We developed an efficient method for Monte Carlo simulations with long-range interacting systems. The present method is based on the stochastic potential switching algorithm as in the case of the stochastic cutoff (SCO) method. Compared with the SCO method, the present method is efficient for systems with complicated lattice structures, e.g., amorphous systems and translationally invariant systems with large unit cells. Using the present method, we investigated magnetic structures of ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ thin-film magnets based on the atomistic spin model, which contains 68 continuous spins in the unit cell. We found that the anisotropy of Nd ions contributes to that of the whole system only at relatively low temperatures. If the anisotropy of the Fe ions is not considered, a planer magnetic structure arises owing to the dipole-dipole interactions at high temperatures, while it does not with the anisotropy. This difference indicates that the anisotropy of the Fe ions plays an important role in holding the magnetization parallel to the easy axis at the high temperatures.

Stripe domains are narrow, elongated, reversed regions that exist in magnetic materials with perpendicular magnetic anisotropy. They appear as a pair of domain walls that can exhibit topology with a nonzero chirality. Recent experimental and numerical investigations identify an instability of stripe domains along the long direction as a means of nucleating isolated magnetic skyrmions. Here, the onset and nonlinear evolution of transverse instabilities for a dynamic stripe domain known as the bion stripe are investigated. Both nontopological and topological variants of the bion stripe are shown to exhibit a long-wavelength transverse instability with different characteristic features. In the former, small transverse variations in the stripe's width lead to a neck instability that eventually pinches the nontopological stripe into a chain of two-dimensional breathers composed of droplet soliton pairs. In the latter case, small variations in the stripe's center result in a snake instability whose topological structure leads to the nucleation of dynamic magnetic skyrmions and antiskyrmions as well as perimeter-modulated droplets. Quantitative, analytical predictions for both the early, linear evolution and the long-time, nonlinear evolution are achieved using an averaged Lagrangian approach that incorporates both exchange (dispersion) and anisotropy (nonlinearity). The method of analysis is general and can be applied to other filamentary structures.

We investigate topological magnon band crossings of pyrochlore antiferromagnets with all-in-all-out (AIAO) magnetic order. By general symmetry analysis and spin-wave theory, we show that pyrochlore materials with AIAO orders can host Weyl magnons under external magnetic fields or uniaxial strains. Under a small magnetic field, the magnon bands of the pyrochlore with AIAO background can feature two opposite-charged Weyl points, which is the minimal number of Weyl points realizable in quantum materials, and has not been experimentally observed so far. We further show that breathing pyrochlores with AIAO orders can exhibit Weyl magnons upon uniaxial strains. These findings apply to any pyrochlore material supporting AIAO orders, irrespective of the forms of interactions. Specifically, we show that the Weyl magnons are robust against direct (positive) Dzyaloshinskii-Moriya interactions. Because of the ubiquitous AIAO orders in pyrochlore magnets including ${\mathrm{R}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$, and experimentally achievable external strain and magnetic field, our predictions provide a promising arena to witness the Weyl magnons in quantum magnets.

$\beta -\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$, a candidate material for power electronics and UV optoelectronics, shows strong room-temperature photoluminescence (PL). In addition to the three well-known bands of as-grown samples in the UV, blue, and green, also red PL was observed upon nitrogen doping. This raises the possibility of applying $\beta -\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ nanostructures as white phosphors. Using an optimized, Koopmans-compliant hybrid functional, we show that most intrinsic point defects, as well as substitutional nitrogen, act as deep acceptors, and each of the observed PL bands can be explained by electron recombination with a hole trapped in one of them. We suggest this mechanism to be general in wide-band-gap semiconductors which can only be doped $n$-type. Calculations on the nitrogen acceptor reproduce the observed red luminescence accurately. Earlier we have shown that not only the energy, but the polarization properties of the UV band can be explained by self-trapped hole states. Here we find that the blue band has its origin mainly in singly negative Ga-O divacancies, and the green band is caused dominantly by interstitial O atoms (with minor contribution of Ga vacancies to both). These assignments can explain the experimentally observed dependence of the PL bands on free-electron concentration and stoichiometry. The information provided here paves the way for the conscious tuning of light emission from $\beta -\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$.

