We theoretically study the high-harmonic generation (HHG) in one-dimensional spin systems. While in electronic systems the driving by ac electric fields produces radiation from the dynamics of excited charges, we consider here the situation where spin systems excited by a magnetic field pulse generate radiation via a time-dependent magnetization. Specifically, we study the magnetic dipole radiation in two types of ferromagnetic spin chain models, the Ising model with static longitudinal field and the XXZ model, and reveal the structure of the spin HHG and its relation to spin excitations. For weak laser amplitude, a peak structure appears which can be explained by time-dependent perturbation theory. With increasing amplitude, plateaus with well-defined cutoff energies emerge. In the Ising model with longitudinal field, the thresholds of the multiple plateaus in the radiation spectra can be explained by the annihilation of multiple magnons. In the XXZ model, which retains the ${\mathbf{Z}}_2$ symmetry, the laser magnetic field can induce a phase transition of the ground state when it exceeds a critical value, which results in a drastic change of the spin excitation character. As a consequence, the first cutoff energy in the HHG spectrum changes from a single-magnon to a two-magnon energy at this transition. Our results demonstrate the possibility of generating high-harmonic radiation from magnetically ordered materials and the usefulness of high-harmonic signals for extracting information on the spin excitation spectrum.

Landau's theory of phase transitions provides a framework for describing phases of matter in thermodynamic equilibrium. Recently, an intriguing new class of quantum many-body localized (MBL) systems that do not reach thermodynamic equilibrium was discovered. The possibility of MBL systems to not heat up under periodic driving, which drastically changes the nature of dynamics in the system, opens the door for new, truly nonequilibrium phases of matter. In this paper we find a two-dimensional nonequilibrium topological phase, the anomalous Floquet insulator (AFI), which arises from the combination of periodic driving and MBL. Having no counterpart in equilibrium, the AFI is characterized by an MBL bulk, and topologically protected delocalized (thermalizing) chiral states at its boundaries. After establishing the regime of stability of the AFI phase in a simple yet experimentally realistic model, we investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that nonuniform particle density profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize. These findings open the possibility of observing quantized edge transport in interacting systems at high temperature.

We study the coupled quantum Hall bilayers each at half-filled first excited Landau levels by varying the layer distance. Based on numerical exact diagonalization on a torus, we identify two distinct phases separated by a critical layer distance $d_c$. From $d_c$ to an infinite layer distance, the topological phase is smoothly connected to a direct tensor product of two Moore-Read states, while interlayer coherence emerges at $d<d_c$ characterized by $xy$ easy-plane ferromagnetic energy spectra, gapless pseudospin excitations, long-range current-current correlations, and finite exciton superfluid stiffness, corresponding to the exciton superfluid state. More interestingly, the results of the ground-state fidelity, the evolution of the energy spectra, and the superfluid stiffness indicate a possible continuous transition. Theoretically, it can be interpreted as a topological phase transition which simultaneously changes the topology of the ground state and breaks symmetry, providing an interesting example of transitions beyond the Landau paradigm.

We analyze a description of twisted graphene bilayers that incorporates the deformation of the layers using state-of-the-art interlayer atomic potentials and a modification of the hopping parameters between layers in the light of the classic Slonczewski-Weiss-McClure parametrization. We obtain narrow bands in all cases, but their nature can be rather different. We will show how to describe the results by equivalent continuum models. Even though such models can be constructed, their complexity can vary, requiring many coupling parameters to be included, and the full in-layer dispersion must be taken into account. The combination of all these effects will have a large impact on the wave functions of the flat bands, and modifications in details of the underlying models can lead to significant changes. A robust conclusion is that the natural strength of the interlayer couplings is higher than usually assumed, leading to shifts in the definition of the magic angles. The structure at the edges of the narrow bands, at the $\mathrm{\Gamma }$ point of the Brillouin zone is also strongly dependent on parametrization. As a result, the existence, and size, of band gaps between the flat bands and the neighboring ones are changed. Hence, the definition of Wannier functions, and descriptions based on local interactions are strongly dependent on the description of the model at the atomic scale.

