We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which ground-state DMRG can be implemented efficiently. In fact, DMRG is obtained as a special case of our scheme for imaginary time evolution with infinite time step.

Starting from a minimal model for a two-dimensional nodal loop semimetal, we study the effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall insulator's Chern number is the phase-winding number of the mass gap terms on the loop. We provide simple lattice models, analyze the topological phases, and generalize a previous index characterizing topological transitions. The responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to a magnetic field's vector potential are also studied both in weak- and strong-field regimes, as well as the edge states in a ribbon geometry.

Cuprate materials, such as those hosting high-temperature superconductivity, represent a famous class of materials where the correlations between the strongly entangled charges and spins produce complex phase diagrams. Several years ago, the Zhang-Rice singlet was proposed as a natural quasiparticle in hole-doped cuprates. The occurrence and binding energy of this quasiparticle, consisting of a pair of bound holes with antiparallel spins on the same ${\mathrm{CuO}}_4$ plaquette, depends on the local electronic interactions, which are fundamental quantities for understanding the physics of the cuprates. Here, we employ state-of-the-art resonant inelastic x-ray scattering (RIXS) to probe the correlated physics of the ${\mathrm{CuO}}_4$ plaquettes in the quasi-one-dimensional chain cuprate ${\mathrm{Li}}_2{\mathrm{CuO}}_2$. By tuning the incoming photon energy to the O $K$ edge, we populate bound states related to the Zhang-Rice quasiparticles in the RIXS process. Both intra- and interchain Zhang-Rice singlets are observed and their occurrence is shown to depend on the nearest-neighbor spin-spin correlations, which are readily probed in this experiment. We also extract the binding energy of the Zhang-Rice singlet and identify the Zhang-Rice triplet excitation in the RIXS spectra.

We report details of single-crystal growth of stoichiometric bismuthide ${\mathrm{PtBi}}_2$ whose structure consists of alternate stacking of a Pt layer and Bi bilayer along the $c$ axis. The compound crystallizes in space group $P3$ with a hexagonal unit cell of $a=b=6.553\text{Å},c=6.165\text{Å}$. Its $T$-dependent resistivity is typical of a metal whereas a large anisotropy was observed for the in-plane and interplane electrical transport. The magnetization data show opposite sign for fields parallel and perpendicular to the Pt layers, respectively. The magnetic field response of this material shows clearly two types of charge carriers, consistent with the multiple Fermi surfaces revealed in our band structure calculations. The hydrostatic pressure is shown to suppress the resistivity at high $T$ systematically but has little bearing on its low-$T$ transport. Through calorimetric measurements, the density of states at the Fermi level and the Debye temperature are determined to be 0.$94{\mathrm{eV}}^{-1}$ per molecule and 145 K, respectively. In addition, the electronic structures and parity analyses are also presented. We find a minimum value of 0.05 eV gap opening at around 2 eV under the Fermi level by invoking spin-orbit interaction. A slab calculation further indicates a surface Dirac cone appearing in the gap of bulk states. We discuss the possibility of $\mathrm{PtBi}{}_2$ being a candidate for a bulk topological metal, in analogy to the recently proposed topological superconductor $\beta \text{−}{\mathrm{PdBi}}_2$.

Time-dependent spin phenomena in condensed matter are most often either described in the weakly correlated limit of metallic Stoner-Slater-like magnetism via band theory or in the strongly correlated limit of Heisenberg-like interacting spins in an insulator. However, many experimental studies, e.g., of (de)magnetization processes, focus on itinerant local-moment materials, such as transition metals and various of their compounds. We here present a general theoretical framework that is capable of addressing correlated spin dynamics, also in the presence of a vanishing charge gap. A real-space implementation of the time-dependent rotational-invariant slave boson methodology allows us to treat nonequilibrium spins numerically fast and efficiently beyond linear response as well as beyond the band-theoretical or Heisenberg limit.

The structure of the quasicrystalline approximant ${\mathrm{Al}}_{13}{\mathrm{Co}}_4$(100) has been determined by surface x-ray diffraction (SXRD) and complementary density-functional-theory (DFT) calculations. Thanks to the use of a two-dimensional pixel detector, which speeds up the data acquisition enormously, an exceptionally large set of experimental data, consisting of 124 crystal truncation rods, has been collected and used to refine this complex structure of large unit cell and low symmetry. Various models were considered for the SXRD analysis. The best fit is consistent with a surface termination at the puckered type of planes but with a depletion of the protruding Co atoms. The surface energy of the determined surface model was calculated using DFT, and it takes a rather low value of $1.09{\mathrm{J}/\mathrm{m}}^2$. The results for the atomic relaxation of surface planes found by SXRD or DFT were in excellent agreement. This work opens up additional perspectives for the comprehension of related quasicrystalline surfaces.

