$2H\text{−}{\mathrm{NbS}}_2$ is a classic example of an anisotropic multiband superconductor, with significant recent work focusing on the interesting responses seen when high magnetic fields are applied precisely parallel to the hexagonal niobium planes. It is often contrasted with its sister compound $2H\text{−}{\mathrm{NbSe}}_2$ because they have similar onset temperatures for superconductivity, but $2H\text{−}{\mathrm{NbS}}_2$ has no charge density wave whereas in $2H\text{−}{\mathrm{NbSe}}_2$ the charge density wave order couples strongly to the superconductivity. Using small-angle neutron scattering, a bulk-sensitive probe, we have studied the vortex lattice and how it responds to the underlying superconducting anisotropy. This is done by controlling the orientation of the field with respect to the Nb planes. The superconducting anisotropy, ${\mathrm{\Gamma }}_{ac}=7.07\pm 0.2$, is found to be field independent over the range measured (0.15 to 1.25 T), and the magnetic field distribution as a function of the applied magnetic field is found to be in excellent quantitative agreement with anisotropic London theory modified with a core-size cutoff correction, providing the first complete validation of this model. We find values of ${\lambda }_{ab}=141.9\pm 1.5$ nm for the in-plane London penetration depth, and ${\lambda }_c\sim 1\mu \mathrm{m}$ for the out-of-plane response. The field-independence indicates that we are primarily sampling the larger of the two gaps generating the superconductivity in this material.

Probabilistic context-free grammars (PCFGs), which are commonly used to generate trees randomly, have been well analyzed theoretically, leading to applications in various domains. Despite their utility, the distributions that the grammar can express are limited to those in which the distribution of a subtree depends only on its root and not on its context. This limitation presents a challenge for modeling various real-world phenomena, such as natural languages. To overcome this limitation, a probabilistic context-sensitive grammar (PCSG) is introduced, where the distribution of a subtree depends on its context. Numerical analysis of a PCSG reveals that the distribution of a symbol does not constitute a qualitative difference from that in the context-free case, but mutual information does. Furthermore, a novel metric introduced to directly quantify the breaking of this limitation detects a distinct difference between PCFGs and PCSGs. This metric, applicable to an arbitrary distribution of a tree, allows for further investigation and characterization of various tree structures that PCFGs cannot express.

The energy landscape of sodium chloride-nitrogen mixtures has been comprehensively explored to examine the ability of the formation of unknown compounds under pressures of up to 100 GPa, using swarm-intelligence structure prediction methodology and first-principles calculations. We identified a thermodynamically stable ${\mathrm{NaN}}_5{\mathrm{ClN}}_5$ compound containing two cyclo-${\mathrm{N}}_5$ species under pressures exceeding 53 GPa, representing milder conditions in comparison to those requisite for pure solid nitrogen. In ${\mathrm{NaN}}_5{\mathrm{ClN}}_5$, the high electron affinity of the cyclo-${\mathrm{N}}_5$ motif allows it to oxidize the chlorine atoms, resulting in the formation of two cyclo-${\mathrm{N}}_5$ anions. Additionally, the weak covalent interactions between Cl and nearby N atoms plays a key role in stabilization of structure. It has been demonstrated that simple ${\mathrm{NaN}}_5$ salt was a suitable precursor for the synthesis of ${\mathrm{NaN}}_5{\mathrm{ClN}}_5$ at high pressure. Ab initio molecular dynamics simulations demonstrated the recoverability of ${\mathrm{NaN}}_5{\mathrm{ClN}}_5$ as a metastable phase at ambient pressure-temperature conditions. Additionally, ${\mathrm{NaN}}_5{\mathrm{ClN}}_5$ exhibits a higher energy density of 3.86 kJ/g and a lower mass density of 1.67 g/${\mathrm{cm}}^3$ in comparison to metal pentazolate salts, highlighting its potential as a high energy-density material.

There has been a growing interest in non-Hermitian physics. One of its main goals is to engineer dissipation and to explore ensuing functionality. In magnonics, the effect of dissipation due to local damping on magnon transport has been explored. However, the effects of nonlocal damping on the magnonic analog of the Josephson effect remain missing, despite that nonlocal damping is inevitable and has been playing a central role in magnonics. Here, we uncover theoretically that a surprisingly rich dynamics can emerge in magnetic junctions due to intrinsic nonlocal damping, using analytical and numerical methods. In particular, under microwave pumping, we show that coherent spin precession in the right and left insulating ferromagnet (FM) of the junction becomes synchronized by nonlocal damping and thereby a magnonic analog of the $\phi$ Josephson junction emerges, where $\phi$ stands here for the relative precession phase of right and left FM in the stationary limit. Remarkably, $\phi$ decreases monotonically from $\pi$ to $\pi /2$ as the magnon-magnon interaction, arising from spin anisotropies, increases. Moreover, we also find a magnonic diode effect giving rise to rectification of magnon currents. Our predictions are readily testable with current device and measurement technologies at room temperatures.