We present a joint experimental and theoretical study that demonstrates how to efficiently control a canted state of magnetization in Fe films grown on Ag(001) vicinal surface and precisely characterize it with the magneto-optical Kerr effect. It is shown that by employing different mechanisms to tune the magnetization tilting angle, any magnetization orientation within the plane perpendicular to the step edges can be achieved. In particular, increasing the Fe film thickness leads to continuous rotation of the magnetization easy axis toward the film surface and the sense of this rotation in uncovered films is opposite to that in films covered with Au. Another tuning mechanism is provided by oscillatory changes of the tilting angle at low temperatures due to formation of quantum well states in Fe films. The observed canting of magnetization is explained within a phenomenological model by an interplay of the shape anisotropy and two magnetocrystalline anisotropy terms, perpendicular and step-induced anisotropies, which results in an effective uniaxial magnetic anisotropy. The fitted thickness dependencies of the anisotropy constants accurately reproduce experimental variations of the tilting angle with both Fe and Au thicknesses as well as transient changes of the magnetization orientation in ultrathin Fe films upon submonolayer Au coverage, observed with spin-polarized low-energy electron microscopy.

Monolayer $\mathrm{WS}{\mathrm{e}}_2$ hosts a series of exciton Rydberg states denoted by the principal quantum number $n=1$, 2, 3, etc. While most research focuses on their absorption properties, their optical emission is also important but much less studied. Here we measure the photoluminescence from the $1s–5s$ exciton Rydberg states in ultraclean monolayer $\mathrm{WS}{\mathrm{e}}_2$ encapsulated by boron nitride under magnetic fields from −31 to 31 T. The exciton Rydberg states exhibit similar Zeeman shifts but distinct diamagnetic shifts from each other. From their luminescence spectra, Zeeman shifts, and diamagnetic shifts, we deduce the binding energies, $g$ factors, and radii of the $1s–4s$ exciton states. Our results are consistent with theoretical predictions and results from prior magnetoabsorption experiments.

We show that Dirac fermion systems in two dimensions generally exhibit a disorder-induced nodal arc replacing the nodal point and tilted Dirac cone, provided that the two components of the Dirac fermion correspond to two distinct orbitals unrelated by symmetry. This result is explicitly demonstrated using renormalization-group analysis in a disordered Dirac model that we introduce, where the disorder potential acts differently on the two orbitals. As we show by numerical simulations and self-consistent Born approximation calculation, this drives the system into a new strongly disordered phase.

We combine state-of-the-art large-scale first-principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $\theta =1.{08}^{\circ }$. We show that the energy width of the flat-band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes.

We propose a systematic method to generate a complete orthonormal basis set of multipole expansion for magnetic structures in arbitrary crystal structure. The key idea is the introduction of a virtual atomic cluster of a target crystal on which we can clearly define the magnetic configurations corresponding to symmetry-adapted multipole moments. The magnetic configurations are then mapped onto the crystal so as to preserve the magnetic point group of the multipole moments, leading to the magnetic structures classified according to the irreducible representations of the crystallographic point group. We apply the present scheme to pyrochlore and hexagonal $AB{\mathrm{O}}_3$ crystal structures and demonstrate that the multipole expansion is useful to investigate the macroscopic responses of antiferromagnets.

We study the error correcting properties of Majorana surface codes (MSCs), topological quantum codes constructed out of interacting Majorana fermions, which can be used to store quantum information and perform quantum computation. These quantum memories suffer from purely “fermionic” errors, such as quasiparticle poisoning (QP), that have no analog in conventional platforms with bosonic qubits. In physical realizations where QP dominates, we show that errors can be corrected provided that the poisoning rate is below a threshold of $\sim 11\%$. When QP is highly suppressed and fermionic bilinear (“bosonic”) errors become dominant, we find an error threshold of $\sim 16\%$, which is much higher than the threshold for spin-based topological memories like the surface code or the color code. In addition, we derive lattice gauge theories to account for measurement errors. These results, together with the inherent error suppression provided by the superconducting gap in physical realizations of the MSCs, makes this a strong candidate for a robust topological quantum memory.

