In topologically ordered quantum states of matter in $(2+1)\mathrm{D}$ (spacetime dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property that is directly related to global transformations of the ground-state wave functions on a torus (the modular transformations). On the other hand, there are theoretical descriptions of various topologically ordered states in $(3+1)\mathrm{D}$, which exhibit both pointlike and looplike excitations, but systematic understanding of the fundamental physical distinctions between phases, and how these distinctions are connected to quantum statistics of excitations, is still lacking. One main result of this work is that the three-dimensional generalization of modular transformations, when applied to topologically ordered ground states, is directly related to a certain braiding process of looplike excitations. This specific braiding surprisingly involves three loops simultaneously, and can distinguish different topologically ordered states. Our second main result is the identification of the three-loop braiding as a process in which the worldsheets of the three loops have a nontrivial triple linking number, which is a topological invariant characterizing closed two-dimensional surfaces in four dimensions. In this work, we consider realizations of topological order in $(3+1)\mathrm{D}$ using cohomological gauge theory in which the loops have Abelian statistics and explicitly demonstrate our results on examples with $Z_2\times Z_2$ topological order.

The collisions of two simultaneously generated impulses in the giant axons of both earthworms and lobsters propagating in orthodromic and antidromic direction are investigated. The experiments have been performed on the extracted ventral cords of Lumbricus terrestris and the abdominal ventral cord of a lobster, Homarus americanus, by using external stimulation and recording. The collision of two nerve impulses of orthodromic and antidromic propagation did not result in the annihilation of the two signals, contrary to the common notion that is based on the existence of a refractory period in the well-known Hodgkin-Huxley theory. However, the results are in agreement with the electromechanical soliton theory for nerve-pulse propagation, as suggested by Heimburg and Jackson [On Soliton Propagation in Biomembranes and Nerves, Proc. Natl. Acad. Sci. U.S.A. 102, 9790 (2005).].

Online social networks (OSNs) enable researchers to study the social universe at a previously unattainable scale. The worldwide impact and the necessity to sustain the rapid growth of OSNs emphasize the importance of unraveling the laws governing their evolution. Empirical results show that, unlike many real-world growing networked systems, OSNs follow an intricate path that includes a dynamical percolation transition. In light of these results, we present a quantitative two-parameter model that reproduces the entire topological evolution of a quasi-isolated OSN with unprecedented precision from the birth of the network. This allows us to precisely gauge the fundamental macroscopic and microscopic mechanisms involved. Our findings suggest that the coupling between the real preexisting underlying social structure, a viral spreading mechanism, and mass media influence govern the evolution of OSNs. The empirical validation of our model, on a macroscopic scale, reveals that virality is 4–5 times stronger than mass media influence and, on a microscopic scale, individuals have a higher subscription probability if invited by weaker social contacts, in agreement with the “strength of weak ties” paradigm.

Recent developments have led to an explosion of activity on skyrmions in three-dimensional (3D) chiral magnets. Experiments have directly probed these topological spin textures, revealed their nontrivial properties, and led to suggestions for novel applications. However, in 3D the skyrmion crystal phase is observed only in a narrow region of the temperature-field phase diagram. We show here, using a general analysis based on symmetry, that skyrmions are much more readily stabilized in two-dimensional (2D) systems with Rashba spin-orbit coupling. This enhanced stability arises from the competition between field and easy-plane magnetic anisotropy and results in a nontrivial structure in the topological charge density in the core of the skyrmions. We further show that, in a variety of microscopic models for magnetic exchange, the required easy-plane anisotropy naturally arises from the same spin-orbit coupling that is responsible for the chiral Dzyaloshinskii-Moriya interactions. Our results are of particular interest for 2D materials like thin films, surfaces, and oxide interfaces, where broken surface-inversion symmetry and Rashba spin-orbit coupling naturally lead to chiral exchange and easy-plane compass anisotropy. Our theory gives a clear direction for experimental studies of 2D magnetic materials to stabilize skyrmions over a large range of magnetic fields down to $T=0$.

