Spin-orbit entangled pseudospins hold promise for a wide array of exotic magnetism ranging from a Heisenberg antiferromagnet to a Kitaev spin liquid depending on the lattice and bonding geometry, but many of the host materials suffer from lattice distortions and deviate from idealized models in part due to inherent strong pseudospin-lattice coupling. Here, we report on the synthesis of a magnetic superlattice comprising the single $(n=1)$ and the double $(n=2)$ layer members of the Ruddlesden-Popper series iridates ${\mathrm{Sr}}_{n+1}{\mathrm{Ir}}_n{\mathrm{O}}_{3n+1}$ alternating along the $c$ axis, and provide a comprehensive study of its lattice and magnetic structures using scanning transmission electron microscopy, resonant elastic and inelastic x-ray scattering, third harmonic generation measurements, and Raman spectroscopy. The superlattice is free of the structural distortions reported for the parent phases and has a higher point group symmetry, while preserving the magnetic orders and pseudospin dynamics inherited from the parent phases, featuring two magnetic transitions with two symmetry-distinct orders. We infer weaker pseudospin-lattice coupling from the analysis of Raman spectra and attribute it to frustrated magnetic-elastic couplings. Thus, the superlattice expresses a near ideal network of effective spin-one-half moments on a square lattice.

We study out-of-time-ordered correlation (OTOC) functions in various random quantum circuits and show that the average dynamics is governed by a Markovian propagator. This is then used to study relaxation of OTOC to its long-time average value in circuits with random single-qubit unitaries, finding that relaxation in general proceeds in two steps: In the first phase that lasts upto an extensively long time the relaxation rate is given by a phantom eigenvalue of a nonsymmetric propagator, whereas in the second phase the rate is determined by the true 2nd largest propagator eigenvalue. We also obtain exact OTOC dynamics on the lightcone and an expression for the average OTOC in finite random circuits with random two-qubit gates.

Machine learning techniques have recently gained prominence in physics, yielding a host of new results and insights. One key concept is that of backpropagation, which computes the exact gradient of any output of a program with respect to any input. This is achieved efficiently within the differentiable programming paradigm, which utilizes automatic differentiation (AD) of each step of a computer program and the chain rule. A classic application is in training neural networks. Here, we apply this methodology instead to the numerical renormalization group (NRG), a powerful technique in computational quantum many-body physics. We demonstrate how derivatives of NRG outputs with respect to Hamiltonian parameters can be accurately and efficiently obtained. Physical properties can be calculated using this differentiable NRG scheme—for example, thermodynamic observables from derivatives of the free energy. Susceptibilities can be computed by adding source terms to the Hamiltonian, but still evaluated with AD at precisely zero field. As an outlook, we briefly discuss the derivatives of dynamical quantities and a possible route to the vertex.

We study the emergence of quasiperiodic Bloch wave functions in quasicrystals, employing the one-dimensional Fibonacci model as a test case. We find that despite the fact that Bloch functions are not eigenfunctions themselves, superpositions of relatively small numbers of nearly degenerate eigenfunctions give rise to extended quasiperiodic Bloch functions. These functions possess the structure of earlier ancestors of the underlying Fibonacci potential, and it is often possible to obtain different ancestors as different superpositions around the same energy. There exists an effective crystal momentum that characterizes these ancestors, which is determined by the mean energy of the superimposed eigenfunctions, giving rise to an effective dispersion curve. We also find that quasiperiodic Bloch functions do emerge as eigenfunctions when weak disorder is introduced into the otherwise perfect quasiperiodic potential. These theoretical results may explain a number of experimental observations, and may have practical consequences on emerging theories of band topology and correlated electrons in quasicrystals.

We present a detailed investigation of the topological phases and Majorana fermion (MF) excitations that arise from the bulk interplay between (un)conventional one- and two-band spin-singlet superconductivity and a number of magnetic texture crystals. The latter define inhomogeneous magnetization profiles which consist of a periodically repeating primitive cell. Here we focus on magnetic texture crystals with a primitive cell of the helix, whirl, and skyrmion types, which feature distinct symmetry properties. We identify a multitude of accessible topological phases which harbor flat, unidirectional, bidirectional, (quasi)helical, or chiral MF edge modes. This rich variety originates from the interplay between topological phases with gapped and nodal bulk energy spectra. The types of the emerging topological superconducting phases and the features of the arising MFs are solely determined by the properties and compatibility of the so-called magnetic and pairing point and space groups. Our analysis is general and does not rely on specific parameters of the models employed here to exemplify the topological scenarios which become accessible. Therefore, our results can be extended to systems with multiple bands, are relevant for a wide range of layered materials and hybrid devices, and provide predictions for strong, weak, and crystalline topological phases.