We consider Mott insulators driven by periodic coherent laser radiation, using both single-orbital and multiorbital models, noting that the latter is of more interest in solid-state systems. We derive general expressions for the resulting periodically driven spin models and spin-orbital models using time-dependent perturbation theory. First, we show that the effective exchange interactions of the Floquet Hamiltonians are highly tunable by the frequency, amplitude, and polarization of the laser. Second, we take the effect of finite bandwidth of excitations into account and study possible heating effects. Using the same formalism with a slight modification we also consider the small-frequency regime and study the dielectric breakdown of Mott insulators.

A non-Hermitian system can exhibit extensive sensitivity of its complex energy spectrum to the imposed boundary conditions, which is beyond any known phenomenon from Hermitian systems. In addition to topologically protected boundary modes, macroscopically many “skin” boundary modes may appear under open boundary conditions. We rigorously derive universal results for characterizing all avenues of boundary modes in non-Hermitian systems for arbitrary hopping ranges. For skin modes, we introduce how exact energies and decay lengths can be obtained by threading an imaginary flux. Furthermore, for one-dimensional topological boundary modes, we derive a generic criterion for their existence in non-Hermitian systems which, in contrast to previous formulations, does not require specific tailoring to the system at hand. Our approach is intimately based on the complex analytical properties of in-gap exceptional points, and gives a lower bound for the winding number related to the vorticity of the energy Riemann surface. It also reveals that the topologically nontrivial phase is partitioned into subregimes where the boundary mode's decay length depends differently on complex momenta roots.

We extend the density functional perturbation theory formalism to the case of noncollinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the noncollinearity of the system. Most of the present XC functionals are constructed at the collinear level, such that the off-diagonal (containing magnetization densities along $x$ and $y$ directions) derivatives cannot be calculated simply in the noncollinear framework. To solve this problem, we consider here possibilities to transform the noncollinear XC derivatives to a local collinear basis, where the $z$ axis is aligned with the local magnetization at each point. The two methods we explore are (i) expanding the spin rotation matrix as a Taylor series and (ii) evaluating explicitly the XC for the local density approximation through an analytical expression of the expansion terms. We compare the two methods and describe their practical implementation. We show their application for atomic displacement and electric field perturbations at the second order, within the norm-conserving pseudopotential methods.

Interplay of Fermi surface topology and electron correlation is the quintessential ingredient underlying spontaneous symmetry breaking in itinerant electronic systems. In one-dimensional (1D) systems at half filling, the inherent Fermi surface nesting makes the translationally invariant metallic state unstable, which is known as Peierls instability. Extending the scope of Peierls instability to two (2D) or three dimensions (3D), however, is not straightforward, since the Fermi surface in higher dimensions is generally not nested. In this work, we show that a perfectly nested Fermi surface can be realized in a class of 2D perovskite oxides, giving rise to 2D Peierls instability. Here the central role is played by the zone-boundary Dirac line node (DLN) protected by two orthogonal glide mirrors induced by the rotation of oxygen octahedra. Especially at a critical angle of the octahedron rotation, the zone-boundary DLN flattens, leading to logarithmically diverging susceptibility. We propose the 2D Peierls instability driven by dispersionless DLN as a principle mechanism for spontaneous symmetry breaking in various layered perovskite oxides including the antiferromagnetism of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$. As a clear signature of the 2D Peierls instability, we predict that the magnetic domain wall in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ hosts localized soliton modes.