We show how it is possible to trap two-dimensional massless Dirac fermions in spatially inhomogeneous magnetic fields, as long as the formed magnetic quantum dot (or ring) is of a slowly decaying nature. It is found that a modulation of the depth of the magnetic quantum dot leads to successive confinement-deconfinement transitions of vortexlike states with a certain angular momentum, until a regime is reached where only states with one sign of angular momentum are supported. We illustrate these characteristics with both exact solutions and a hitherto unknown quasi-exactly solvable model utilizing confluent Heun functions.

We address electrodynamic effects in plasma oscillations of a lossy 2D electron system whose dc 2D conductivity ${\sigma }_0$ is comparable to the speed of light $c$. We argue that the perpendicular constant magnetic field $B$ causes astonishing features of magnetoplasma dynamics. We show that plasmon-polariton spectra can be classified using a “relativistic” phase diagram ${\sigma }_0/c$ versus $B$. An extraordinarily low damping branch in magnetoplasmon-polariton spectra emerges at two phases of this diagram. Some magnetoplasmons at these phases are predicted to be undamped waves.

Recently, chiral-induced spin selectivity has been attracting intense interest. Here, we report a theoretical study of spin-dependent electron transport in achiral nanotubes contacted by nonmagnetic leads. Our results reveal that by properly connecting to the leads, the achiral nanotubes can present a pronounced spin filtering phenomenon even if the spin-orbit coupling is very weak. In addition, the spin selectivity effect holds for various achiral nanotubes with different radii and is still significant in the presence of strong disorder and dephasing. These findings open new opportunities of using achiral molecules in spintronic applications and could motivate further studies on spin transport along achiral systems.

Thorium and its compounds have received considerable attention in recent years due to the renewed interest in developing the thorium fuel cycle as an alternative nuclear energy technology. There is pressing current need to explore the physical properties essential to the fundamental understanding and practical application of these materials. Here we report on a computational study of thorium disulfide (${\mathrm{ThS}}_2$), which plays an important role in the thorium fuel reprocessing cycle. We have employed the density functional theory and evolutionary structure search methods to determine the crystal structures, electronic band structures, phonon dispersions and density of states, and thermodynamic properties of ${\mathrm{ThS}}_2$ under various pressure and temperature conditions. Our calculations identify several crystalline phases of ${\mathrm{ThS}}_2$ and a series of structural phase transitions induced by pressure and temperature. The calculated results also reveal electronic phase transitions from the semiconducting state in the low-pressure phases of ${\mathrm{ThS}}_2$ in the $Pnma$ and $Fm\overline{3}m$ symmetry to the metallic state in the high-pressure phases of ${\mathrm{ThS}}_2$ in the $Pnma$ and $I4/mmm$ symmetry. These results explain the experimental observation of the thermodynamic stability of the $Pnma$ phase of ${\mathrm{ThS}}_2$ at the ambient conditions and a pressure-induced structural phase transition in ${\mathrm{ThS}}_2$ around 40 GPa. Moreover, the present study reveals considerable additional information on the structural and electronic properties of ${\mathrm{ThS}}_2$ in a wide range of pressure and temperature. Such information provides key insights into the fundamental material behavior and the underlying mechanisms that lay the foundation for further exploration and application of ${\mathrm{ThS}}_2$.

The domain wall dynamics in magnetic nanowires is numerically studied with the Landau-Lifshitz-Gilbert equation. Below the Walker breakdown threshold, the domain wall presents a stable propagation, while above the threshold where the retrograde mode dominates, the oscillation period is controlled by the external field and anisotropy. More importantly, the dynamic effects of quenched disorder on the domain wall motion are explored. A continuous pinning-depinning phase transition is detected. The dynamic scaling form is analyzed with the data collapse of the domain wall velocity, and both the static and dynamic critical exponents are extracted.

High transverse magnetic field and zero field muon spin rotation and relaxation measurements have been carried out in a lightly oxygen-doped high-$T_c$ parent compound ${\mathrm{La}}_2{\mathrm{CuO}}_4$ in a temperature range from 2 K to 300 K. As in the stoichiometric compound, muon spin rotation spectra reveal, along with the antiferromagnetic local field, the presence of an additional source of magnetic field at the muon. The results indicate that this second magnetic order is driven by the antiferromagnetism at low temperature but the two magnetic orders decouple at higher temperature. The ability of ${\mu }^{+}\mathrm{SR}$ to detect this additional magnetism deteriorates with doping, thus rendering the technique impotent to reveal time-reversal symmetry breaking in superconductors.

We demonstrate robust interface strain-induced perpendicular magnetic anisotropy in atomically flat ferrimagnetic insulator $\mathrm{T}{\mathrm{m}}_3\mathrm{F}{\mathrm{e}}_5{\mathrm{O}}_{12}$ (TIG) films grown with pulsed laser deposition on a substituted $\mathrm{G}{\mathrm{d}}_3\mathrm{G}{\mathrm{a}}_5{\mathrm{O}}_{12}$ substrate which maximizes the tensile strain at the interface. In bilayers consisting of Pt and TIG, we observe large squared Hall hysteresis loops over a wide range of thicknesses of Pt at room temperature. When a thin Cu layer is inserted between Pt and TIG, the Hall hysteresis magnitude decays but stays finite as the thickness of Cu increases up to 5 nm. However, if the Cu layer is placed atop Pt instead, the Hall hysteresis magnitude is consistently larger than when the Cu layer with the same thickness is inserted in between for all Cu thicknesses. These results suggest that both the proximity-induced ferromagnetism and spin current contribute to the anomalous Hall effect.

