issue by combining buffer gas cooling to quench the ${\mathrm{H}}_2^{+}$ rovibrational excitation with quantum logic operations between ${\mathrm{H}}_2^{+}$ and a cotrapped “helper” ion to control the molecule’s hyperfine structure. This enables us to perform pure quantum state preparation, coherent control, and nondestructive readout, which we use to demonstrate high-resolution microwave spectroscopy in the hyperfine structure of ${\mathrm{H}}_2^{+}$ with a precision of 2 Hz. Our results pave the way for high-precision spectroscopy of ${\mathrm{H}}_2^{+}$ in both the microwave and optical domains. Because of the wide applicability of buffer gas cooling, our method provides a general tool for molecular ion species that are hard to control with quantum logic tools alone.

Many hot, diffuse astrophysical plasmas are collisionless, with collision times that exceed dynamical timescales of interest. Without a standard viscosity, the mechanisms by which mechanical energy dissipates into heat via a turbulent cascade are complex and nonuniversal, with important consequences for the partition of heat between different species and directions. Recent theory has argued that in some parameter regimes a barrier to the turbulent cascade of energy forms at small scales, profoundly altering the nature of the heating of the plasma by changing how fluctuations dissipate. The solar wind is an environment, when in this parameter regime, where such a barrier would be expected to form. Here, using data from NASA’s Parker Solar Probe, we find that the shape of the magnetic energy spectrum around ion scales varies with solar wind parameters in a manner consistent with the presence of the barrier. This allows us to identify critical values of parameters necessary for the barrier to form; we show that the barrier appears fully developed for ion plasma beta of below $\simeq 0.5$ and becomes increasingly prominent with increasing normalized cross helicity (the difference in energy in wave packets propagating parallel and antiparallel to the background magnetic field) for values greater than $\simeq 0.4$. As these conditions are frequently met in the solar wind, particularly close to the Sun, our results suggest that the barrier is likely playing a significant role in turbulent dissipation in the solar wind and so is an important mechanism in explaining its heating and acceleration.

The recently introduced “fuzzy-sphere” method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the noncommutative geometry of the lowest Landau level filled by electrons, such that the charge is trivially gapped due to the Pauli exclusion principle at filling factor $\nu =1$, while the electron spins encode the desired CFT. Successful applications of the fuzzy sphere to paradigmatic CFTs, such as the 3D Ising model, raise an important question: How finely tuned does the underlying electron system need to be? Here, we show that the 3D Ising CFT can also be realized at fractional electron fillings. In such cases, the CFT spectrum is intertwined with the charge-neutral spectrum of the underlying fractional quantum Hall state—a feature that is trivially absent in the previously studied $\nu =1$ case. Remarkably, we show that the mixing between the CFT spectrum and the fractional quantum Hall spectrum is strongly suppressed within the numerically accessible system sizes. Moreover, we demonstrate that the CFT critical point is unaffected by the exchange statistics of the particles and by the nature of topological order in the charge sector. Our results set the stage for the fuzzy-sphere exploration of conformal critical points between topologically ordered states.

The traditional view of the anomalous Hall effect (AHE) in ferromagnets is that it arises from the magnetization perpendicular to the measurement plane and that there is a linear dependence on the latter. Underlying such a view is the thinking that the AHE is a time-reversal symmetry breaking phenomenon and can therefore be treated in terms of a power series in the magnetic order. However, this view is squarely challenged by a number of recent experiments, urging for a thorough theoretical investigation on the fundamental level. We find that for strong magnets, it is more appropriate and fruitful to regard the AHE as a spin-group symmetry breaking phenomenon where the critical parameter is the spin-orbit interaction strength, which involves a much smaller energy scale. In collinear ferromagnets, the spin-orbit coupling breaks the $\infty 2^{\prime }$ spin rotation symmetry, and the key to characterizing such symmetry breaking is the identification of spin-orbit vectors which transform regularly under spin-group operations. Born out of our framework is a rich multipolar relationship between the anomalous Hall conductivity and the magnetization direction, with each pole being expanded progressively in powers of the spin-orbit coupling strength. For the leading order contribution, i.e., the dipole, its isotropic part corresponds to the traditional view, and its anisotropic part can lead to the in-plane AHE where the magnetization lies within the measurement plane. Beyond the dipolar structure, the octupolar structure offers the leading order source of nonlinearity and hence introduces unique anisotropy where the dipolar structure cannot. Our theory thus offers a unified explanation for the in-plane AHE recently observed in various ferromagnets, and further extends the candidate material systems. It can also be generalized to study the anomalous Hall effect in crystals with any periodic spin structure and to study the nonlinear Hall effect and the spin Hall effect. Our theory lays the ground for decoding the coupling between various transport and optical phenomena and the magnetic orders.