We investigate approximate emergent non-Abelian symmetry in a class of weakly first-order ‘deconfined’ phase transitions using Monte Carlo simulations and a renormalization group analysis. We study a transition in a 3D classical loop model that is analogous to a deconfined $2+1\mathrm{D}$ quantum phase transition in a magnet with reduced lattice symmetry. The transition is between the Néel phase and a twofold degenerate valence bond solid (lattice-symmetry-breaking) phase. The combined order parameter at the transition is effectively a four-component superspin. It has been argued that in some weakly first-order ‘pseudocritical’ deconfined phase transitions, the renormalization group flow can take the system very close to the ordered fixed point of the symmetric $\mathrm{O}\left(N\right)$ sigma model, where $N$ is the total number of ‘soft’ order parameter components, despite the fact that $\mathrm{O}\left(N\right)$ is not a microscopic symmetry. This yields a first-order transition with unconventional phenomenology. We argue that this occurs in the present model, with $N=4$. This means that there is a regime of length scales in which the transition resembles a ‘spin-flop’ transition in the ordered $\mathrm{O}\left(4\right)$ sigma model. We give numerical evidence for (i) the first-order nature of the transition, (ii) the emergence of $\mathrm{O}\left(4\right)$ symmetry to an accurate approximation, and (iii) the existence of a regime in which the emergent $\mathrm{O}\left(4\right)$ is ‘spontaneously broken,’ with distinctive features in the order parameter probability distribution. These results may be relevant for other models studied in the literature, including $2+1\mathrm{D}$ QED with two flavors, the ‘easy-plane’ deconfined critical point, and the Néel-VBS transition on the rectangular lattice.

We present the first full-potential method that solves the fully relativistic four-component Dirac-Kohn-Sham equation for materials in the solid state within the framework of atom-centered Gaussian-type orbitals (GTOs). Our GTO-based method treats one-, two-, and three-dimensional periodic systems on an equal footing, and allows for a seamless transition to the methodology commonly used in studies of molecules with heavy elements. The scalar relativistic effects as well as the spin-orbit interaction are handled variationally. The full description of the electron-nuclear potential in the core region of heavy nuclei is straightforward due to the local nature of the GTOs and does not pose any computational difficulties. We show how the time-reversal symmetry and a quaternion algebra-based formalism can be exploited to significantly reduce the increased methodological complexity and computational cost associated with multiple wave-function components coupled by the spin-orbit interaction. We provide a detailed description of how to employ the matrix form of the multipole expansion and an iterative renormalization procedure to evaluate the conditionally convergent infinite lattice sums arising in studies of periodic systems. Next, we investigate the problem of inverse variational collapse that arises if the Dirac operator containing a repulsive periodic potential is expressed in a basis that includes diffuse functions, and suggest a possible solution. Finally, we demonstrate the validity of the method on three-dimensional silver halide ($\mathrm{Ag}X$) crystals with large relativistic effects and two-dimensional honeycomb structures (silicene and germanene) exhibiting the spin-orbit-driven quantum spin Hall effect. Our results are well-converged with respect to the basis set limit using standard bases developed for molecular calculations and indicate that the common rule of removing basis functions with small exponents should not be applied when transferring the molecular basis to solids.

In a Weyl orbit, the Fermi arc surface states on opposite surfaces of the topological semimetal are connected through the bulk Weyl or Dirac nodes. Having a real-space component, these orbits accumulate a sample-size-dependent phase. Following recent work on the three-dimensional Dirac semimetal cadmium arsenide (${\mathrm{Cd}}_3{\mathrm{As}}_2$), we have sought evidence for this thickness-dependent effect in quantum oscillations and quantum Hall plateaus in (112)-oriented ${\mathrm{Cd}}_3{\mathrm{As}}_2$ thin films grown by molecular beam epitaxy. We compare quantum transport in films of varying thicknesses at apparently identical gate-tuned carrier concentrations and find no clear dependence of the relative phase of the quantum oscillations on the sample thickness. We show that small variations in carrier densities, difficult to detect in low-field Hall measurements, lead to shifts in quantum oscillations that are commensurate with previously reported phase shifts. Future claims of Weyl orbits based on the thickness dependence of quantum transport data require additional studies that demonstrate that these competing effects have been disentangled.

