Deep learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing increasingly more powerful and involved layers. Contrarily, Taylor coefficients of DNNs still appear mainly in the light of interpretability studies, where they are computed at most to first order. However, especially in theoretical physics, numerous problems benefit from accessing higher orders, as well. This gap motivates a general formulation of neural network (NN) Taylor expansions. Restricting our analysis to multilayer perceptrons (MLPs) and introducing quantities we refer to as propagators and vertices, both depending on the MLP's weights and biases, we establish a graph-theoretical approach. Similarly to Feynman rules in quantum field theories, we can systematically assign diagrams containing propagators and vertices to the corresponding partial derivative. Examining this approach for S-wave scattering lengths of shallow potentials, we observe NNs to adapt their derivatives mainly to the leading order of the target function's Taylor expansion. To circumvent this problem, we propose an iterative NN perturbation theory. During each iteration we eliminate the leading order, such that the next-to-leading order can be faithfully learned during the subsequent iteration. After performing two iterations, we find that the first- and second-order Born terms are correctly adapted during the respective iterations. Finally, we combine both results to find a proxy that acts as a machine-learned second-order Born approximation.

Large bosonic or continuous variable nonlinearities can have numerous applications, ranging from the generation of cat states for quantum computation, through to quantum sensing where the sensitivity exceeds Heisenberg scaling in the resources. However, the generation of ultra-large nonlinearities has proved immensely challenging experimentally. We describe a novel protocol where one can effectively generate large Kerr-type nonlinearities via the conditional application of a linear operation on an optical mode by an ancilla mode, followed by a measurement of the ancilla and corrective operation on the probe mode. Our protocol can generate high-quality Schrödinger cat states useful for quantum computing and can be used to perform sensing of an unknown rotation or displacement in phase space, with super-Heisenberg scaling in the resources. We finally describe a potential experimental implementation using atomic ensembles interacting with optical modes via the Faraday effect.

We study coherent electronic transport through a Coulomb blockaded superconducting Rashba wire in the cotunneling regime between conductance resonances. By varying an external Zeeman field the wire can be tuned into a topological regime, where nonlocal transport through Majorana zero modes is the dominant mechanism. We model coherent transport in the cotunneling regime by using a scattering matrix formalism, and find that the transmission amplitude has a maximum as a function of Zeeman field, whose height is proportional to the wire length. We relate the transmission amplitude to the Majorana correlation length, and argue that the Zeeman field and length dependence of the transmission amplitude are unique signatures for the presence of Majorana zero modes.

The interplay between structural and electronic phases in iron-based superconductors is a central theme in the search for the superconducting pairing mechanism. While electronic nematicity is competing with superconductivity, the effect of purely structural orthorhombic order is unexplored. Here, using x-ray diffraction and angle-resolved photoemission spectroscopy, we reveal a structural orthorhombic phase in the electron-doped iron-pnictide superconductor ${\mathrm{Pr}}_4{\mathrm{Fe}}_2{\mathrm{As}}_2{\mathrm{Te}}_{0.88}{\mathrm{O}}_4$ ($T_{\mathrm{c}}=25$ K), which is distinct from orthorhombicity in the nematic phase in underdoped pnictides. Despite the high electron doping we find an exceptionally high orthorhombic onset temperature ($T_{\mathrm{ort}}\sim 250$ K), no signatures of phase competition with superconductivity, and absence of electronic nematic order as the driving mechanism for orthorhombicity. Combined, our results establish a high-temperature phase in the phase diagram of iron-pnictide superconductors and impose strong constraints for the modeling of their superconducting pairing mechanism.

We theoretically propose the long-range spin transport mediated by the gapless surface states of a topological Dirac semimetal (TDSM). Low-dissipation spin current is a building block of next-generation spintronics devices. While conduction electrons in metals and spin waves in ferromagnetic insulators (FMIs) are the major carriers of spin current, their propagation length is inevitably limited due to Joule heating or Gilbert damping. In order to suppress dissipation and realize long-range spin transport, we here make use of the spin-helical surface states of TDSMs, such as ${\mathrm{Cd}}_3{\mathrm{As}}_2$ and ${\mathrm{Na}}_3\mathrm{Bi}$, which are robust against disorder. Based on a junction of two FMIs connected by a TDSM, we demonstrate that the magnetization dynamics in one FMI induces a spin current on the TDSM surface flowing to the other FMI. By both the analytical transport theory on the surface and the numerical simulation of real-time evolution in the bulk, we find that the induced spin current takes a universal semiquantized value that is insensitive to the microscopic coupling structure between the FMI and the TDSM. We show that this surface spin current is robust against disorder over a long range, which indicates that the TDSM surface serves as a promising system for realizing spintronics devices.