The Kitaev interaction, found in candidate materials such as $\alpha \text{−}{\mathrm{RuCl}}_3$, occurs through the metal ($M$)-ligand ($X$)-metal ($M$) paths of the edge-sharing octahedra because the large spin-orbit coupling (SOC) on the metal atoms activates directional spin interactions. Here, we show that even in $3d$ transition-metal compounds, where the SOC of the metal atom is negligible, heavy ligands can induce bond-dependent Kitaev interactions. In this work, we take as an example the $3d$ transition-metal chalcogenophosphate ${\mathrm{NiPSe}}_3$ and show that the key is found in the presence of a sizable SOC on the Se $p$ orbital, one which mediates the super-exchange between the nearest-neighbor Ni sites. Our study provides a pathway for engineering enhanced Kitaev interactions through the interplay of SOC strength, lattice distortions, and chemical substitutions.

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground state only contains short-range entanglement and does not break symmetries spontaneously, they generically realize crystalline fermionic symmetry-protected topological phases (cFSPTs), supporting gapless modes at the boundaries or at the lattice defects. Here, we provide an exhaustive classification of cFSPTs in two dimensions with $\mathrm{U}\left(1\right)$ charge-conservation and spinful time-reversal symmetries, namely, those generically present in spin-orbit coupled insulators, for any of the 17 wallpaper groups. It has been shown that the classification of cFSPTs can be understood from appropriate real-space decorations of lower-dimensional subspaces, and we expose how these relate to the Wyckoff positions of the lattice. We find that all nontrivial one-dimensional decorations require electronic interactions. Furthermore, we provide model Hamiltonians for various decorations, and discuss the signatures of cFSPTs. This classification paves the way to further explore topological interacting insulators, providing the backbone information in generic model systems and ultimately in experiments.

We study the problem of two harmonically trapped atoms in the presence of spin-orbital-angular-momentum (SOAM) coupling. The two-body energy spectrum is numerically calculated by utilizing the exact diagonalization method. We analyze how the degeneracy of energy levels is lifted under the interplay between the interatomic interaction and SOAM coupling. The exact numerical results show excellent agreement with that of perturbation theory in the weak-interaction limit as well as that in the absence of SOAM coupling. The properties of correlations between the two atoms are also discussed with respect to the interaction strength. The findings in this paper may provide valuable insights into few-body physics subjected to SOAM coupling and the possible experimental detection of spectrum functions in many-body systems, such as radiofrequency spectroscopy.

The realization of excitonic insulators in transition metal dichalcogenide systems has opened the door to explorations of the exotic properties that such a state exhibits. We study theoretically the potential for excitonic insulators to show an anomalous form of quantum oscillations: the de Haas–van Alphen effect in an insulating system. We focus on the role of the interactions that generate the energy gap and show that it is crucial to consider quantum fluctuations that go beyond the mean-field treatment. Remarkably, quantum fluctuations can be dominant and lead to quantum oscillations that are significantly larger than those predicted using mean-field theory. Indeed, in experimentally accessible parameter regimes these fluctuation-generated quantum oscillations can even be larger than what would be found for the corresponding gapless system.

We report on a photonic simulator of the critical state forming at the quantum phase transition between topologically distinct Anderson insulator phases. We observe a time-staggered profile in the circular photon polarization, which originates from the interplay of a chiral and sublattice symmetry, and has recently been suggested as a signature for topological Anderson criticality within the setup. We discuss the role of statistical detuning from criticality and show that the controlled breaking of phase coherence removes the signal, revealing its origin in quantum coherence.

In this study, we discuss a type of bulk-boundary correspondence, which holds for topological insulators and superconductors when the parity-time ($PT$) and/or parity-particle-hole ($PC$) symmetry are present. In these systems, even when the bulk topology is nontrivial, the edge spectrum is generally gapped, and thus the conventional bulk-boundary correspondence does not hold. We find that, instead of the edge spectrum, the single-particle entanglement spectrum becomes gapless when the bulk topology is nontrivial: i.e., the bulk-entanglement spectrum correspondence holds in $PT$- and/or $PC$-symmetric topological insulators and superconductors. After showing the correspondence using $K$-theoretic approach, we provide concrete models for each symmetry class up to three dimensions where nontrivial topology because of $PT$ and/or $PC$ is expected. An implication of our results is that, when the bulk topology under $PT$ and/or $PC$ symmetry is nontrivial, the noninteracting many-body entanglement spectrum is multiply degenerate in one dimension and is gapless in two or higher dimensions.

The mixed-valence compound ${\mathrm{SmB}}_6$ with partially filled samarium $4f$ flat bands hybridizing with $5d$ conduction bands is a paramount example of a correlated topological heavy-fermion system. In this study, we revisit the topology of ${\mathrm{SmB}}_6$ within the formalism of topological quantum chemistry and symmetry-based indicators. Based on this approach, we reach a detailed classification of the material's topology, and we reformulate the origin of topology in terms of band representations. We corroborate these aspects by constructing a minimal TB model that is consistent with all the symmetries of the system and is able to reproduce the topology of the material. We finally unveil the previously overlooked formation of multiple topological gaps, and we discuss its implications for experiments.

