There is considerable research interest in discovering new permanent magnetic materials that perform equally as champion neomagnets, with the minimal use of critical rare-earth elements. Recently ${\mathrm{ThMn}}_{12}$-type (1:12) rare-earth iron (Ce-Fe) intermetallic materials have been on the frontline of research as Ce is naturally abundant that drastically lowers the cost of permanent magnets. Here, we investigate the lattice stability and electronic and magnetic properties of Ti- or Zr-substituted ${\mathrm{CeFe}}_{12}$ and ${\mathrm{CeFe}}_{12}\mathrm{N}$ using density functional theory. We find negative formation energy for all compositions in the bulk structure with respect to unaries except for ${\mathrm{CeFe}}_{12}$. The inclusion of nitrogen in the interstitial sites of ${\mathrm{CeFe}}_{12}$ improves its chemical stability by reducing the formation energy. The first time successfully calculated phonon frequencies including $4f$ electrons indicate that all compositions are dynamically stable. With the help of electronic structure calculations, we demonstrate that cerium exhibits the mixed-valence character in 1:12 materials. The mixed-valency sensibly affects the magnetocrystalline anisotropy (MCA) and magnetic moment. Nitrogen improves the net magnetic moment by influencing the spin polarization with extra electrons, although it has the opposite effect in the MCA constant, $K_1$. The predicted value of $K_1$ confirms all compounds uniaxial along the crystalline $c$ axis. Especially for ${\mathrm{CeZrFe}}_{11}$, $K_1$ is the largest in which Ce exhibits ${\mathrm{Ce}}^{3+}$ $(S=1/2)$, and $\mathrm{Ce}\left(4f\right)$ spin-density contour is elongated towards the uniaxial direction. The substantially large values of the MCA and magnetic moments suggest that these critical element-free materials qualify for high-performance permanent magnets.

The layered perovskite ${\mathrm{YBaCuFeO}}_5$ is a rare example of a cycloidal spiral magnet whose ordering temperature $T_{\text{spiral}}$ can be tuned far beyond room temperature by adjusting the degree of ${\mathrm{Cu}}^{2+}/{\mathrm{Fe}}^{3+}$ chemical disorder in the structure. This unusual property qualifies this material as one of the most promising spin-driven multiferroic candidates. However, very little is known about the response of the spiral to magnetic fields, crucial for magnetoelectric cross-control applications. Using bulk magnetization and neutron powder diffraction measurements under magnetic fields up to 9 T, we report here a temperature-magnetic field phase diagram of this material. Besides revealing a strong stability of the spiral state, our data uncover the presence of weak ferromagnetism coexisting with the spiral modulation. Since ferromagnets can be easily manipulated with magnetic fields, this observation opens new perspectives for the control of the spiral orientation, directly linked to the polarization direction, as well as for a possible future use of this material in technological applications.

We develop a general framework for studying the equilibrium and non-equilibrium properties of arbitrary networks of Sachdev-Ye-Kitaev clusters coupled to thermal baths. We proceed to apply this technique to the problem of energy transport, which is known to be diffusive due to the strange metal behavior of these models. We use the external baths to impose a temperature gradient in the system and study the emerging non-equilibrium steady state using the Schwinger-Keldysh formalism. We consider two different configurations for the baths, implementing either a boundary or bulk driving, and show that the latter leads to a significantly faster convergence to the steady state. This setup allows us to compute both the temperature and frequency dependence of the diffusion constant. At low temperatures, our results agree perfectly with the previously known values for diffusivity in the conformal limit. We also establish a relationship between energy transport and quantum chaos by showing that the diffusion constant is upper bounded by the chaos propagation rate at all temperatures. Moreover, we find a simple analytical form for the non-equilibrium Green's functions in the linear response regime and use it to derive exact closed-form expressions for the diffusion constant in various limits. We mostly focus on uniform one-dimensional chains, but we also discuss higher-dimensional generalizations.