Cross-frequency phase-amplitude coupling (PAC) describes the phenomenon where the power of a high-frequency oscillation evolves with the phase of a low-frequency one. It has been widely observed in the brain and linked to various brain functions. In this paper, we show that Stuart-Landau oscillators coupled in a nonlinear fashion can give rise to PAC in two commonly accepted architectures, namely, (1) a high-frequency neural oscillation driven by an external low-frequency input and (2) two interacting local oscillations with distinct, locally generated frequencies. We characterize the parameters that affect PAC behavior, thus providing insight on this phenomenon observed in neuronal networks. Inspired by some empirical studies, we further present an interconnection structure for brain regions wherein cross-region interactions are established only by low-frequency oscillations. We then demonstrate that low-frequency phase synchrony can integrate high-frequency activities regulated by local PAC and control the direction of information flow between distant regions.

A dense cloud of atoms with randomly changing positions exhibits coherent and incoherent scattering. We show that an atomic cloud of subwavelength dimensions can be modeled as a single scatterer where both coherent and incoherent components of the scattered photons can be fully explained based on effective multipole moments. This model allows us to arrive at a relation between the coherent and incoherent components of scattering based on the conservation of energy. Furthermore, using superposition of four plane waves, we show that one can selectively excite different multipole moments and thus tailor the scattering of the atomic cloud to control the cooperative shift, resonance linewidth, and the radiation pattern. Our approach provides a new insight into the scattering phenomena in atomic ensembles and opens a pathway toward controlling scattering for applications such as generation and manipulation of single-photon states.

How topological defects, unavoidable at symmetry-breaking phase transitions in a wide range of systems, evolve through consecutive phase transitions with different broken symmetries remains unexplored. ${\mathrm{Nd}}_2\mathrm{Sr}{\mathrm{Fe}}_2{\mathrm{O}}_7$, a bilayer ferrite, exhibits two intriguing structural phase transitions and dense networks of the so-called type II ${\mathrm{Z}}_8$ structural vortices at room temperature, so it is an ideal system to explore the topological defect evolution. From our extensive experimental investigation, we demonstrate that the cooling rate at the second-order transition (1290°C) plays a decisive role in determining the vortex density at room temperature, following the universal Kibble-Zurek mechanism. In addition, we discovered a transformation between topologically distinct vortices (${\mathrm{Z}}_8$ to ${\mathrm{Z}}_4$ vortices) at the first-order transition (550°C), which conserves the number of vortex cores. Remarkably, the ${\mathrm{Z}}_4$ vortices consist of two phases with an identical symmetry but two distinct magnitudes of an order parameter. Furthermore, when lattice distortion is enhanced by chemical doping, an alternative type of topological defects emerges: loop domain walls with orthorhombic distortions in the tetragonal background, resulting in unique pseudo-orthorhombic twins. Our findings open an avenue to explore the evolution of topological defects through multiple phase transitions.

We generalize the concept of local states (LS) for the prediction of high-dimensional, potentially mixed chaotic systems. The construction of generalized local states (GLS) relies on defining distances between time series on the basis of their (non-)linear correlations. We demonstrate the prediction capabilities of our approach based on the reservoir computing (RC) paradigm using the Kuramoto-Sivashinsky (KS), the Lorenz-96 (L96), and a combination of both systems. In the mixed system a separation of the time series belonging to the two different systems is made possible with GLS. More importantly, prediction remains possible with GLS, where the LS approach must naturally fail. Applications for the prediction of very heterogeneous time series with GLSs are briefly outlined.

We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two different levels: quantum states and quantum channels. At the level of states, we show how several well-studied quantifiers of chaos are, in fact, quantum coherence measures in disguise (or closely related to them). We further this connection for all quantum coherence measures by using tools from majorization theory. Then we numerically study the coherence of chaotic-versus-integrable eigenstates and find excellent agreement with random matrix theory in the bulk of the spectrum. At the level of channels, we show that the coherence-generating power (CGP)—a measure of how much coherence a dynamical process generates on average—emerges as a subpart of the out-of-time-ordered correlator (OTOC), a measure of information scrambling in many-body systems. Via numerical simulations of the (nonintegrable) transverse-field Ising model, we show that the OTOC and CGP capture quantum recurrences in quantitatively the same way. Moreover, using random matrix theory, we analytically characterize the OTOC-CGP connection for the Haar and Gaussian ensembles. In closing, we remark on how our coherence-based signatures of chaos relate to other diagnostics, namely, the Loschmidt echo, OTOC, and the Spectral Form Factor.