Impurities and defects frequently govern materials properties, with the most prominent example being the doping of bulk semiconductors where a minute amount of foreign atoms can be responsible for the operation of the electronic devices. Several computational schemes based on a supercell approach have been developed to get insights into types and equilibrium concentrations of point defects, which successfully work in bulk materials. Here, we show that many of these schemes cannot directly be applied to two-dimensional (2D) systems, as formation energies of charged point defects are dominated by large spurious electrostatic interactions between defects in inhomogeneous environments. We suggest two approaches that solve this problem and give accurate formation energies of charged defects in 2D systems in the dilute limit. Our methods, which are applicable to all kinds of charged defects in any 2D system, are benchmarked for impurities in technologically important $h$-BN and ${\mathrm{MoS}}_2$ 2D materials, and they are found to perform equally well for substitutional and adatom impurities.

Here, we report the experimental observation of a dynamical quantum phase transition in a strongly interacting open photonic system. The system studied, comprising a Jaynes-Cummings dimer realized on a superconducting circuit platform, exhibits a dissipation-driven localization transition. Signatures of the transition in the homodyne signal and photon number reveal this transition to be from a regime of classical oscillations into a macroscopically self-trapped state manifesting revivals, a fundamentally quantum phenomenon. This experiment also demonstrates a small-scale realization of a new class of quantum simulator, whose well-controlled coherent and dissipative dynamics is suited to the study of quantum many-body phenomena out of equilibrium.

We introduce here the concept of acoustic parity-time ($\mathcal{P}\mathcal{T}$) symmetry and demonstrate the extraordinary scattering characteristics of the acoustic $\mathcal{P}\mathcal{T}$ medium. On the basis of exact calculations, we show how an acoustic $\mathcal{P}\mathcal{T}$-symmetric medium can become unidirectionally transparent at given frequencies. Combining such a $\mathcal{P}\mathcal{T}$-symmetric medium with transformation acoustics, we design two-dimensional symmetric acoustic cloaks that are unidirectionally invisible in a prescribed direction. Our results open new possibilities for designing functional acoustic devices with directional responses.

Recently, two interesting candidate quantum phases—the chiral spin-density wave state featuring anomalous quantum Hall effect and the $d+id$ superconductor—were proposed for the Hubbard model on the honeycomb lattice at $1/4$ doping. Using a combination of exact diagonalization, density matrix renormalization group, the variational Monte Carlo method, and quantum field theories, we study the quantum phase diagrams of both the Hubbard model and the $t\text{−}J$ model on the honeycomb lattice at $1/4$ doping. The main advantage of our approach is the use of symmetry quantum numbers of ground-state wave functions on finite-size systems (up to 32 sites) to sharply distinguish different quantum phases. Our results show that for $1\lesssim U/t<40$ in the Hubbard model and for $0.1<J/t<0.80(2)$ in the $t\text{−}J$ model, the quantum ground state is either a chiral spin-density wave state or a spin-charge-Chern liquid, but not a $d+id$ superconductor. However, in the $t\text{−}J$ model, upon increasing $J$, the system goes through a first-order phase transition at $J/t=0.80(2)$ into the $d+id$ superconductor. Here, the spin-charge-Chern liquid state is a new type of topologically ordered quantum phase with Abelian anyons and fractionalized excitations. Experimental signatures of these quantum phases, such as tunneling conductance, are calculated. These results are discussed in the context of $1/4$-doped graphene systems and other correlated electronic materials on the honeycomb lattice.

The diversities in crystal structures and ways of doping result in extremely diversified phase diagrams for iron-based superconductors. With angle-resolved photoemission spectroscopy, we have systematically studied the effects of chemical substitution on the electronic structure of various series of iron-based superconductors. Beyond the Fermi-surface alteration that has been reported most often in the past, we found two more extraordinary effects of doping: (1) the site and band dependencies of quasiparticle scattering and, more importantly, (2) the ubiquitous and significant change of electronic correlation by both isovalent and heterovalent dopants in the iron-anion layer. Moreover, we found that the electronic correlation could be suppressed by applying either the chemical pressure or doping electrons but not by doping holes. Together with other findings provided here, these results complete the microscopic picture of the electronic effects of dopants, which facilitates a unified understanding of the diversified phase diagrams and resolutions to many open issues of various iron-based superconductors.