We present results for many-body perturbation theory for the one-body Green's function at finite temperatures using the Matsubara formalism. Our method relies on the accurate representation of the single-particle states in standard Gaussian basis sets, allowing to efficiently compute, among other observables, quasiparticle energies and Dyson orbitals of atoms and molecules. In particular, we challenge the second-order treatment of the Coulomb interaction by benchmarking its accuracy for a well-established test set of small molecules, which includes also systems where the usual Hartree-Fock treatment encounters difficulties. We discuss different schemes how to extract quasiparticle properties and assess their range of applicability. With an accurate solution and compact representation, our method is an ideal starting point to study electron dynamics in time-resolved experiments by the propagation of the Kadanoff-Baym equations.

We report a detailed theoretical study of the electronic structure, spectral properties, and lattice parameters of bulk FeSe under pressure using a fully charge self-consistent implementation of the density functional theory plus dynamical mean-field theory method (DFT+DMFT). In particular, we perform a structural optimization and compute the evolution of the lattice parameters (volume, $c/a$ ratio, and the internal $z$ position of Se) and the electronic structure of the tetragonal (space group $P4/nmm$) unit cell of paramagnetic FeSe. Our results for the lattice parameters obtained by structural optimization using DFT+DMFT are in good quantitative agreement with experiment, implying a crucial importance of electron correlations in determining the correct lattice properties of FeSe. Most importantly, upon compression to 10 GPa our results reveal a topological change in the Fermi surface (Lifshitz transition) which is accompanied by a two- to three-dimensional crossover and a small reduction of the quasiparticle mass renormalization compared to ambient pressure. The behavior of the momentum-resolved magnetic susceptibility $\chi \left(\mathbf{q}\right)$ shows no topological changes of magnetic correlations under pressure but demonstrates a reduction of the degree of the in-plane $(\pi ,\pi )$ stripe-type nesting. Our results for the electronic structure and lattice parameters of FeSe are in good qualitative agreement with recent experiments on its isoelectronic counterpart ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$.

We have synthesized single crystals of Dirac semimetal candidates $A{\mathrm{ZnBi}}_2$ with $A=\text{Ba}$ and Sr. In contrast to $A=\text{Sr}$, the Ba material displays a local Zn vacancy ordering, which makes the observation of quantum oscillations in out-of-plane magnetic fields possible. As a Dirac semimetal candidate, ${\mathrm{BaZnBi}}_2$ exhibits a small cyclotron electron mass, high quantum mobility, and nontrivial Berry phases. Three Dirac dispersions are observed by angle-resolved photoemission spectroscopy and identified by first-principles band-structure calculations. Compared to $A\text{Mn}{(\text{Bi}/\mathrm{Sb})}_2$ systems which host Mn magnetic moments, ${\mathrm{BaZnBi}}_2$ acts as a nonmagnetic analog to investigate the intrinsic properties of Dirac fermions in this structure family.

Spectra of magnetoplasma excitations have been investigated in two-dimensional electron systems in AlAs quantum wells (QWs) of different widths. The magnetoplasma spectrum has been found to change profoundly when the quantum well width becomes thinner than 5.5 nm, indicating a drastic change in the conduction electron energy spectrum. The transformation can be interpreted in terms of transition from the in-plane strongly anisotropic $X_x-X_y$ valley occupation to the out-of-plane isotropic $X_z$ valley in the QW plane. Strong enhancement of the cyclotron effective mass over the band value in narrow AlAs QWs is reported.