We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both bosonic and fermionic Gaussian states in terms of so-called linear complex structures $J$. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our findings in one- and two-dimensional systems, including the paradigmatic Kitaev honeycomb model. While typically supersymmetry preserves features like area law scaling of the entanglement entropies on either side, we find a peculiar phenomenon, namely, an amplified scaling of the entanglement entropy (“super area law”) in bosonic subsystems when the dual fermionic subsystems develop almost maximally entangled modes.

Despite their fundamental importance in dictating the quantum-mechanical properties of a system, ground states of many-body local quantum Hamiltonians form a set of measure zero in the many-body Hilbert space. Hence determining whether a given many-body quantum state is ground-stateable is a challenging task. Here we propose an unsupervised machine learning approach, dubbed Entanglement Clustering (“EntanCl”), to separate out ground-stateable wave functions from those that must be excited-state wave functions using entanglement structure information. EntanCl uses snapshots of an ensemble of swap operators as input and projects these high-dimensional data to two dimensions, preserving important topological features of the data associated with distinct entanglement structure using the uniform manifold approximation and projection. The projected data are then clustered using K-means clustering with $k=2$. By applying EntanCl to two examples, a one-dimensional free fermion model and the two-dimensional toric code, we demonstrate that EntanCl can successfully separate ground states from excited states with high computational efficiency. Being independent of a Hamiltonian and associated energy estimates, EntanCl offers a new paradigm for addressing quantum many-body wave functions in a computationally efficient manner.

Floquet topological systems exhibit rich physics associated with quasienergy band structures and new topological states; nevertheless, they are usually explored in Hermitian systems. Recent studies have shown the capability of non-Hermiticity in engineering topological states, while the interplay of Floquet topological phases and non-Hermiticity remains unclear. Here, we reveal that the non-Hermitian modulation can induce the phase transitions between trivial and nontrivial topological Floquet states. Our study theoretically predicts that the non-Hermitian modulation can create a Floquet $\pi$ mode in an originally topological trivial system according to the reopening of quasienergy band gap (i.e., the $\pi$ gap), which is well confirmed experimentally in the silicon waveguide platform. Our approach shows the powerful capability of non-Hermitian modulation in engineering topological modes in Floquet photonics systems and would inspire different possibilities in optical field manipulation in open systems.

We theoretically demonstrate that interacting symmetry-protected topological (SPT) phases can be realized with ultracold spinful bosonic atoms loaded on the lattices which have a flat band at the bottom of the band structure. Ground states of such systems are not conventional Mott insulators in the sense that the ground states possess not only spin fluctuations but also non-negligible charge fluctuations. The SPT phases in such systems are determined by both spin and charge fluctuations at zero temperature. We find that the many-body ground states of such systems can be exactly obtained in some special cases, and these exact ground states turn out to serve as representative states of the SPT phases. As a concrete example, we demonstrate that spin-1 bosons on a sawtooth chain can be in an SPT phase protected by ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ spin rotation symmetry or time-reversal symmetry, and this SPT phase is a result of spin fluctuations. We also show that spin-3 bosons on a kagome lattice can be in an SPT phase protected by $D_2$ point group symmetry, but this SPT phase is, however, a result of charge fluctuations.

We present a probabilistic generative model and efficient algorithm to model reciprocity in directed networks. Unlike other methods that address this problem such as exponential random graphs, it assigns latent variables as community memberships to nodes and a reciprocity parameter to the whole network rather than fitting order statistics. It formalizes the assumption that a directed interaction is more likely to occur if an individual has already observed an interaction towards her. It provides a natural framework for relaxing the common assumption in network generative models of conditional independence between edges, and it can be used to perform inference tasks such as predicting the existence of an edge given the observation of an edge in the reverse direction. Inference is performed using an efficient expectation-maximization algorithm that exploits the sparsity of the network, leading to an efficient and scalable implementation. We illustrate these findings by analyzing synthetic and real data, including social networks, academic citations, and the Erasmus student exchange program. Our method outperforms others in both predicting edges and generating networks that reflect the reciprocity values observed in real data, while at the same time inferring an underlying community structure. We provide an open-source implementation of the code online.