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green’s function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.

Recent progress in nanoscale quantum optics and superconducting qubits has made the creation of strongly correlated, and even topologically ordered, states of photons a real possibility. Many of these states are gapped and exhibit anyon excitations, which could be used for a robust form of quantum information processing. However, while numerous qubit array proposals exist to engineer the Hamiltonian for these systems, the question of how to stabilize the many-body ground state of these photonic quantum simulators against photon losses remains largely unanswered. We here propose a simple mechanism that achieves this goal for Abelian and non-Abelian fractional quantum Hall states of light. Our construction uses a uniform two-photon drive field to couple the qubits of the primary lattice with an auxiliary “shadow” lattice, composed of qubits with a much faster loss rate than the qubits of the primary quantum simulator itself. This coupling causes hole states created by photon losses to be rapidly refilled, and the system’s many-body gap prevents further photons from being added once the strongly correlated ground state is reached. The fractional quantum Hall state (with a small, transient population of quasihole excitations) is thus the most stable state of the system, and all other configurations will relax toward it over time. The physics described here could be implemented in a circuit QED architecture, and the device parameters needed for our scheme to succeed are in reach of current technology. We also propose a simple six-qubit device, which could easily be built in the near future, that can act as a proof of principle for our scheme.

Photoelectric properties of noncentrosymmetric, similarly oriented metallic nanoparticles embedded in a homogeneous semiconductor matrix are theoretically studied. Because of the asymmetric shape of the nanoparticle boundary, photoelectron emission acquires a preferred direction, resulting in a photocurrent flow in that direction when nanoparticles are uniformly illuminated by a homogeneous plane wave. This effect is a direct analogy of the photogalvanic (or bulk photovoltaic) effect known to exist in media with noncentrosymmetric crystal structure, such as doped lithium niobate or bismuth ferrite, but is several orders of magnitude stronger. Termed the giant plasmonic photogalvanic effect, the reported phenomenon is valuable for characterizing photoemission and photoconductive properties of plasmonic nanostructures and can find many uses for photodetection and photovoltaic applications.

We show how off-resonant light scattering can provide quantitative information on antiferromagnetic ordering of a two-species fermionic atomic gas in a tightly-confined two-dimensional optical lattice. We analyze the emerging magnetic ordering of atoms in the mean-field and in random phase approximations and show how the many-body static and dynamic correlations, evaluated in the standard Feynman-Dyson perturbation series, can be detected in the scattered light signal. The staggered magnetization reveals itself in the magnetic Bragg peaks of the individual spin components. These magnetic peaks, however, can be considerably suppressed in the absence of a true long-range antiferromagnetic order. The light scattered outside the diffraction orders can be collected by a lens with highly improved signal-to-shot-noise ratio when the diffraction maxima are blocked. The collective and single-particle excitations are identified in the spectrum of the scattered light. We find that the spin-conserving and spin-exchanging atomic transitions convey information on density, longitudinal spin, and transverse spin correlations. The different correlations and scattering processes exhibit characteristic angular distribution profiles for the scattered light, and e.g., the diagnostic signal of transverse spin correlations could be separated from the optical response by the scattering direction, frequency, or polarization. We also analyze the detection accuracy by estimating the number of required measurements, constrained by the heating rate that is determined by inelastic light-scattering events. The imaging technique could be extended to the two-species fermionic states in other regions of the phase diagram where the ground-state properties are still not fully understood.

