Fundamental physical properties, such as phase transitions, electronic structures, and spin excitations, in all magnetic ordered materials, were ultimately believed to rely on the symmetry theory of magnetic space groups. Recently, it has come to light that a more comprehensive group, known as the spin space group (SSG), which combines separate spin and spatial operations, is necessary to fully characterize the geometry and underlying properties of magnetic ordered materials. However, the basic theory of SSG has seldom been developed. In this work, we present a systematic study of the enumeration and the representation theory of the SSG. Starting from the 230 crystallographic space groups and finite translation groups with a maximum order of eight, we establish an extensive collection of over 100 000 SSGs under a four-index nomenclature as well as international notation. We then identify inequivalent SSGs specifically applicable to collinear, coplanar, and noncoplanar magnetic configurations. To facilitate the identification of the SSG, we develop an online program that can determine the SSG symmetries of any magnetic ordered crystal. Moreover, we derive the irreducible corepresentations of the little group in momentum space within the SSG framework. Finally, we illustrate the SSG symmetries and physical effects beyond the framework of magnetic space groups through several representative material examples, including a candidate altermagnet ${\mathrm{RuO}}_2$, spiral spin polarization in the coplanar antiferromagnet ${\mathrm{CeAuAl}}_3$, and geometric Hall effect in the noncoplanar antiferromagnet ${\mathrm{CoNb}}_3{\mathrm{S}}_6$. Our work advances the field of group theory in describing magnetic ordered materials, opening up avenues for deeper comprehension and further exploration of emergent phenomena in magnetic materials.

In this work, we exhaust all the spin space symmetries, which fully characterize collinear, noncollinear, and commensurate spiral as well as incommensurate spiral magnetism, etc., and investigate enriched features of electronic bands that respect these symmetries. We achieve this by systematically classifying the so-called spin space groups (SSGs)—joint symmetry groups of spatial and spin operations that leave the magnetic structure unchanged. Generally speaking, they are accurate (approximate) symmetries in systems where spin-orbit coupling (SOC) is negligible (finite but weaker than the energy scale of interest), but we also show that specific SSGs could remain valid even in the presence of strong SOC. In recent years, SSGs have played increasingly pivotal roles in various fields such as altermagnetism, topological electronic states, and topological magnon, etc. However, due to its complexity, a complete SSG classification has not been completed up to now. By representing the SSGs as $\mathrm{O}(N)$ representations, we—for the first time—obtain the complete classifications of 1421, 9542, and 56 512 distinct SSGs for collinear ($N=1$), coplanar ($N=2$), and noncoplanar ($N=3$) magnetism, respectively. SSG not only fully characterizes the symmetry of spin degrees of freedom, but also gives rise to exotic electronic states, which, in general, form projective representations of magnetic space groups (MSGs). Surprisingly, electronic bands in SSGs exhibit features never seen in MSGs, such as (i) nonsymmorphic SSG Brillouin zone, where SSG operations behave as a glide or screw when acting on momentum, (ii) effective $\pi$ flux, where translation operators anticommute with each other and yield duplicate bands, (iii) higher-dimensional representations unexplained by MSGs, and (iv) unconventional spin texture on a Fermi surface, which is completely determined by SSGs, independent of Hamiltonian details. To apply our theory, we identify the SSG for each of the 1595 published magnetic structures in the MAGNDATA database on the Bilbao Crystallographic Server. Material examples exhibiting the novel features (i)–(iv) are discussed with emphasis. We also investigate new types of SSG-protected topological electronic states that are unprecedented in MSGs. In particular, we propose a 3D ${\mathbb{Z}}_2$ topological insulator state with a fourfold degenerate Dirac point on the surface and a new scenario of anomalous ${\mathbb{Z}}_2$ helical states that appear on magnetic domain walls.

