For a model with many-to-one connectivity it is widely expected that mean-field theory captures the exact many-particle $N\to \infty$ limit, and that higher-order cumulant expansions of the Heisenberg equations converge to this same limit whilst providing improved approximations at finite $N$. Here we show that this is in fact not always the case. Instead, whether mean-field theory correctly describes the large-$N$ limit depends on how the model parameters scale with $N$, and the convergence of cumulant expansions may be nonuniform across even and odd orders. Further, even when a higher-order cumulant expansion does recover the correct limit, the error is not monotonic with $N$ and may exceed that of mean-field theory.

We address magnetic neutron scattering in the presence of local noncentrosymmetric asymmetries of the magnetization density. Such inversion-symmetry breaking, combined with the absence of time-reversal symmetry, can be described in terms of magnetoelectric multipoles which form the second term after the magnetic dipole in the multipole expansion of the magnetization density. We provide a pedagogical review of the theoretical formalism of magnetic neutron diffraction in terms of the multipole expansion of the scattering cross-section. In particular, we show how to compute the contribution of magnetoelectric multipoles to the scattering amplitude starting from ab initio calculations. We also provide general guidelines on how to experimentally detect long-range order of magnetoelectric multipoles using either unpolarized or polarized neutron scattering. We apply the formalism to CuO, and we discuss first-principles predictions and experimental spherical neutron polarimetry measurements that are consistent with the presence of magnetoelectric multipoles in CuO.

For decades transition-metal oxides have generated a huge interest due to the multitude of physical phenomena they exhibit. In this class of materials, the rare-earth nickelates, $R{\mathrm{NiO}}_3$, stand out for their rich phase diagram stemming from complex couplings between the lattice, electronic, and magnetic degrees of freedom. Here, we present a first-principles study of the low-temperature phase for two members of the $R{\mathrm{NiO}}_3$ series, with $R=$ Pr, Y. We employ density-functional theory with Hubbard corrections accounting not only for the onsite localizing interactions among the Ni-$3d$ electrons ($U$), but also the intersite hybridization effects between the transition metals and the ligands ($V$). All the $U$ and $V$ parameters are calculated from first principles using density-functional perturbation theory, resulting in a fully ab initio methodology. Our simulations show that the inclusion of the intersite interaction parameters $V$ is necessary to simultaneously capture the features well-established by experimental characterizations of the low-temperature state: insulating character, antiferromagnetism, and bond disproportionation. On the contrary, for some magnetic orderings the inclusion of onsite interaction parameters $U$ alone completely suppresses the breathing distortion occurring in the low-temperature phase and produces an erroneous electronic state with a vanishing band gap. In addition—only when both the $U$ and $V$ are considered—we predict a polar phase with a magnetization-dependent electric polarization, supporting recent experimental observations that suggest a possible occurrence of type-II multiferroicity for these materials.

Phantom relaxation is relaxation with a rate that is not given by a finite spectral gap. Studying the average purity dynamics in a staircase random Haar circuit and the spectral decomposition of a nonsymmetric matrix describing the underlying Markovian evolution, we explain how that can arise out of an ordinary-looking spectrum. Crucial are alternating expansion coefficients that diverge in the thermodynamic limit due to the non-Hermitian skin effect in the matrix describing the average purity dynamics under an overall unitary evolution. The mysterious phantom relaxation emerges out of localized generalized eigenvectors describing the Jordan normal form kernel, and, independently, also out of interesting trigonometric sums due to localized true eigenvectors. All this shows that when dealing with non-Hermitian matrices it can happen that the spectrum is not the relevant object; rather, it is the pseudospectrum or, equivalently, a delicate cancellation enabled by localized eigenvectors.

Unextendible product bases (UPBs) play a key role in the study of quantum entanglement and nonlocality. Here we provide an equivalent characterization of UPBs in graph-theoretic terms. Different from previous graph-theoretic investigations of UPBs, which focused mostly on the orthogonality relations between different product states, our characterization includes a graph-theoretic reformulation of the unextendibility condition. Building on this characterization, we develop a constructive method for building UPBs in low dimensions and shed light on the open question of whether there exist genuinely unextendible product bases (GUPBs), that is, multipartite product bases that are unextendible with respect to every possible bipartition. We derive a lower bound on the size of any candidate GUPB, significantly improving over the state of the art. Moreover, we show that every minimal GUPB saturating our bound must be associated to regular graphs and discuss a possible path towards the construction of a minimal GUPB in a tripartite system of minimal local dimension. Finally, we apply our characterization to the problem of distinguishing UPB states under local operations and classical communication, deriving a necessary condition for reliable discrimination in the asymptotic limit.