Low-energy Hamiltonians with a linear crossing in their energy dispersion (dubbed Dirac Hamiltonians) have recently been the subject of intense investigations. The linear dispersion is often the result of an approximation in the energy dispersion at the band-touching point in which higher order terms are discarded. In this paper, we show that, in terms of nonadiabatic transitions, by passing through a touching point, certain types of quadratic terms could not be omitted, even in the arbitrary vicinity of it, i.e., quadratic terms could significantly affect the transition probability, hence the Hamiltonian is not reducible to a linear one. We further show that the presence of terms with exponents larger than two only affects the transition probability away from the touching point. In the end, we discuss conditions that may lead to the appearance of oscillations in the transition probability profile.

Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in understanding these processes. Classifying a system as chaotic entails estimating its largest Lyapunov exponent (LLE), which quantifies the average rate of convergence or divergence of initially close trajectories in state space. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in low-dimensional systems affected by a small amount of dynamical noise, which are used to model many real-world processes, and in particular biological systems. We describe a method for accurately estimating the largest Lyapunov exponent from noisy data, based on training deep learning models on synthetically generated trajectories. Once the deep learning models are trained, they can be used to detect the LLE from empirical data without any assumption on the underlying dynamics. Our method naturally extends to different input topologies, allowing us to analyze tree-shaped data, characteristic of inheritance dynamics, where near-identical replication offers a unique and hitherto unstudied avenue to detect chaos. We also characterize the input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.

Can the antiferromagnetic (AF) order be induced via the local moments' hybridization with the heavy electrons instead of conduction electrons? We address this intriguingly fundamental question via a prototypical model to describe the interplay between local moments and heavy electrons. We discover that the AF order can be mediated via the heavy electrons through the mechanism of the high-order Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Moreover, our analysis employing a slave-spin representation uncovers that the heavy electron band can enhance the RKKY interaction of local moments (despiteits high-order nature) via enlarging its effective mass. The potential relevance to the heavy fermion compound ${\mathrm{Ce}}_3(\mathrm{Pt}/\mathrm{Pd}){\mathrm{In}}_{11}$ is also discussed.

We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous-time nonlinear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs). To do so, we present a neural ODE control (NODEC) framework and find that it can learn feedback control signals that drive graph dynamical systems toward desired target states. While we use loss functions that do not constrain the control energy, our results show, in accordance with related work that NODEC produces low energy control signals. Finally, we evaluate the performance and versatility of NODEC against well-known feedback controllers and deep reinforcement learning. We use NODEC to generate feedback controls for more than one thousand coupled, nonlinear ODEs that represent epidemic processes and coupled oscillators.

In recent years, high-precision x-ray polarimeters have become a key method for the investigation of fundamental physical questions from solid-state physics to quantum optics. Here, we report on the verification of a polarization purity of better than $8\times {10}^{-11}$ at an x-ray free-electron laser, which implies a suppression of the incoming photons to the noise level in the crossed polarizer setting. This purity provides exceptional sensitivity to tiny polarization changes and offers intriguing perspectives for fundamental tests of quantum electrodynamics.

${\mathrm{NbSe}}_2$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered ${\mathrm{NbSe}}_2$, but absent for even-number-layered ${\mathrm{NbSe}}_2$ with the inversion symmetry. In this paper we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered ${\mathrm{NbSe}}_2$ based on an effective tight-binding model which includes $d_{z^2}$, $d_{x^2-y^2}$, and $d_{xy}$ orbitals of Nb atoms. We show that the nonlinear optical Hall conductivity for the second harmonic generation (SHG) process has a nonvanishing value in odd-number-layered ${\mathrm{NbSe}}_2$. Also, we provide a nonlinear optical selection rule in few-layered ${\mathrm{NbSe}}_2$ and their polarization dependencies. Furthermore, for the even-number-layered case, the nonlinear optical Hall currents can be generated by applying electric fields which break inversion symmetry. We also discuss that the nonlinear optical Hall effect is expected to occur in TMDC materials in general. Thus, our results will serve to design potential opt-spintronics devices based on 2D materials to generate the spin Hall current by SHG.

In the field of light-matter interactions, it is often assumed that a classical light field that interacts with a quantum particle remains almost unchanged and thus contains nearly no information about the manipulated particles. To investigate the validity of this assumption, we develop and theoretically analyze a simple Gedanken experiment, which involves the interaction of a coherent state with a quantum particle in an optical cavity. We quantify the resulting alteration of the light field by calculating the fidelity of its initial and equilibrium states. Using Bayesian inference, we demonstrate the information transfer through photon statistics. In addition, we employ the concepts of quantum entropy and mutual information to quantify the entropy transfer from the particle to the light field. In the weak coupling limit, we validate the usually assumed negligible alteration of the light field and entropy transfer. In the strong coupling limit, however, we observe that the information of the initial particle state can be fully encoded in the light field, even for large photon numbers. Nevertheless, we show that spontaneous emission is a sufficient mechanism for removing the entropy initially stored in the particle. Our analysis provides a deeper understanding of the entropy exchange between quantum matter and classical light.

Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the Berry curvature, an intuitive understanding of the quantum metric is lacking. Here, we show that the quantum metric of Bloch electrons leads to a momentum-space gravity. In particular, by extending the semiclassical formulation of electron dynamics to second order, we find that the resulting velocity is modified by a geodesic term and becomes the momentum-space dual of the Lorentz force in curved space. We calculate this geodesic response for magic-angle twisted bilayer graphene and show that moiré systems with flat bands are ideal candidates to observe this effect. Extending this analogy with gravity further, we find that the momentum-space dual of the Einstein field equations remains sourceless for pure states, while for mixed states it acquires a source term that depends on the von Neumann entropy for small entropies. We compare this stress-energy equation with the weak-field limit of general relativity, and we conclude that the von Neumann entropy is the momentum-space dual of the gravitational potential. Consequently, the momentum-space geodesic equation for mixed states is modified by a term resembling an entropic force. Our results highlight connections between quantum geometry, momentum-space gravity, and quantum information, prompting further exploration of this dual gravity in quantum materials.

We study the DC current generation in a periodically driven Bloch system connected to a heat bath. Under a relaxation time approximation, the density matrix for such a system is obtained, which is related to two equilibria: a Floquet quasiequilibrium where the density matrix is diagonal under the Floquet-Bloch eigenbasis and an instantaneous Bloch thermal equilibrium. Then, the current responses and their power features, i.e., the power input behavior, are discussed in a unified manner, which reveals that there exist an intrinsic current and an extrinsic correction. Remarkably, the intrinsic part consumes no energy and corresponds to the Floquet quasiequilibrium, while the extrinsic part needs a sustained energy input and originates from a shift between two equilibrium ensembles. We further investigate the role of the external driving field strength finding that large DC currents can be generated under a relatively strong but not too strong driving field.

It has long been believed that the anomalous Hall effect (AHE) can only be observed in ferromagnets. However, any magnetic material can exhibit AHE due to the broken time-reversal symmetry. In this work, we present a nontrivial AHE on the compensated ferrimagnet ${\mathrm{Mn}}_3\mathrm{Al}$ using symmetry arguments and first-principles calculations. Nonzero components of anomalous Hall conductivity ${\sigma }_{\alpha \beta }$ are determined based on the magnetic space group of ${\mathrm{Mn}}_3\mathrm{Al}$. The explicit first-principles calculation confirms ${\sigma }_{xy}=-320{\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$. The nature of Berry curvature responsible for the intrinsic origin of AHE is further identified using group theory: lifted degeneracies at $\frac{1}{2}K\mathrm{\Gamma }$, $L$, and $\frac{1}{2}{K}^{\prime }\mathrm{\Gamma }$ induced by spin-orbit interactions. Moreover, the global behaviors of Berry curvatures are shown over the whole Brillouin zone which reveal the overlooked contributions around $X^{\prime }$.

The use of the nuclear spins surrounding electron spin qubits as quantum registers and long-lived memories opens the way to new applications in quantum information and biological sensing. Hence, there is a need for generic and robust forms of control of the nuclear registers. Although adiabatic gates are widely used in quantum information, they can become too slow to outpace decoherence. Here, we introduce a technique whereby adiabatic gates arise from the dynamical decoupling protocols that simultaneously extend coherence. We illustrate this pulse-based adiabatic control for nuclear spins around NV centers in diamond. We obtain a closed-form expression from Landau-Zener theory and show that it reliably describes the dynamics. By identifying robust Floquet states, we show that the technique enables polarization, one-shot flips, and state storage for nuclear spins. These results introduce a control paradigm that combines dynamical decoupling with adiabatic evolution.

Optimal design for model training is a critical topic in machine learning. Active learning aims at obtaining improved models by querying samples with maximum uncertainty according to the estimation model for artificially labeling; this has the additional advantage of achieving successful performances with a reduced number of labeled samples. We analyze its capability as an assistant for the design of experiments, extracting maximum information for learning with the minimal cost in fidelity loss, or reducing total operation costs of labeling in the laboratory. We present two typical applications as quantum information retrieval in qutrits and phase boundary prediction in many-body physics. For an equivalent multinomial classification problem, we achieve the correct rate of 99% with less than 2% of samples labeled. We reckon that active-learning-inspired physics experiments will remarkably save budget without loss of accuracy.