Group-IV color centers in diamond are promising candidates for quantum networks due to their dominant zero-phonon line and symmetry-protected optical transitions that connect to coherent spin levels. The negatively charged tin-vacancy (SnV) center possesses long electron spin lifetimes due to its large spin-orbit splitting. However, the magnetic dipole transitions required for microwave spin control are suppressed, and strain is necessary to enable these transitions. Recent work has shown spin control of strained emitters using microwave lines that suffer from Ohmic losses, restricting coherence through heating. We utilize a superconducting coplanar waveguide to measure SnV centers subjected to strain, observing substantial improvement. A detailed analysis of the SnV center electron spin Hamiltonian based on the angle-dependent splitting of the ground and excited states is performed. We demonstrate coherent spin manipulation and obtain a Hahn echo coherence time of up to $T_2=430\mathrm{\mu }\mathrm{s}$. With dynamical decoupling, we can prolong coherence to $T_2=10\mathrm{ms}$, about a sixfold improvement compared to earlier works. We also observe a nearby coupling ${}^{13}\mathrm{C}$ spin, which may serve as a quantum memory, thus substantiating the potential of SnV centers in diamond and demonstrates the benefit of superconducting microwave structures.

Estimating global properties of many-body quantum systems such as entropy or bipartite entanglement is a notoriously difficult task, typically requiring a number of measurements or classical postprocessing resources growing exponentially in the system size. In this work, we address the problem of estimating global entropies and mixed-state entanglement via partial-transposed (PT) moments and show that efficient estimation strategies exist under the assumption that all the spatial correlation lengths are finite. Focusing on one-dimensional systems, we identify a set of approximate factorization conditions (AFCs) on the system density matrix, which allow us to reconstruct entropies and PT moments from information on local subsystems. This identification yields a simple and efficient strategy for entropy and entanglement estimation. Our method could be implemented in different ways, depending on how information on local subsystems is extracted. Focusing on randomized measurements providing a practical and common measurement scheme, we prove that our protocol requires only polynomially many measurements and postprocessing operations, assuming that the state to be measured satisfies the AFCs. We prove that the AFCs hold for finite-depth quantum-circuit states and translation-invariant matrix-product density operators and provide numerical evidence that they are satisfied in more general, physically interesting cases, including thermal states of local Hamiltonians. We argue that our method could be practically useful to detect bipartite mixed-state entanglement for large numbers of qubits available in today’s quantum platforms.

We present a deterministic algorithm for the efficient evaluation of imaginary-time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary-time Green’s functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary-time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong-coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an $M$th-order diagram at inverse temperature $\beta$ and spectral width ${\omega }_{\max }$ from $\mathcal{O}\mathbf{(}(\beta {\omega }_{\max }{)}^{2M-1}\mathbf{)}$ for a direct quadrature to $\mathcal{O}\mathbf{(}M(\log (\beta {\omega }_{\max }){)}^{M+1}\mathbf{)}$, with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multiband impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$, demonstrating the promise of the method for modeling realistic strongly correlated multiband materials. For both strong and weak coupling expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust blackbox evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams.

We explore generalized global symmetries in theories of physics beyond the standard model. Theories of $Z^{\prime }$ bosons generically contain “noninvertible” chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well motivated $\mathrm{U}(1{)}_{L_{\mu }-L_{\tau }}$, there is a noninvertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g., $\mathrm{U}(1{)}_{L_{\mu }-L_{\tau }}\subset \mathrm{SU}(3{)}_H$, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas, e.g., $y_{\nu }\sim y_{\tau }\exp (-S_{\mathrm{inst}})$. These theories require no bevy of new fields nor ad hoc additional global symmetries but are instead simple, natural, and predictive: The discovery of a lepton family $Z^{\prime }$ at low energies will reveal the scale at which $L_{\mu }-L_{\tau }$ emerges from a larger gauge symmetry.