The observation of magnetic ordering in atomically thin ${\mathrm{CrI}}_3$ and ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ monolayers has aroused intense interest in condensed-matter physics and material science. Studies of van de Waals two-dimensional (2D) magnetic materials are of both fundamental importance and application interest. In particular, exciton-enhanced magneto-optical properties revealed in ${\mathrm{CrI}}_3$ and ${\mathrm{CrBr}}_3$ monolayers have expanded the understanding of exciton physics in 2D materials. Unlike ${\mathrm{CrI}}_3$ and ${\mathrm{CrBr}}_3$, with out-of-plane magnetization, CrSBr has an in-plane magnetic moment, therefore providing a good opportunity to study the magnetic linear dichroism and high-order magneto-optical effects. Here, based on the many-body perturbation method within density-functional theory, we have studied quasiparticle electronic structure, exciton, and optical properties in CrSBr monolayer. A strongly bounded exciton has been identified with the first bright exciton located at 1.35 eV, in good agreement with an experiment of photoluminescence [Wilson et al., Nat. Mater. 20, 1657 (2021)]. Strong contrast in the optical absorption is found between the electric fields lying along the in-plane two orthogonal directions. In accordance with a typical and realistic experimental setup, we show that the rotation angle of linear polarized light, either reflected or transmitted, could be comparable with those revealed in black phosphorene. Such large linear dichroism arises mainly from the anisotropic in-plane crystal structure. The magnetic contribution from the off-diagonal component of dielectric function to the linear dichroism in CrSBr is negligible. Our findings not only have revealed the excitonic effect on the optical and magneto-optical properties in 2D ferromagnet CrSBr, but also have shown its potential applications in 2D optics and optoelectronics.

Robust and tunable topological Josephson junctions (TJJs) are highly desirable platforms for investigating the anomalous Josephson effect and topological quantum computation applications. Experimental demonstrations have been done in hybrid superconducting-two dimensional topological insulator (2DTI) platforms, sensitive to magnetic disorder and interactions with phonons and other electrons. In this work, we propose a robust and electrostatically tunable TJJ by combining the physics of the integer quantum Hall (IQH) regime and of superconductors. We provide analytical insights about the corresponding Andreev bound state spectrum, the Josephson current and the anomalous current. We demonstrate the existence of protected zero-energy crossings, that can be controlled through electrostatic external gates. This electrostatic tunability has a direct advantage to compensate for non-ideal interfaces and undesirable reflections that may occur in any realistic samples. TJJs in the IQH regime could be realized in graphene and other 2D materials. They are of particular relevance towards scalable and robust Andreev-qubit platforms, and also for efficient phase batteries.

We propose a variational quantum eigensolver (VQE) for the simulation of strongly correlated quantum matter based on a multiscale entanglement renormalization ansatz (MERA) and gradient-based optimization. This MERA quantum eigensolver can have substantially lower computation costs than corresponding classical algorithms. Due to its narrow causal cone, the algorithm can be implemented on noisy intermediate-scale quantum (NISQ) devices and still describe large systems. It is particularly attractive for ion-trap devices with ion-shuttling capabilities. The number of required qubits is system-size independent and increases only to a logarithmic scaling when using quantum amplitude estimation to speed up gradient evaluations. Translation invariance can be used to make computation costs square-logarithmic in the system size and describe the thermodynamic limit. We demonstrate the approach numerically for a MERA with Trotterized disentanglers and isometries. With a few Trotter steps, one recovers the accuracy of the full MERA.

It is a general notion that disorder, introduced by either chemical substitution or intercalation as well as by electron irradiation, is detrimental to the realization of long-range charge density wave (CDW) order. We study the disorder-induced suppression of in-plane CDW orders in two-dimensional Pd-intercalated ${\mathrm{ErTe}}_3$ compositions by exploring the real part of the optical conductivity with light polarized along the in-plane $a$ and $c$ axes. Our findings reveal an anisotropic charge dynamics with respect to both incommensurate unidirectional CDW phases of ${\mathrm{ErTe}}_3$, occurring within the $ac$ plane. The anisotropic optical response gets substantially washed out with Pd intercalation, hand in hand with the suppression of both CDW orders. The spectral weight analysis, though, advances the scenario, for which the CDW phases evolve from a (partially) depleted Fermi surface already above their critical onset temperatures. We therefore argue that the long-range CDW orders of ${\mathrm{ErTe}}_3$ tend to be progressively dwarfed by Pd intercalation, which favors the presence of short-range CDW segments for both crystallographic directions persisting in a broad temperature $\left(T\right)$ interval up to the normal state, and being suggestive of precursor effects of the CDW orders as well as possibly coexisting with superconductivity at low $T$.

Quantifying the stability of an equilibrium is central in the theory of dynamical systems as well as in engineering and control. A comprehensive picture must include the response to both small and large perturbations, leading to the concepts of local (linear) and global stability. Here, we show how systems displaying Hopf bifurcations show contrarian results for these two aspects of stability: Global stability is large close to the point where the system loses its stability altogether. We demonstrate this effect for an elementary model system, an anharmonic oscillator, and a realistic model of power system dynamics with delayed control. Detailed investigations of the bifurcation explain the seeming paradox in terms of the location of the attractors relative to the equilibrium.