Spin-forbidden ($\mathrm{\Delta }S\ne 0$) multiplet excitations and their coupling to magnetic properties are of increasing importance for magneto-optical studies of correlated materials. Nonetheless, the mechanisms for optically brightening these transitions and their generality remain poorly understood. Here, we report magnetic circular dichroism (MCD) spectroscopy on the van der Waals ferromagnet (FM) ${\mathrm{CrI}}_3$. Previously unreported spin-forbidden ($\mathrm{\Delta }S=1$) ${{}^{4}A}_{2\mathrm{g}}\to {{}^{2}E}_{\mathrm{g}}/{{}^{2}T}_{1\mathrm{g}}$ ${\mathrm{Cr}}^{3+}$ $dd$ excitations are observed near the ligand-to-metal charge-transfer excitation threshold. The assignment of these excitations and their ${\mathrm{Cr}}^{3+}$ multiplet character is established through complementary Cr $L_3$-edge resonant inelastic x-ray scattering measurements along with charge-transfer multiplet calculations and chemical trends in the chromium trihalide series ($\mathrm{Cr}{X}_3$, $X=$ Cl, Br, I). We utilize the high sensitivity of MCD spectroscopy to study the thickness-dependent optical response. The spin-forbidden excitations remain robust down to the monolayer limit, and we observe a significant magnetic-field dependence of the MCD spectrum across the antiferromagnetic-to-FM transition in few-layer samples. We preliminarily attribute this behavior to changes in the metal-ligand covalency with magnetic state. Our results clarify the magneto-optical response of ${\mathrm{CrI}}_3$ and identify covalency as a central mechanism for the brightening and field tunability of spin-forbidden multiplet excitations.

We report charge pickup reaction cross sections for 24 $p$-shell isotopes, including ${}^{8,9}\mathrm{Li}$, ${}^{10-12}\mathrm{Be}$, ${}^{10,13-15}\mathrm{B}$, ${}^{12,14-19}\mathrm{C}$, and ${}^{14,15,17-22}\mathrm{N}$, measured at relativistic energies (approximately $900A\mathrm{MeV}$) on both hydrogen and carbon targets. For the first time, we reveal a universal rapid increase in the charge pickup cross sections of unstable projectiles with isospin asymmetry along several isotopic chains. The cross sections can be decoupled into distinct contributions from the mass number and isospin asymmetry of the projectile, highlighting the critical role of the latter, and can be formulated empirically.

The effect of decoherence on topological order (TO) has been most deeply understood for the toric code, the paragon of Abelian TOs. We show that certain non-Abelian TOs can be analyzed and understood to a similar degree, despite being significantly richer. We consider both wave-function deformations and quantum channels acting on $D_4$ TO, which has recently been realized on a quantum processor. By identifying the corresponding local statistical mechanical spin or rotor model with $D_4$ symmetry, we find a remarkable stability against proliferating non-Abelian anyons. This is shown by leveraging a reformulation in terms of the tractable O(2) loop model in the pure state case and $n$ coupled O(2) loop models for Rényi-$n$ quantities in the decoherence case—corresponding to worldlines of the proliferating anyon with quantum dimension 2. In particular, we find that the purity ($n=2$) remains deep in the $D_4$ TO for any decoherence strength, while the $n\to \infty$ limit becomes critical upon maximally decohering a particular anyon type, similar to our wave-function deformation result. The information-theoretic threshold ($n\to 1$) appears to be controlled by a disordered version of these statistical mechanical models, akin to the toric code case although significantly more robust. We furthermore use Monte Carlo simulations to explore the phase diagrams when multiple anyon types proliferate at the same time, leading to a continued stability of the $D_4$ TO in addition to critical phases with emergent U(1) symmetry. Instead of loop models, these are now described by net models corresponding to different anyon types coupled together according to fusion rules. This opens up the exploration of statistical mechanical models for decohered non-Abelian TO, which can inform optimal decoders and which in an ungauged formulation provides examples of non-Abelian strong-to-weak symmetry breaking.

Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest. Recently, a strong notion of quantum ergodicity has been proposed, namely, that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity. Here, we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment. For a closed system, where the environment is a complementary subsystem, we predict and observe a smooth quantum-to-classical transition in that observables progress from large, quantum fluctuations to small, Gaussian fluctuations as the bath size grows. This transition exhibits universal properties on a quantitative level among a wide range of systems, including those at finite temperature, those with itinerant particles, and random circuits. For an open system, where the environment is uncontrolled, we predict the statistics of observables under largely arbitrary noise channels including those with correlated errors, allowing us to discriminate between candidate error models both for continuous Hamiltonian time evolution and for digital random circuits. This allows for computationally efficient experimental noise learning and, more broadly, is a new avenue for quantitatively classifying the behavior of noisy quantum systems. Ultimately, our results clarify the role of ergodicity in quantum dynamics, with fundamental and practical consequences.