Generation of high harmonics in a monolayer graphene initiated by a strong coherent radiation field, taking into account electron-electron Coulomb interaction, is investigated. A microscopic theory describing the nonlinear optical response of graphene is developed. The Coulomb interaction of electrons is treated in the scope of dynamic Hartree-Fock approximation. The closed set of integrodifferential equations for the single-particle density matrix of a graphene quantum structure is solved numerically. The obtained solutions show the significance of many-body Coulomb interaction on the high harmonic generation process in graphene.

By means of a nonlinear two-component hydrodynamic model, we study the valley-polarized collective motion of electrons in a strained graphene sheet. The self-consistent numerical solution in real space indicates the existence of valley-polarized edge plasmons due to a strain-induced pseudomagnetic field. The valley polarization of the edge pseudomagnetoplasmon can occur in a specific valley, depending on the pseudomagnetic field and the electron density in equilibrium. A full valley polarization is achieved at the edge of the graphene sheet for a pseudomagnetic field of tens of Tesla, which is a realistic value in current experimental technologies.

A repulsive Coulomb interaction between electrons in different orbitals in correlated materials can give rise to bound quasiparticle states. We study the nonhybridized two-orbital Hubbard model with intra- (inter)orbital interaction $U\left(U_{12}\right)$ and different bandwidths using an improved dynamical mean-field theory numerical technique which leads to reliable spectra on the real energy axis directly at zero temperature. We find that a finite density of states at the Fermi energy in one band is correlated with the emergence of well-defined quasiparticle states at excited energies $\mathrm{\Delta }=U-U_{12}$ in the other band. These excitations are interband holon-doublon bound states. At the symmetric point $U=U_{12}$, the quasiparticle peaks are located at the Fermi energy, leading to a simultaneous and continuous Mott transition settling a long-standing controversy.

We study the connections among particle statistics, frustration, and ground-state energy in quantum many-particle systems. In the absence of interaction, the influence of particle statistics on the ground-state energy is trivial: the ground-state energy of noninteracting bosons is lower than that of free fermions because of Bose-Einstein condensation and Pauli exclusion principle. In the presence of hard-core or other interaction, however, the comparison is not trivial. Nevertheless, the ground-state energy of hard-core bosons is proved to be lower than that of spinless fermions, if all the hopping amplitudes are non-negative. The condition can be understood as the absence of frustration among hoppings. By mapping the many-body Hamiltonian to a tight-binding model on a fictitious lattice, we show that the Fermi statistics of the original particles introduces an effective magnetic flux in the fictitious lattice. The latter can be effectively regarded as a kind of frustration since it leads to a destructive interference among different paths along which a single particle is propagating. If we introduce hopping frustration, the hopping frustration is expected to compete with the effective frustration due to the Fermi statistics, leading to the possibility that the ground-state energy of hard-core bosons can be higher than that of fermions. We present several examples, in which the ground-state energy of hard-core bosons is proved to be higher than that of fermions due to the hopping frustration. The basic ideas were reported in a previous paper [W.-X. Nie, H. Katsura, and M. Oshikawa, Phys. Rev. Lett. 111, 100402 (2013)]; more details and several extensions, including one to the spinful case, are discussed in this paper.

The theory of correlated electron systems on a lattice proves notoriously complicated because of the exponential growth of Hilbert space. Mean-field approaches provide valuable insight when the self-energy has a dominant local structure. Additionally, the extraction of effective low-energy theories from the generalized many-body representation is highly desirable. In this respect, the rotational-invariant slave-boson (RISB) approach in its mean-field formulation enables versatile access to correlated lattice problems. However, in its original form, due to numerical complexity, the RISB approach is limited to about three correlated orbitals per lattice site. We thus present a thorough symmetry-adapted advancement of RISB theory, suited to efficiently deal with multiorbital Hubbard Hamiltonians for complete atomic-shell manifolds. It is utilized to study the intriguing problem of Hund's physics for three- and especially five-orbital manifolds on the correlated lattice, including crystal-field terms as well as spin-orbit interaction. The well-known Janus-face phenomenology, i.e., strengthening of correlations at smaller-to-intermediate Hubbard $U$ accompanied by a shift of the Mott transition to a larger $U$ value, has a stronger signature and more involved multiplet resolution for five-orbital problems. Spin-orbit interaction effectively reduces the critical local interaction strength and weakens the Janus-face behavior. Application to the realistic challenge of Fe chalcogenides underlines the subtle interplay of the orbital degrees of freedom in these materials.