We suggest indirect excitons in two-dimensional semiconductor heterostructures as a platform for the realization of a bosonic analog of the Bardeen-Cooper-Schrieffer superconductor. The quantum phase transition to a biexcitonic gapped state can be controlled in situ by tuning the electric field applied to the structure in the growth direction. The proposed playground should allow one to go to strongly correlated and high-temperature regimes, unattainable with Feshbach resonant atomic gases.

Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators $\left({\mathrm{l}}^{*}\text{-bits}\right)$ underlie localization in such systems. In dimensions $d>1$, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to ${\mathrm{l}}^{*}\text{-bits}$. Physical consequences of ${\mathrm{l}}^{*}\text{-bits}$ include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in $d=1$ and thermal eigenstates at all parameters in $d>1$. Near-term experiments in ultracold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of ${\mathrm{l}}^{*}\text{-bits}$.

We study a system-bath description in the strong-coupling regime where it is not possible to derive a master equation for the reduced density matrix by a direct expansion in the system-bath coupling. A particular example is a bath with significant spectral weight at low frequencies. Through a unitary transformation, it can be possible to find a more suitable small expansion parameter. Within such an approach, we construct a formally exact expansion of the master equation on the Keldysh contour. We consider a system diagonally coupled to a bosonic bath and expansion in terms of a nondiagonal hopping term. The lowest-order expansion is equivalent to the so-called $P\left(E\right)$ theory or noninteracting blip approximation. The analysis of the higher-order contributions shows that there are two different classes of higher-order diagrams. We study how the convergence of this expansion depends on the form of the spectral function with significant weight at zero frequency.

We theoretically investigate the ground-state properties of a quantum dot defined on the surface of a strong three-dimensional time-reversal invariant topological insulator. Confinement is realized by ferromagnetic barriers and Coulomb interaction is treated numerically for up to seven electrons in the dot. Experimentally relevant intermediate interaction strengths are considered. The topological origin of the dot has several consequences: (i) spin polarization increases and the ground state exhibits quantum phase transitions at specific angular momenta as a function of interaction strength, (ii) the onset of Wigner correlations takes place mainly in one spin channel, and (iii) the ground state is characterized by a robust persistent current that changes sign as a function of the distance from the center of the dot.

We propose a realization of pure spin currents and perfect valley filters based on a quantum anomalous Hall insulator, around which edge states with up spin and down spin circulate. By applying staggered sublattice potential on the strips along the edges of sample, the edge states with down spin can be pushed into the inner boundaries of the strips while the other edge states with up spin remain on the outer boundaries, resulting in spatially separated chiral states with perfect spin polarization. Moreover, a valley filter, which is immune to both long-range and short-range scatterers, can be engineered by additionally applying boundary potentials on the outmost lattices of the sample. We also find that the boundary potential can be used to control the size effect induced oscillation of the inner chiral states. The connection of the boundary potential to size effect is revealed.

We study theoretically the spontaneous edge current in a small chiral superconductor with surface roughness. We obtained self-consistent solutions of the pair potential and the vector potential by solving the quasiclassical Eilenberger equation and the Maxwell equation simultaneously. We then employed them to calculate numerically the spatial distribution of the chiral edge current in a small superconductor. The characteristic behavior of the spontaneous edge current depends strongly on the symmetries of the order parameters such as chiral $p$-, chiral $d$-, and chiral $f$-wave pairing. The edge current is robust under the surface roughness in the chiral $p$- and chiral $d$-wave superconductors. In the chiral $d$-wave case, the surface roughness tends to flip the direction of the chiral current. On the other hand, the edge current in a chiral $f$-wave superconductor is fragile when there is surface roughness. We also discuss the temperature dependence of a spontaneous magnetization, which is a measurable value in standard experiments.

Photonic crystal slabs are able to support optical bound states in the continuum. The latter are eigenmodes of the structure that are truly guided (no radiation leakage) despite the fact that they lie above the light cone within the continuum of radiation modes. Such peculiar states can be viewed as modes with an infinite quality factor $Q$. Therefore, the question of the behavior of Fano resonances, as optogeometrical parameters are tuned close to optical bound states in the continuum, is of importance for applications of photonic crystal slabs with ultrahigh $Q$ factors. We study theoretically the reflection and transmission of a photonic crystal slab close to an optical bound state in the continuum with a phenomenological approach involving the poles and zeros of the scattering matrix. In particular, we derive a general relation valid for asymmetric structures that gives the position of a pole in the complex plane as a function of the positions of the zeros. We provide closed-form expressions for the reflection and transmission. The proposed phenomenological approach is validated through rigorous numerical calculations.