The topological understanding of nematic liquid crystals has traditionally centered on defects and their classification via homotopy invariants. Here, we draw upon several aspects of Morse theory to describe a finer approach to topology that characterizes the isotopy invariants within a given homotopy class. This approach unifies various disparate ideas in liquid crystal physics, including the homotopy and Volterra classifications of defects, the winding and self-linking of disclinations, and the Pontryagin-Thom construction. Specifically, we use singularity theory and dividing curves to characterize nematic textures via tomography, as well as to provide a full topological classification of the rewiring and crossing of disclination lines. This process reveals the central role that nonsingular but nontrivial topological solitons—so-called merons—play in mediating interactions between disclination lines. We also clarify the notion of the charge of a disclination line, give a simple method for computing it, and apply this to examples drawn from experiment. In particular, this method shows that restricting a disclination line’s charge modulo 2 is incorrect; we construct examples of disclinations with point defect charges 0 and $-2$, which have the same local structure but very different global structures, underscoring the need for a more nuanced topological understanding of nematic systems.

The quantum mechanics of three interacting particles gives rise to fundamental and universal phenomena, such as the staircase of Efimov trimers predicted in the context of nuclear physics and observed in ultracold gases. Here, we observe a novel type of halo trimer using radio-frequency spectroscopy in an ultracold mixture of ${}^{23}\mathrm{Na}$ and ${}^{40}\mathrm{K}$ atoms. The trimers consist of two light bosons and one heavy fermion, and they have the structure of a Feshbach dimer weakly bound to one additional boson. We find that the trimer peak closely follows the dimer resonance over the entire range of explored interaction strengths and across an order-of-magnitude variation of the dimer energy, as reproduced by our theoretical analysis. The presence of this halo trimer is of direct relevance for many-body physics in ultracold mixtures and the association of ultracold molecules.

Allostery, the phenomenon by which the perturbation of a molecule at one site alters its behavior at a remote functional site, enables control over biomolecular function. Allosteric modulation is a promising avenue for drug discovery and is employed in the design of mechanical metamaterials. However, a general principle of allostery, i.e., a set of quantitative and transferable “ground rules,” remains elusive. It is neither a set of structural motifs nor intrinsic motions. Focusing on elastic network models, we here show that an allosteric lever—a mode-coupling pattern induced by the perturbation—governs the directional, source-to-target, allosteric communication: A structural perturbation of an allosteric site couples the excitation of localized hard elastic modes with concerted long-range soft-mode relaxation. Perturbations of nonallosteric sites instead couple hard and soft modes uniformly. The allosteric response is shown to be generally nonlinear and nonreciprocal, and allows for minimal structural distortions to be efficiently transmitted to specific changes at distant sites. Allosteric levers exist in proteins and “pseudoproteins”—networks designed to display an allosteric response. Interestingly, protein sequences that constitute allosteric transmission channels are shown to be evolutionarily conserved. To illustrate how the results may be applied in drug design, we use them to successfully predict known allosteric sites in proteins.

Qudits hold great promise for efficient quantum computation and the simulation of high-dimensional quantum systems [1]. However, existing control and measurement schemes for qudit systems scale unfavorably with qudit dimension since they decompose $SU(d)$ operations into series of qubitlike rotations and perform measurements on a small number of states [2–6]. Here, we address these challenges by employing simultaneous multifrequency drives to generate rotations and projections in an effective spin-$7/2$ system mapped onto the energy eigenstates of a superconducting circuit. We implement single-shot readout of the eight states using a multitone dispersive readout ($F_{\text{assignment}}=88.3\%$) and exploit the strong nonlinearity in a high-$E_J/E_C$ transmon to simultaneously address each transition and realize a spin displacement operator. Combining this displacement operator with a virtual SNAP gate, we realize arbitrary single-qudit unitary operations in $\mathcal{O}(d)$ physical pulses and extract spin displacement gate fidelities ranging from 0.997 to 0.989 for virtual spins of size $j=1$ to $j=7/2$. We demonstrate the potential of our control scheme in three ways: the direct measurement of the spin qudit Wigner function, randomized benchmarking of a logical qubit encoded into the qudit state, and randomized benchmarking of the full qudit Clifford group. In the latter experiment, we implement the $d$-dimensional quantum Fourier transform with an average gate fidelity of 0.91(6) in $d=8$. Our multifrequency approach to qudit control and measurement can be readily extended to other physical platforms that realize a multilevel system coupled to a cavity and can become a building block for efficient qudit-based quantum computation and simulation.