Quantum many-fermion systems give rise to diverse states of matter that often reveal themselves in distinctive transport properties. While some of these states can be captured by microscopic models accessible to numerical exact quantum Monte Carlo simulations, it nevertheless remains challenging to numerically access their transport properties. Here, we demonstrate that quantum loop topography (QLT) can be used to directly probe transport by machine learning current-current correlations in imaginary time. We showcase this approach by studying the emergence of superconducting fluctuations in the negative-$U$ Hubbard model and a spin-fermion model for a metallic quantum critical point. For both sign-free models, we find that the QLT approach detects a change in transport in very good agreement with their established phase diagrams. These proof-of-principle calculations combined with the numerical efficiency of the QLT approach point a way to identify hitherto elusive transport phenomena such as non-Fermi liquids using machine learning algorithms.

Phase transitions and their associated crossovers are imprinted in the behavior of fluctuations. Motivated by recent experiments on ultracold atoms in optical lattices, we compute the thermodynamic density fluctuations $\delta N^2$ of the two-dimensional fermionic Hubbard model with plaquette cellular dynamical mean-field theory. To understand the length scale of these fluctuations, we separate the local from the nonlocal contributions to $\delta N^2$. We determine the effects of particle statistics, interaction strength $U$, temperature $T$, and density $n$. At high temperature, our theoretical framework reproduces the experimental observations in the doping-driven crossover regime between metal and Mott insulator. At low temperature, there is an increase of thermodynamic density fluctuations, analogous to critical opalescence, accompanied by a surprising reduction of the absolute value of their nonlocal contributions. This is a precursory sign of an underlying phase transition between a pseudogap phase and a metallic phase in doped Mott insulators, which should play an important role in the cuprate high-temperature superconductors. Predictions for ultracold atom experiments are made.

We present an ab initio disordered local moment theory for the Gibbs free energy of a magnetic material. Two central objects are calculated: the lattice Fourier transform of the direct local moment – local moment correlation functions in the paramagnetic state and local internal magnetic fields as functions of magnetic order. We identify the potentially most stable magnetic phases from the first, which can include noncollinear and long-period states in complex multiatom unit cells, and extract higher-order correlations among the local moments from the second. We propose that these latter entities produce a picture of effective multisite magnetic interactions depending on the state and extent of magnetic order and discuss its relation to other approaches. We show how magnetic phase diagrams for temperature, magnetic field, and lattice structure and also magnetocaloric and mechanocaloric effects can be obtained from this approach. The theory accurately predicts the order of transitions and quantifies contributions to first-order and order-order magnetic phase transitions from both purely electronic sources and magnetoelastic effects. Our case study is the apparently frustrated magnetism of the ${\mathrm{Mn}}_{3}A$ class of materials in all its cubic, hexagonal, and tetragonal structures. The theory produces magnetic phases and transition temperatures in good agreement with experiment. We explain the first-order triangular antiferromagnetic to collinear antiferromagnetic transition in cubic ${\mathrm{Mn}}_3\mathrm{Pt}$ as a magnetovolume driven effect, and its absence for $A$=Ir and Rh. We also construct the magnetic phase diagram of ${\mathrm{Mn}}_3\mathrm{Pt}$ and explore its potential as a barocaloric material. Finally, we prepare the groundwork for future fully relativistic studies of the temperature dependence of the magnetism of ${\mathrm{Mn}}_{3}A$, including ${\mathrm{Mn}}_3\mathrm{Sn},{\mathrm{Mn}}_3\mathrm{Ga}$, and ${\mathrm{Mn}}_3\mathrm{Ge}$.