Despite the widespread adoption of higher-order mathematical structures such as hypergraphs, methodological tools for their analysis lag behind those for traditional graphs. This work addresses a critical gap in this context by proposing two microcanonical random null models for directed hypergraphs: the directed hypergraph degree model (dhdm) and the directed hypergraph JOINT model (dhjm). These models preserve essential structural properties of directed hypergraphs such as node in- and out-degree sequences and hyperedge head- and tail-size sequences, or their joint tensor. We also describe two efficient Markov chain Monte Carlo algorithms, nudhy-degs and nudhy-joint, to sample random hypergraphs from these ensembles. To showcase the interdisciplinary applicability of the proposed null models, we present three distinct use cases in sociology, epidemiology, and economics. First, we reveal the oscillatory behavior of increased homophily in opposition parties in the U.S. Congress over a 40-year span, emphasizing the role of higher-order structures in quantifying political group homophily. Second, we investigate a nonlinear contagion in contact hypernetworks, demonstrating that disparities between simulations and theoretical predictions can be explained by considering higher-order joint degree distributions. Last, we examine the economic complexity of countries in the global trade network, showing that local network properties preserved by nudhy explain the main structural economic complexity indexes. This work advances the development of null models for directed hypergraphs, addressing the intricate challenges posed by their complex entity relations, and providing a versatile suite of tools for researchers across various domains.

Active matter systems evade the constraints of thermal equilibrium, leading to the emergence of intriguing collective behavior. A paradigmatic example is given by motor-filament mixtures, where the motion of motor proteins drives alignment and sliding interactions between filaments and their self-organization into macroscopic structures. After defining a microscopic model for these systems, we derive continuum equations, exhibiting the formation of active supramolecular assemblies such as micelles, bilayers, and foams. The transition between these structures is driven by a branching instability, which destabilizes the orientational order within the micelles, leading to the growth of bilayers at high microtubule densities. Additionally, we identify a fingering instability, modulating the shape of the micelle interface at high motor densities. We study the role of various mechanisms in these two instabilities, such as contractility, active splay, and anchoring, allowing for generalization beyond the system considered here.

Trapped-ion systems are a leading platform for quantum information processing, but they are currently limited to 1D and 2D arrays, which imposes restrictions on both their scalability and their range of applications. Here, we propose a path to overcome this limitation by demonstrating that Penning traps can be used to realize remarkably clean bilayer crystals, wherein hundreds of ions self-organize into two well-defined layers. These bilayer crystals are made possible by the inclusion of an anharmonic trapping potential, which is readily implementable with current technology. We study the normal modes of this system and discover salient differences compared to the modes of single-plane crystals. The bilayer geometry and the unique properties of the normal modes open new opportunities—in particular, in quantum sensing and quantum simulation—that are not straightforward in single-plane crystals. Furthermore, we illustrate that it may be possible to extend the ideas presented here to realize multilayer crystals with more than two layers. Our work increases the dimensionality of trapped-ion systems by efficiently utilizing all three spatial dimensions, and it lays the foundation for a new generation of quantum information processing experiments with multilayer 3D crystals of trapped ions.

We consider the statistical properties of eigenstates of the time-evolution operator in chaotic many-body quantum systems. Our focus is on correlations between eigenstates that are specific to spatially extended systems and that characterize entanglement dynamics and operator spreading. In order to isolate these aspects of dynamics from those arising as a result of local conservation laws, we consider Floquet systems in which there are no conserved densities. The correlations associated with scrambling of quantum information lie outside the standard framework established by the eigenstate thermalization hypothesis (ETH). In particular, ETH provides a statistical description of matrix elements of local operators between pairs of eigenstates, whereas the aspects of dynamics we are concerned with arise from correlations among sets of four or more eigenstates. We establish the simplest correlation function that captures these correlations and discuss features of its behavior that are expected to be universal at long distances and low energies. We also propose a maximum-entropy ansatz for the joint distribution of a small number $n$ of eigenstates. In the case $n=2$, this ansatz reproduces ETH. For $n=4$ it captures both the growth with time of entanglement between subsystems, as characterized by the purity of the time-evolution operator, and also operator spreading, as characterized by the behavior of the out-of-time-order correlator. We test these ideas by comparing results from Monte Carlo sampling of our ansatz with exact diagonalization studies of Floquet quantum circuits.