Tip-based structures offer a pathway to strong-field, optical-driven field emission, holding the potential for generating high-brightness ultrashort electron sources. While direct optical-field-driven electron emission and acceleration within the single optical subcycle provides a straightforward solution for ultrafast electron generation, achieving precise control over the emission process to generate high-quality electron beams suitable for practical applications remains challenging. Here, we present THz-driven subcycle electron field emission in a ridged waveguide cavity, achieving the first practical high-energy femtosecond field-emission source. This ridged cavity is engineered to spatially and temporally confine the electric field, effectively minimizing dispersion and suppressing field leakage. Through carrier-envelope phase control of the THz field, we achieve subcycle field emission, generating, for the first time, isolated electron bunches with a 940-fs (FWHM) duration. Using dual $24\mathrm{\mu }\mathrm{J}$ ($2\times 24\mathrm{\mu }\mathrm{J}$) of THz energy, we achieve a peak field strength of approximately $23\mathrm{GV}/\mathrm{m}$, accelerating electrons to a record energy of 46 keV with a charge of 2 pC per bunch, thereby enabling single-shot imaging. The high-field strength suppresses emittance blowup due to space-charge effects, ensuring excellent beam quality. The generated electron pulse exhibits high stability. As an initial application, we investigate transient electric-field dynamics in real time and space using time-resolved schlieren radiography with this field-emission electron source. These proof-of-principle results signify a critical advancement in developing compact, high-performance electron sources for user-oriented applications.

We use symmetry analysis and density functional theory to show that changes in magnetic order at a surface with respect to magnetic order in the bulk can be generically determined by considering local magnetoelectric responses of the crystal. Specifically, analysis of the local atomic-site magnetoelectric responses, or, equivalently, the corresponding atomic-site magnetic multipoles, can be used to predict all surface magnetic modifications arising purely from symmetry lowering via termination of the bulk magnetic order. This analysis applies even in materials with no bulk magnetoelectric response or net surface magnetization. We then demonstrate our arguments for two example antiferromagnets, topological semimetal CuMnAs and rocksalt NiO. We find that the (010) and $(1\overline{1}0)$ surfaces of CuMnAs and NiO, respectively, exhibit a series of antiferroically, as well as roughness-sensitive, ferroically ordered, modifications of the surface magnetic dipole moments, via canting or changes in sublattice magnitude, consistent with the bulk ordering of the magnetic multipoles. Our findings demonstrate a universal bulk-boundary correspondence allowing the general prediction of minimal possible surface and interface magnetic modifications, even in materials with no net magnetoelectric response. Furthermore, it paves the way for more accurate interpretations of a wide variety of surface-sensitive measurements.

Current progress in artificial intelligence is centered around so-called large language models that consist of neural networks processing long sequences of high-dimensional vectors called tokens. Statistical physics provides powerful tools to study the functioning of learning with neural networks and has played a recognized role in the development of modern machine learning. The statistical physics approach relies on simplified and analytically tractable models of data. However, simple tractable models for long sequences of high-dimensional tokens are largely underexplored. Inspired by the crucial role models such as the single-layer teacher-student perceptron (also known as generalized linear regression) played in the theory of fully connected neural networks, in this paper, we introduce and study the bilinear sequence regression (BSR) as one of the most basic models for sequences of tokens. We note that modern architectures naturally subsume the BSR model due to the skip connections. Building on recent methodological progress, we compute the Bayes-optimal generalization error for the model in the limit of long sequences of high-dimensional tokens and provide a message-passing algorithm that matches this performance. We quantify the improvement that optimal learning brings with respect to vectorizing the sequence of tokens and learning via simple linear regression. We also unveil surprising properties of the gradient descent algorithms in the BSR model.

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.

It is known that particles with exotic properties can emerge in systems made of simple constituents such as qubits, due to long-range quantum entanglement. In this paper, we provide quantitative characterizations of entanglement necessary for emergent anyons and fermions by using the geometric entanglement measure (GEM), which quantifies the maximal overlap between a given state and any short-range-entangled states. For systems with emergent anyons, based on the braiding statistics, we show that the GEM scales linearly in the system size regardless of microscopic details. The phenomenon of emergent anyons can also be understood within the framework of quantum error correction (QEC). Specifically, we show that the GEM of any 2D stabilizer codes must be at least quadratic in the code distance. Our proof is based on a generic prescription for constructing string operators, establishing a rigorous and direct connection between emergent anyons and QEC. For systems with emergent fermions, despite that the ground state subspaces could be exponentially huge and their coding properties could be rather poor, we show that the GEM also scales linearly in the system size. Our analysis establishes an intriguing link between quantum anomaly and entanglement: A quantum state respecting anomalous 1-form symmetries must be long-range entangled and have large GEM. Our results also extend to mixed states, such as the $ZX$-dephased toric code, providing a provably nontrivial class of intrinsically mixed-state phases.