Hydrogen-rich superhydrides are believed to be very promising high critical temperature (high $T_c$) superconductors, with experimentally observed critical temperatures near room temperature, as shown in recently discovered lanthanide superhydrides at very high pressures, e.g., ${\mathrm{LaH}}_{10}$ at 170 GPa and ${\mathrm{CeH}}_9$ at 150 GPa. With the motivation of discovering new hydrogen-rich high $T_c$ superconductors at the lowest possible pressure, quantitative theoretical predictions are needed. In these promising compounds, superconductivity is mediated by the highly energetic lattice vibrations associated with hydrogen and their interplay with the electronic structure, requiring fine descriptions of the electronic properties, notoriously challenging for correlated $f$ systems. In this paper, we propose a first-principles calculation platform with the inclusion of many-body corrections to evaluate the detailed physical properties of the Ce-H system and to understand the structure, stability, and superconductivity of ${\mathrm{CeH}}_9$ at high pressure. We report how the calculation of $T_c$ is affected by the hierarchy of many-body corrections and obtain a compelling increase in $T_c$ at the highest level of theory, which goes in the direction of experimental observations. Our findings shed significant light on the search for superhydrides in close similarity with atomic hydrogen within a feasible pressure range. We provide a practical platform to further investigate and understand conventional superconductivity in hydrogen-rich superhydrides.

The bulk-boundary correspondence guarantees topologically protected edge states in a two-dimensional topological superconductor. Unlike in topological insulators, these edge states are, however, not connected to a quantized (spin) current as the electron number is not conserved in a Bogolyubov–de Gennes Hamiltonian. Still, edge currents are in general present. Here we use the two-dimensional Rashba system as an example to systematically analyze the effect symmetry reductions have on the order-parameter mixing and the edge properties in a superconductor of Altland-Zirnbauer class DIII (time-reversal-symmetry preserving) and D (time-reversal-symmetry breaking). In particular, we employ both Ginzburg-Landau and microscopic modeling to analyze the bulk superconducting properties and edge currents appearing in a strip geometry. We find edge (spin) currents independent of bulk topology and associated topological edge states which evolve continuously even when going through a phase transition into a topological state. Our findings emphasize the importance of symmetry over topology for the understanding of the nonquantized edge currents.

Non-Hermitian topological systems exhibit a plethora of unusual topological phenomena including the extreme localization of eigenstates, known as the non-Hermitian skin effect (NHSE), which occurs in open chains. However, the non-Hermitian characteristics of coupled non-Hermitian chains remain largely unexplored. Here, we report on the eigenstate localization in coupled non-Hermitian chains with dissimilar inverse skin lengths in which the NHSE can be switched on and off by modulating the interchain coupling strength. In the limit of small interchain strength, the NHSE is present at both ends of the coupled system because of the weak hybridization of the eigenstates of the individual chains. The eigenspectrum under open boundary conditions (OBC) exhibits a discontinuous jump known as the critical NHSE (CNHSE) as the chain length increases. However, when the interchain coupling strength and hence, the hybridization between eigenstates become significant, the NHSE and CNHSE vanish. Instead, a peculiar “half-half skin localization” occurs in composite chains with opposite signs of inverse skin lengths, where half of the eigenstates are exponentially localized at one chain and the remainder of the eigenstates on the other chain. Our results provide new insights into the non-Hermitian phenomena in coupled systems.

We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near $1/8$ doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about $1/5$ doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.

Nonequilibrium topological matter has been a fruitful topic of both theoretical and experimental interest. A great variety of exotic topological phases unavailable in static systems may emerge under nonequilibrium situations. How to locate the borders between different nonequilibrium topological phases is an important issue to facilitate topological characterization and further understand phase transition behaviors. In this paper, we develop an unsupervised machine-learning protocol to distinguish between different Floquet (periodically driven) topological phases possessed by theoretical models, by incorporating the system's dynamics within one driving period, adiabatic deformation in the time dimension, plus the system's symmetry all into our machine-learning algorithm. Results from two rich case studies indicate that machine learning is able to reliably reveal intricate topological phase boundaries and can hence be a powerful tool to analyze and discover previously unknown topological phases afforded by the time dimension. As inspired by previous elegant methods in analyzing Floquet topological phases, one essential ingredient in our machine-learning approach is to directly investigate the system's evolution operators parametrized by time.

We report a type of termination of the $\alpha \text{−}{\mathrm{Al}}_2{\mathrm{O}}_3\left(0001\right)$ surface with low concentration of hydroxyl groups. Using density functional theory calculations, we show that this termination is more stable than previously reported structures for low chemical potentials of water. This means that hydroxyl groups remain thermodynamically stable up to much higher temperatures than predicted previously, for example, up to around 1000 K at 1 mbar partial pressure of water. We also study the formation of these hydroxylated surfaces from adsorbed water and show that the initial steps for surface reconstruction are favorable thermodynamically and also proceed with accessible barriers.

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.

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.