Imaging of nanoscale magnetic textures within extended material systems is of critical importance to both fundamental research and technological applications. While high-resolution magnetic imaging of thin nanoscale samples is well established with electron and soft x-ray microscopy, the extension to micrometer-thick systems currently requires hard x rays, which limits high-resolution imaging to rare-earth magnets. Here, we overcome this limitation by establishing soft x-ray magnetic imaging of micrometer-thick systems using the pre-edge phase x-ray magnetic circular dichroism signal, thus making possible the study of a wide range of magnetic materials. By performing dichroic spectroptychography, we demonstrate high spatial resolution imaging of magnetic samples up to $1.7\mathrm{\mu }\mathrm{m}$ thick, an order of magnitude higher than conventionally possible with soft x-ray absorption-based techniques. We demonstrate the applicability of the technique by harnessing the pre-edge phase to image thick chiral helimagnets, and naturally occurring magnetite particles, gaining insight into their three-dimensional magnetic configuration. This new regime of magnetic imaging makes possible the study of extended non-rare-earth systems that have until now been inaccessible, including magnetic textures for future spintronic applications, non-rare-earth permanent magnets for energy harvesting, and the magnetic configuration of giant magnetofossils.

Circumnutations are widespread in plants and typically associated with exploratory movements; however, a quantitative understanding of their role remains elusive. In this study we report, for the first time, the role of noisy circumnutations in facilitating an optimal growth pattern within a crowded group of mutually shading plants. We revisit the problem of self-organization observed for sunflowers, mediated by shade response interactions. Our analysis reveals that circumnutation movements conform to a bounded random walk characterized by a remarkably broad distribution of velocities, covering 3 orders of magnitude. In motile animal systems such wide distributions of movement velocities are frequently identified with enhancement of behavioral processes, suggesting that circumnutations may serve as a source of functional noise. To test our hypothesis, we developed a Langevin-type parsimonious model of interacting growing disks, informed by experiments, successfully capturing the characteristic dynamics of individual and multiple interacting plants. Employing our simulation framework we examine the role of circumnutations in the system, and find that the observed breadth of the velocity distribution represents a sharp transition in the force-noise ratio, conferring advantageous effects by facilitating exploration of potential configurations, leading to an optimized arrangement with minimal shading. These findings represent the first report of functional noise in plant movements and establish a theoretical foundation for investigating how plants navigate their environment by employing computational processes such as task-oriented processes, optimization, and active sensing. Since plants move by growing, space and time are coupled, and dynamics of self-organization lead to emergent 3D patterns. As such, this system provides conceptual insight for other interacting growth-driven systems such as fungal hyphae, neurons and self-growing robots, as well as active matter systems where agents interact with past trajectories of their counterparts, such as stigmergy in social insects. This foundational insight has implications in statistical physics, ecological dynamics, agriculture, and even swarm robotics.

The initial immune response to an acute primary infection is a coupled process of antigen proliferation, molecular recognition by naive B cells, and their subsequent clonal expansion. This process contains a fundamental problem: the recognition of an exponentially time-dependent antigen signal. Here, we show that an efficient immune response must be stringently constrained to B-cell lineages with high antigen binding affinity. We propose a tuned proofreading mechanism for primary recognition of new antigens, where the molecular recognition machinery is adapted to the complexity of the immune repertoire. We show that this process produces potent, specific, and fast recognition of antigens, maintaining a spectrum of genetically distinct B-cell lineages as input for affinity maturation. Our analysis maps the proliferation-recognition dynamics of a primary infection to a generalized Luria-Delbrück process, akin to the dynamics of the classic fluctuation experiment. This map establishes a link between signal recognition dynamics and evolution. We derive the resulting statistics of the activated immune repertoire: Antigen binding affinity, expected size, and frequency of active B-cell clones are related by power laws, which define the class of generalized Luria-Delbrück processes. Their exponents depend on the antigen and B-cell proliferation rate, the number of proofreading steps, and the lineage density of the naive repertoire. We extend the model to include spatiotemporal processes, including the diffusion-recognition dynamics of a vaccination. Empirical data of activated mouse immune repertoires are found to be consistent with activation involving about three proofreading steps. The model predicts key clinical characteristics of acute infections and vaccinations, including the emergence of elite neutralizers and the effects of immune aging. More broadly, our results establish infections and vaccinations as a new probe into the global architecture and functional principles of immune repertoires.