There exist numerous effective techniques for influencing linear systems to desired outcomes, but control of general nonlinear complex systems remains an open problem. One promising technique, which exploits our deep understanding of linear systems, involves linearizing at the current position and then applying linear optimal control to move the system to a local target from which it should be easier to reach the desired final state. However, nonlocal trajectories are often required to influence linear systems even to local targets, meaning that local linearization-based strategies can lead to inefficient jagged trajectories with high path length and large control energy cost. To address these limitations, here we propose an alternative control strategy with two innovations. The first is avoiding fixation on varying local targets. Instead, we exercise foresight by consistently planning a complete route to the final target, moving a short distance along the planned route, and then updating the plan according to the new local conditions. The second refinement, which we term relaxation, discourages overinvestment in control strategies which are optimal according to the linearization at the current point but could be inefficient according to dynamical conditions encountered at later times. We evaluate our strategy on complex systems from neuroscience and statistical mechanics, showing that our innovations substantially increase the success rate of control for a given path length or energy expenditure, and that these advantages persist as system size increases.

Here, by making use of medium and high resolution autocorrected off-axis electron holography, we directly probe the electrostatic potential as well as in-plane structural reconstruction at edges and steps in multilayer hexagonal boron nitride. In combination with ab initio calculations, the data allows revealing the formation of folded zigzag edges at steps comprising two monolayers and their absence at monolayer steps.

The ultrastrong coupling between the elementary excitations of matter and microcavity modes is studied in a fully analytical quantum-mechanical theoretical framework. The elementary excitation could be phonons, excitons, plasmons, etc. From the diagonalization of the Hamiltonian, we obtain the ground state of the polariton Hamiltonian. The ground state belongs to the Gaussian class. Using the Gaussian property, we calculate the quantum entanglement in the ground state. We use two different measures for quantum entanglement—entanglement entropy and the logarithmic negativity parameter—and obtain rather simple analytical expressions for the entanglement measures. Our findings show that the amount of quantum entanglement in the ground state is quite significant in the ultrastrong-coupling regime. It can be obtained from the measurement of the polariton frequencies.

Liquid crystals can self-organize into a layered smectic phase. While the smectic layers are typically straight, forming a lamellar pattern in bulk, external confinement may drastically distort the layers due to the boundary conditions imposed on the orientational director field. Resolving this distortion leads to complex structures with topological defects. Here, we explore the configurations adopted by two-dimensional colloidal smectics made from nearly hard rod-like particles in complex confinements, characterized by a button-like structure with two internal boundaries (inclusions): a two-holed disk and a double annulus. The topology of the confinement generates new structures which we classify in reference to previous work as generalized laminar and generalized Shubnikov states. To explore these configurations, we combine particle-resolved experiments on colloidal rods with three complementary theoretical approaches: Monte Carlo simulation, first-principles density functional theory, and phenomenological $\mathbf{Q}$-tensor modeling. This yields a consistent and comprehensive description of the structural details. In particular, we characterize a nontrivial tilt angle between the direction of the layers and symmetry axes of the confinement.

We propose a way to identify strongly Hund-correlated materials by unveiling a key signature of Hund correlations at the two-particle level. The defining feature is the sign of the response of the frozen spin ratio (the long-time local spin-spin correlation function divided by the instantaneous value) under variation of electron density. The underlying physical reason is that the sign is closely related to the strength of charge fluctuations between the dominant atomic multiplets and higher-spin ones in a neighboring charge subspace. It is the predominance of these fluctuations that promotes Hund metallicity. The temperature dependence of the frozen spin ratio can further reveal a non-Fermi-liquid behavior and thus the Hund metal states. We analyze both degenerate and nondegenerate multiorbital Hubbard models and corroborate our argument by taking doped ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and LaFeAsO as representative material examples, respectively, of Mott and Hund metals. Our proposal should be applicable to systems with non-half-filled integer electron fillings and their doped cases provided the doping drove the electron density toward the half filling.

We use analytically tractable dielectric response models, which are supported by ab initio calculations for anisotropic two-dimensional (2D) materials and quasi-2D metals that host slow plasmons, to reveal a rich variety of the plasmonic wake patterns in the electric potential induced by a charged particle moving parallel to those materials. Using the method of stationary phase, we discover surprising analogies with Kelvin's ship wakes and atmospheric wakes regarding the asymmetry of the wake, slowing down of the plasmon dispersion, and the onset of Mach-like wake due to nonlocal effects in the dielectric response.

Topological phases have been reported on self-similar structures in the presence of a perpendicular magnetic field. Here, we present an understanding of these phases from a perspective of spectral flow and charge pumping. We study the Harper-Hofstadter model on self-similar structures constructed from the Sierpinski gasket. We numerically investigate the spectral flow and the associated charge pumping when a flux tube is inserted through the structure and the flux through the tube is varied adiabatically. We find that the nature of the spectral flow is qualitatively different from that of translationally invariant noninteracting systems with a perpendicular magnetic field. We show that the instantaneous eigenspectra can be used to understand the quantization of the charge pumped over a cycle, and hence to understand the topological character of the system. We show the correspondence between the local contributions to the Hall conductivity and the spectral flow of the edgelike states. We also show that the edgelike states can be approximated by eigenstates of the discrete angular-momentum operator, their chiral nature being a consequence of this.