The evolution of single particle excitations of bilayer graphene under effects of non-Markovian noise is described with focus on the decoherence process of lattice-layer (LL) maximally entangled states. Once the noiseless dynamics of an arbitrary initial state is identified by the correspondence between the tight-binding Hamiltonian for the AB-stacked bilayer graphene and the Dirac equation—which includes pseudovectorlike and tensorlike field interactions—the noisy environment is described as random fluctuations on bias voltage and mass terms. The inclusion of noisy dynamics reproduces the Ornstein-Uhlenbeck processes: A non-Markovian noise model with a well-defined Markovian limit. Considering that an initial amount of entanglement shall be dissipated by the noise, two profiles of dissipation are identified. On one hand, for eigenstates of the noiseless Hamiltonian, deaths and revivals of entanglement are identified along the oscillation pattern for long interaction periods. On the other hand, for departing LL Werner and Cat states, the entanglement is suppressed although, for both cases, some identified memory effects compete with the pure noise-induced decoherence in order to preserve the the overall profile of a given initial state.

Unsupervised machine learning via a restricted Boltzmann machine is a useful tool in distinguishing an ordered phase from a disordered phase. Here we study its application on the two-dimensional Ashkin-Teller model, which features a partially ordered product phase. We train the neural network with spin configuration data generated by Monte Carlo simulations and show that distinct features of the product phase can be learned from nonergodic samples resulting from symmetry breaking. Careful analysis of the weight matrices inspires us to define a nontrivial machine-learning motivated quantity of the product form, which resembles the conventional product order parameter.

Quantum criticality of the spin-1/2 ferromagnetic-leg ladder 3-I-V [=3-(3-iodophenyl)-1,5-diphenylverdazyl] has been examined with respect to the antiferromagnetic to paramagnetic phase transition near the saturation field $H_c$. The phase boundary $T_c\left(H\right)$ follows the power-law $T_c\left(H\right)\propto H_c-H$ for a wide temperature range. This characteristic behavior is discussed as a quasi-one-dimensional (quasi-1D) Bose-Einstein condensation, which is predicted theoretically for weakly coupled quasi-1D ferromagnets. Thus, 3-I-V provides the first promising candidate for this attractive prediction.

We study coherent quantum phase slips which lift the ground state degeneracy in a Josephson junction ring, pierced by a magnetic flux of the magnitude equal to half of a flux quantum. The quantum phase-slip amplitude is sensitive to the normal mode structure of superconducting phase oscillations in the ring (Mooij-Schön modes). These, in turn, are affected by spatial inhomogeneities in the ring. We analyze the case of weak periodic modulations of the system parameters and calculate the corresponding modification of the quantum phase-slip amplitude.

We present clear experimental evidence for the momentum-dependent heavy fermionic electronic structures of the $4f$-based strongly correlated system ${\mathrm{CeNi}}_2{\mathrm{Ge}}_2$ by soft x-ray angle-resolved photoemission spectroscopy. A comparison between the experimental three-dimensional quasiparticle dispersion of ${\mathrm{LaNi}}_2{\mathrm{Ge}}_2$ and ${\mathrm{CeNi}}_2{\mathrm{Ge}}_2$ has revealed that heavy fermionic electronic structures are seen in the region surrounding a specific momentum. Furthermore, the wave vectors between the observed “heavy spots” are consistent with a result of neutron scattering reflecting magnetic correlations, which could be a trigger for the superconductivity in ${\mathrm{CeNi}}_2{\mathrm{Ge}}_2$.

The infinite projected entangled-pair state (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the corner transfer matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground-state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground-state fidelity, and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.