Exciton-exciton interactions are key to understanding nonlinear optical and transport phenomena in van der Waals heterobilayers, which emerged as versatile platforms to study correlated electronic states. We present a combined theory-experiment study of excitonic many-body effects based on first-principle band structures and Coulomb interaction matrix elements. Key to our approach is the explicit treatment of the fermionic substructure of excitons and dynamical screening effects for density-induced energy renormalization and dissipation. We demonstrate that dipolar blueshifts are almost perfectly compensated by many-body effects, mainly by screening-induced self-energy corrections. Moreover, we identify a crossover between attractive and repulsive behavior at elevated exciton densities. Theoretical findings are supported by experimental studies of spectrally narrow, mobile interlayer excitons in atomically reconstructed, $h$-BN-encapsulated ${\mathrm{MoSe}}_2/{\mathrm{WSe}}_2$ heterobilayers. Both theory and experiment show energy renormalization on a scale of a few meV even for high injection densities in the vicinity of the Mott transition. Our results revise the established picture of dipolar repulsion dominating exciton-exciton interactions in van der Waals heterostructures and open up opportunities for their external design.

Hybrid Josephson junctions (JJs) realized in superconductor-semiconductor heterostructures host fermionic modes known as Andreev bound states (ABSs). In these structures, a promising and yet unexplored avenue for harnessing spin and parity degrees of freedom is offered by JJs with three or more superconducting terminals, where phase-induced spin polarization and transitions of the ground state to an odd parity were predicted to arise. Here we spectroscopically probe the two-dimensional band structure of ABSs in a phase-controlled $\mathrm{InAs}/\mathrm{Al}$ three-terminal JJ. Andreev bands show signatures of spin-degeneracy breaking, with level splitting in excess of $\sim 9\mathrm{GHz}$, and zero-energy crossings associated to ground state fermion parity transitions. Spin splitting and parity transitions are enabled and controlled by locally applied magnetic fluxes, in the absence of Zeeman effect or Coulomb blockade. Our results underscore the potential of multiterminal hybrid devices for phase engineering ABSs, with significant implications for spin- and parity-based quantum devices.

We report an extensive high-sensitivity search for axion dark matter above 1 GHz at the Center for Axion and Precision Physics Research (CAPP). The cavity resonant search, exploiting the coupling between axions and photons, explored the frequency (mass) range of 1.025 GHz ($4.24\mathrm{\mu }\mathrm{eV}$) to 1.185 GHz ($4.91\mathrm{\mu }\mathrm{eV}$). We have introduced a number of innovations in this field, demonstrating the practical approach of optimizing all the relevant parameters of axion haloscopes, extending presently available technology. The CAPP 12 T magnet with an aperture of 320 mm made of ${\mathrm{Nb}}_3\mathrm{Sn}$ and NbTi superconductors surrounding a 37 l ultralight-weight copper cavity is expected to convert Dine-Fischler-Srednicki-Zhitnitsky axions into approximately ${10}^2$ microwave photons per second. A powerful dilution refrigerator, capable of keeping the core system below 40 mK, combined with quantum-noise-limited readout electronics, achieved a total system noise of about 200 mK or below, which corresponds to a background of roughly $4\times {10}^3$ photons per second within the axion bandwidth. The combination of all those improvements provides unprecedented search performance, imposing the most stringent exclusion limits on axion-photon coupling in this frequency range to date. These results also suggest an experimental capability suitable for highly sensitive searches for axion dark matter above 1 GHz.