In this work we present results to the problem of the Hegselmann-Krause dynamics in networks obtained by an extensive study of the behavior of the standard order parameter sensitive to the onset of consensus: the normalized size of the giant cluster. This order parameter reveals the nontrivial effect of the network topology on the steady states of the dynamics, overlooked by previous works, which concentrated on the onset of unanimity, and allows to detect regions of polarization between the fragmented and the consensus phases. While the previous results on unanimity are confirmed, the consensus threshold shifts in the opposite direction compared to the threshold for unanimity. A detailed finite-size scaling analysis shows that, in general, consensus is easier to obtain in networks than in mixed populations. At a difference with previous studies, we show that the network topology is relevant beyond the finiteness of the average degree with increasing system size. In particular, in pure random networks (either uniform random graphs or scale-free networks), the consensus threshold seems to vanish in the thermodynamic limit. A detailed analysis of the time evolution of the dynamics reveals the role of bridges in the network, which allow for the interaction between agents belonging to clusters of very different opinions, after several repeated interaction steps. These bridges are at the origin of the shift of the confidence threshold to lower values in networks as compared to lattices or the mixed population.

Evidence suggests that the transport rate of a passive particle at long time scales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different temperatures, we probe these effects in dilute solutions and derive long-time friction and self-diffusion coefficients as functions of volume fractions, sizes, and temperatures of particles in $d=2$ and 3 dimensions. Thus, we model excluded-volume interactions for nonequilibrium systems but also extend the scope to short-range soft potentials and compare our results to Brownian-dynamics simulations. Remarkably, we show that both viscosity and energy flux display a nonlinear dependence on size. The simplicity of our formalism allows to discover various interesting scenarios that can be relevant for biological systems and active colloids.

Quantum multifractality is a fundamental property of systems such as noninteracting disordered systems at an Anderson transition and many-body systems in Hilbert space. Here we discuss the origin of the presence or absence of a fundamental symmetry related to this property. The anomalous multifractal dimension ${\mathrm{\Delta }}_q$ is used to characterize the structure of quantum states in such systems. Although the multifractal symmetry relation ${\mathrm{\Delta }}_q={\mathrm{\Delta }}_{1-q}$ is universally fulfilled in many known systems, recently some important examples have emerged where it does not hold. We show that this is the result of two different mechanisms. The first one was already known and is related to Gaussian fluctuations well described by random matrix theory. The second one, not previously explored, is related to the presence of an algebraically localized envelope. While the effect of Gaussian fluctuations can be removed by coarse graining, the second mechanism is robust to such a procedure. We illustrate the violation of the symmetry due to algebraic localization on two systems of very different nature, a 1D Floquet critical system and a model corresponding to Anderson localization on random graphs.

Synchrony is inevitable in many oscillating systems—from the canonical alignment of two ticking grandfather clocks, to the mutual entrainment of beating flagella or spiking neurons. Yet both biological and man-made systems provide striking examples of spontaneous desynchronization, such as failure cascades in alternating current power grids or neuronal avalanches in the mammalian brain. Here, we generalize classical models of synchronization among heterogenous oscillators to include short-range phase repulsion among individuals, a property that allows the emergence of a stable desynchronized state. Surprisingly, we find that our model exhibits self-organized avalanches at intermediate values of the repulsion strength, and that these avalanches have similar statistical properties to cascades seen in real-world systems such as neuronal avalanches. We find that these avalanches arise due to a critical mechanism based on competition between mean-field recruitment and local displacement, a property that we replicate in a classical cellular automaton model of traffic jams. We exactly solve our system in the many-oscillator limit, and we obtain analytical results relating the onset of avalanches or partial synchrony to the relative heterogeneity of the oscillators and their degree of mutual repulsion. Our results provide a minimal analytically tractable example of complex dynamics in a driven critical system.

We study experimentally and theoretically the response of a two-component Fermi condensate in the strongly interacting regime to a quench of the interaction strength. The quench is realized using a radiofrequency $\pi$-pulse to a third internal level with a different interaction strength. We find that the quench excites the monopole mode of the trap in the hydrodynamic regime, and that an initial change of the condensate properties takes place on a timescale comparable or even larger than the quasiparticle relaxation time.