Exploring operational regimes of many-body cavity QED with multilevel atoms remains an exciting research frontier for their enhanced storage capabilities of intralevel quantum correlations. In this work, we consider an experimentally feasible many-body cavity QED model describing a four-level system, where each of those levels is formed from a combination of different spin and momentum states of ultracold atoms in a cavity. The resulting model comprises a pair of Dicke Hamiltonians constructed from pseudospin operators, effectively capturing two intertwined superradiant phase transitions. The phase diagram reveals regions featuring weak and strong entangled states of spin and momentum atomic degrees of freedom. These states exhibit different dynamical responses, ranging from slow to fast relaxation, with the added option of persistent entanglement temporal oscillations. We discuss the role of cavity losses in steering the system's dynamics into such entangled states and propose a readout scheme that leverages different light polarizations within the cavity. Our work paves the way to connect the rich variety of non-equilibrium phase transitions that occur in many-body cavity QED to the buildup of quantum correlations in systems with multilevel atom descriptions.

Quantum correlations are a fundamental property of quantum many-body states. Yet they remain experimentally elusive, hindering certification of genuine quantum behavior, especially in quantum materials. Here we show that the momentum-dependent dynamical susceptibility measured via inelastic neutron scattering enables the systematic reconstruction of a general family of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at an arbitrary mutual distance. Using neutron scattering data for the compound ${\mathrm{KCuF}}_3$—a system of weakly coupled $S=1/2$ Heisenberg chains—and numerically exact quantum Monte Carlo data, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed, they exhibit a different emergent length scale—the quantum coherence length—which is finite at any finite temperature (including when long-range magnetic order develops). Moreover, we show theoretically that coupled Heisenberg spin chains exhibit a form of quantum monogamy, with a trade-off between quantum correlations along and transverse to the spin chains. These results highlight real-space quantum correlators as an informative, model-independent means of probing the underlying quantum state of real quantum materials.

The Dicke model describes an ensemble of two-level atoms that are coupled to a confined light mode of an optical cavity. Above a critical coupling, the cavity becomes macroscopically occupied, and the system enters the superradiant phase. This phase transition can be observed by detecting the photons that are emitted from the cavity; however, it only becomes apparent in the limit of long observation times, while actual experiments are of a finite duration. To circumvent this problem, we here make use of recent advances in Lee-Yang theories of phase transitions to show that the superradiant phase transition can be inferred from the factorial cumulants of the photon emission statistics obtained during a finite measurement time. Specifically, from the factorial cumulants, we can determine the complex singularities of generating functions that describe the photon emission statistics, and by extrapolating their positions to the long-time limit one can detect the superradiant phase transition. We also show that the convergence points determine the tails of the large-deviation statistics of the photon current. Our paper demonstrates how phase transitions in the Dicke model and in other quantum many-body systems can be detected from measurements of a finite duration.

A limit cycle is a self-sustained, periodic, isolated motion appearing in autonomous differential equations. As the period of a limit cycle is a priori unknown, finding it as a stationary state of a rotating ansatz is challenging. Correspondingly, its study commonly relies on numerical methodologies (e.g., brute-force time evolution, and variational shooting methods) or circumstantial evidence such as instabilities of fixed points. Alas, such approaches are (i) unable to find all solutions, as they rely on specific initial conditions, and (ii) do not provide analytical intuition about the physical origin of the limit cycles. Here, we (I) develop a multifrequency rotating ansatz with which we (II) find all limit cycles as stationary-state solutions via a semianalytical homotopy continuation. We demonstrate our approach and its performance on the Van der Pol oscillator. Moving beyond this simple example, we show that our method captures all coexisting fixed-point attractors and limit cycles in a modified nonlinear Van der Pol oscillator. Our results facilitate the systematic mapping of out-of-equilibrium phase diagrams, with implications across multiple fields of the natural sciences.

We have investigated interlayer interactions in the bilayer ${\mathrm{PtTe}}_2$ system, which influence the electronic energy bands near the Fermi level. Our diffusion Monte Carlo (DMC) calculations for the high-symmetry bilayer stackings (AA, AB, AC) manifest distinct interlayer binding characteristics among the stacking modes by revealing significantly different interlayer separations depending on the stacking, which is critical to understanding the interlayer coupling of the twisted bilayers consisting of various local stacking arrangements. Furthermore, a comparison between the interlayer separations obtained from DMC and density functional theory (DFT) shows that meta-generalized gradient approximation (GGA)-based van der Waals–DFT results agree with DMC for different layer stackings, including twisted bilayers, but only the ground-state AA stacking matches well with GGA-based DFT predictions. This underscores the importance of accurate exchange-correlation potentials even for capturing the stacking-dependent interlayer binding properties. We further show that the variability in DFT-predicted interlayer separations is responsible for the large discrepancy of band structures in the $21.{79}^{\circ }$ twisted bilayer ${\mathrm{PtTe}}_2$, affecting its classification as metallic or insulating. These results demonstrate the importance of obtaining a correct description of stacking-dependent interlayer coupling in modeling delicate bilayer systems at finite twists.