Electrically controlled photonic circuits hold promise for information technologies with greatly improved energy efficiency and quantum information processing capabilities. However, weak nonlinearity and electrical response of typical photonic materials have been two critical challenges. Therefore, hybrid electronic-photonic systems, such as semiconductor exciton polaritons, have been intensely investigated for their potential to allow higher nonlinearity and electrical control, with limited success so far. Here we demonstrate an electrically gated waveguide architecture for field induced dipolar polaritons that allows enhanced and electrically controllable polariton nonlinearities, enabling an electrically tuned reflecting switch (mirror) and transistor of the dipolar polaritons. The polariton transistor displays blockade and antiblockade by compressing a dilute dipolar-polariton pulse exhibiting very strong dipolar interactions. The large nonlinearities are explained using a simple density-dependent dipolar polarization field that very effectively screens the external electric field. We project that a quantum blockade at the single polariton level is feasible in such a device.

Many real-world systems undergo abrupt changes in dynamics as they move across critical points, often with dramatic and irreversible consequences. Much existing theory on identifying the time-series signatures of nearby critical points, such as increased signal variance and slower timescales, is derived from analytically tractable systems, typically considering the case of fixed, low-amplitude noise. However, real-world systems are often corrupted by unknown levels of noise that can distort these temporal signatures. Here we aim to develop noise-robust indicators of the distance to criticality (DTC) for systems affected by dynamical noise in two cases: when the noise amplitude is either fixed or is unknown and variable across recordings. We present a highly comparative approach to this problem that compares the ability of over 7000 candidate time-series features to track the DTC in the vicinity of a supercritical Hopf bifurcation. Our method recapitulates existing theory in the fixed-noise case, highlighting conventional time-series features that accurately track the DTC. But in the variable-noise setting, where these conventional indicators perform poorly, we highlight new types of high-performing time-series features and show that their success is accomplished by capturing the shape of the invariant density (which depends on both the DTC and the noise amplitude) relative to the spread of fast fluctuations (which depends on the noise amplitude). We introduce a new high-performing time-series statistic, the rescaled autodensity (RAD), that combines these two algorithmic components. We then use RAD to provide new evidence that brain regions higher in the visual hierarchy are positioned closer to criticality, supporting existing hypotheses about patterns of brain organization that are not detected using conventional metrics of the DTC. Our results demonstrate how large-scale algorithmic comparison can yield theoretical insights that can motivate new theory and interpretable algorithms for solving important real-world problems.

The approach to equilibrium in interacting classical and quantum systems is a challenging problem of both theoretical and experimental interest. One useful organizing principle characterizing equilibration is the dissipative universality class, the most prevalent one being diffusion. In this paper, we use the effective field theory (EFT) of diffusion to systematically obtain universal power-law corrections to diffusion. We then employ large-scale simulations of classical and quantum systems to explore their validity. In particular, we find universal scaling functions for the corrections to the dynamical structure factor $⟨n(x,t)n⟩$, in the presence of a single $\mathrm{U}(1)$ or $\mathrm{SU}(2)$ charge in systems with and without particle-hole symmetry, and present the framework to generalize the calculation to multiple charges. Classical simulations show remarkable agreement with EFT predictions for subleading corrections, pushing precision tests of effective theories for thermalizing systems to an unprecedented level. Moving to quantum systems, we perform large-scale tensor-network simulations in unitary and noisy 1D Floquet systems with conserved magnetization. We find a qualitative agreement with EFT, which becomes quantitative in the case of noisy systems. Additionally, we show how the knowledge of EFT corrections allows for fitting methods, which can improve the estimation of transport parameters at the intermediate times accessible by simulations and experiments. Finally, we explore nonlinear response in quantum systems and find that EFT provides an accurate prediction for its behavior. Our results provide a basis for a better understanding of the nonlinear phenomena present in thermalizing systems.