Weyl semimetals are three-dimensional crystalline systems where pairs of bands touch at points in momentum space, termed Weyl nodes, that are characterized by a definite topological charge: the chirality. Consequently, they exhibit the Adler-Bell-Jackiw anomaly, which in this condensed-matter realization implies that the application of parallel electric ($\mathbf{E}$) and magnetic ($\mathbf{B}$) fields pumps electrons between nodes of opposite chirality at a rate proportional to $\mathbf{E}·\mathbf{B}$. We argue that this pumping is measurable via nonlocal transport experiments, in the limit of weak internode scattering. Specifically, we show that as a consequence of the anomaly, applying a local magnetic field parallel to an injected current induces a valley imbalance that diffuses over long distances. A probe magnetic field can then convert this imbalance into a measurable voltage drop far from source and drain. Such nonlocal transport vanishes when the injected current and magnetic field are orthogonal and therefore serves as a test of the chiral anomaly. We further demonstrate that a similar effect should also characterize Dirac semimetals—recently reported to have been observed in experiments—where the coexistence of a pair of Weyl nodes at a single point in the Brillouin zone is protected by a crystal symmetry. Since the nodes are analogous to valley degrees of freedom in semiconductors, the existence of the anomaly suggests that valley currents in three-dimensional topological semimetals can be controlled using electric fields, which has potential practical “valleytronic” applications.

The theoretical analysis of many problems in physics, astronomy, and applied mathematics requires an efficient numerical exploration of multimodal parameter spaces that exhibit broken ergodicity. Monte Carlo methods are widely used to deal with these classes of problems, but such simulations suffer from a ubiquitous sampling problem: The probability of sampling a particular state is proportional to its entropic weight. Devising an algorithm capable of sampling efficiently the full phase space is a long-standing problem. Here, we report a new hybrid method for the exploration of multimodal parameter spaces exhibiting broken ergodicity. Superposition enhanced nested sampling combines the strengths of global optimization with the unbiased or athermal sampling of nested sampling, greatly enhancing its efficiency with no additional parameters. We report extensive tests of this new approach for atomic clusters that are known to have energy landscapes for which conventional sampling schemes suffer from broken ergodicity. We also introduce a novel parallelization algorithm for nested sampling.

We study the ground state of $N$ weakly interacting electrons (with $N\le 10$) in a two-dimensional parabolic quantum dot with strong Rashba spin-orbit coupling. Using dimensionless parameters for the Coulomb interaction $\lambda \lesssim 1$ and the Rashba coupling $\alpha \gg 1$, the low-energy physics is characterized by an almost flat single-particle dispersion. From an analytical approach for $\alpha \to \infty$ and $N=2$, and from numerical exact-diagonalization and Hartree-Fock calculations, we find a transition from a conventional unmagnetized ground state (for $\lambda <{\lambda }_c$) to an orbital ferromagnet (for $\lambda >{\lambda }_c$), with a large magnetization and a circulating charge current. We show that the critical interaction strength ${\lambda }_c={\lambda }_c(\alpha ,N)$ vanishes in the limit $\alpha \to \infty$.

A common method for extracting true correlations from large data sets is to look for variables with unusually large coefficients on those principal components with the biggest eigenvalues. Here, we show that even if the top principal components have no unusually large coefficients, large coefficients on lower principal components can still correspond to a valid signal. This contradicts the typical mathematical justification for principal component analysis, which requires that eigenvalue distributions from relevant random matrix ensembles have compact support, so that any eigenvalue above the upper threshold corresponds to signal. The new possibility arises via a mechanism based on a variant of the Feynman-Hellmann theorem, and leads to significant correlations between a signal and principal components when the underlying noise is not both independent and uncorrelated, so the eigenvalue spacing of the noise distribution can be sufficiently large. This mechanism justifies a new way of using principal component analysis and rationalizes recent empirical findings that lower principal components can have information about the signal, even if the largest ones do not.

We propose a waveguiding mechanism based on the effective gauge potential for photons. The waveguide geometry consists of core and cladding regions with the same underlying dispersion relation, but subject to different gauge potentials. This geometry can be realized in a dynamically modulated resonator lattice and provides a conceptually straightforward and dynamically reconfigurable mechanism for generating a one-way waveguide.

We show that a spatially well-defined layer of boron dopants in a hydrogen-enriched silicon target allows the production of a high yield of alpha particles of around ${10}^9$ per steradian using a nanosecond, low-contrast laser pulse with a nominal intensity of approximately $3\times {10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}$. This result can be ascribed to the nature of the long laser-pulse interaction with the target and with the expanding plasma, as well as to the optimal target geometry and composition. The possibility of an impact on future applications such as nuclear fusion without production of neutron-induced radioactivity and compact ion accelerators is anticipated.

We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.