We consider the fractional quantum Hall effect at the filling factor $\nu =4/11$, where two independent experiments have observed a well-developed and quantized Hall plateau. We examine the Abelian state described by the “$4\overline{2}{1}^3$” parton wave function and numerically demonstrate it to be a plausible candidate for the ground state at $\nu =4/11$. We work out the low-energy effective theory of the $4\overline{2}{1}^3$ edge and make predictions for experimentally measurable properties of the state.

We extend the recently developed quantum quasi Monte Carlo (QQMC) approach to obtain the full frequency dependence of Green functions in a single calculation. QQMC is a general approach for calculating high-order perturbative expansions in power of the electron-electron interaction strength. In contrast to conventional Markov chain Monte Carlo sampling, QQMC uses low-discrepancy sequences for a more uniform sampling of the multidimensional integrals involved and can potentially outperform Monte Carlo by several orders of magnitude. A core concept of QQMC is the a priori construction of a “model function” that approximates the integrand and is used to optimize the sampling distribution. In this paper, we show that the model function concept extends to a kernel approach for the computation of Green functions. We illustrate the approach on the Anderson impurity model and show that the scaling of the error with the number of integrand evaluations $N$ is $\sim 1/N^{0.86}$ in the best cases and comparable to Monte Carlo scaling $\sim 1/N^{0.5}$ in the worst cases. We find a systematic improvement over Monte Carlo sampling by at least two orders of magnitude while using a basic form of model function. Finally, we compare QQMC results with calculations performed with the fork tensor product state (FTPS) method, a recently developed tensor network approach for solving impurity problems. Applying a simple Padé approximant for the series resummation, we find that QQMC matches the FTPS results beyond the perturbative regime.

We investigate superradiantlike dynamics of a nuclear-spin bath in contact with an electron shuttle, modeled as a moving quantum dot trapping a single electron. The dot is shuttled between two external reservoirs, where electron-nuclear flip flops are associated with tunneling events. For an ideal model with uniform hyperfine interaction, realized through an isotopically enriched “nuclear-spin island”, we discuss in detail the nuclear spin evolution and its relation to superradiance. We then show that the superradiantlike evolution is robust to various extensions of the initial setup, and derive the minimum shuttling time which allows to escape adiabatic spin evolution. We also discuss slow/fast shuttling under the inhomogeneous field of a nearby micromagnet and compare our scheme to a model with stationary quantum dot. Finally, we describe the electrical detection of nuclear entanglement in the framework of Monte Carlo wave-function simulations.

Quantum materials having Dirac fermions in conjunction with superconductivity is believed to be the candidate material to realize exotic physics as well as advanced technology. Angle-resolved photoemission spectroscopy (ARPES), a direct probe of the electronic structure, has been extensively used to study these materials. However, experiments often exhibit conflicting results on dimensionality and momentum of the Dirac fermions (e.g., Dirac states in BiPd, a novel noncentrosymmetric superconductor), which is crucial for the determination of the symmetry, time-reversal invariant momenta, and other emerging properties. Employing high-resolution ARPES at varied conditions, we demonstrated a methodology to identify the location of the Dirac node accurately and discover that the deviation from two dimensionality of the Dirac states in BiPd proposed earlier is not a material property. These results helped to reveal the topology of the anisotropy of the Dirac states accurately. We have constructed a model Hamiltonian considering higher-order spin-orbit terms and demonstrate that this model provides an excellent description of the observed anisotropy. Intriguing features of the Dirac states in a noncentrosymmetric superconductor revealed in this study are expected to have significant implications regarding the properties of topological superconductors.

A detailed account of the implementation of equations of the relativistic density functional theory (RDFT) using basis sets of APW/LAPW type with flexible extensions provided by local orbitals is given. Earlier discoveries of the importance of the high derivative local orbital (HDLO) extension of the APW/LAPW basis set for enhancing the accuracy of DFT calculations are confirmed using a fully relativistic approach and $\alpha -U$ as an example. High energy local orbitals (HELO's), however indispensable for GW calculations, are considerably less efficient in enhancing the accuracy of DFT applications. It is shown that a simplified approach to the relativistic effects, namely considering them only inside the muffin-tin (MT) spheres, produces basically identical results (as compared to fully relativistic approach) for the electronic free energy of the five materials considered in this work. By comparing the effect of the simplified approach on the electronic free energy with its effect on the electronic kinetic energy we conclude that the insensitivity of the free energy to the way we describe the relativistic effects in the interstitial region is related to the variational property of this quantity.

The description of electronic exchange-correlation effects is of paramount importance for many applications in physics, chemistry, and beyond. In a recent paper, Dornheim et al. [Phys. Rev. Lett. 125, 235001 (2020)] have presented the effective static approximation (ESA) to the local field correction (LFC), which allows for the highly accurate estimation of electronic properties such as the interaction energy and the static structure factor. In this work, we give an analytical parametrization of the LFC within ESA that is valid for any wave number, and available for the entire range of densities ($0.7\le r_s\le 20$) and temperatures ($0\le \theta \le 4$) that are relevant for applications both in the ground state and in the warm dense matter regime. A short implementation in python is provided, which can easily be incorporated into existing codes. In addition, we present an extensive analysis of the performance of ESA regarding the estimation of various quantities like the dynamic structure factor, static dielectric function, the electronically screened ion potential, and also the stopping power in an electronic medium. In summary, we find that the ESA gives an excellent description of all these quantities in the warm dense matter regime, and only becomes inaccurate when the electrons start to form a strongly correlated electron liquid ($r_s\sim 20$). Moreover, we note that the exact incorporation of exact asymptotic limits often leads to a superior accuracy compared to the neural-net representation of the static LFC [T. Dornheim et al., J. Chem. Phys. 151, 194104 (2019)].

Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While remarkable progress has been witnessed in recent years for one-dimensional systems, much less has been achieved for interacting quantum models in higher dimensions, since they incorporate an additional layer of complexity. In this work, we employ a variational method that allows for an efficient and controlled computation of the dynamics of quantum many-body systems in one and higher dimensions. The approach presented here introduces a variational class of wave functions based on complex networks of classical spins akin to artificial neural networks, which can be constructed in a controlled fashion. We provide a detailed prescription for such constructions and illustrate their performance by studying quantum quenches in one- and two-dimensional models. In particular, we investigate the nonequilibrium dynamics of a genuinely interacting two-dimensional lattice gauge theory, the quantum link model, for which we have recently shown—employing the technique discussed thoroughly in this paper—that it features disorder-free localization dynamics [P. Karpov et al., Phys. Rev. Lett. 126, 130401 (2021)]. The present work not only supplies a framework to address purely theoretical questions but also could be used to provide a theoretical description of experiments in quantum simulators, which have recently seen an increased effort targeting two-dimensional geometries. Importantly, our method can be applied to any quantum many-body system with a well-defined classical limit.

We study the background (equilibrium), linear, and nonlinear spin currents in two-dimensional (2D) Rashba spin-orbit coupled systems with Zeeman splitting and in three-dimensional (3D) noncentrosymmetric metals using a modified spin current operator by inclusion of the anomalous velocity. The linear spin Hall current arises due to the anomalous velocity of charge carriers induced by the Berry curvature. The nonlinear spin current occurs due to the band velocity and/or the anomalous velocity. For 2D Rashba systems, the background spin current saturates at high Fermi energy (independent of the Zeeman coupling), linear spin current exhibits a plateau at the “Zeeman” gap, and nonlinear spin currents are peaked at the gap edges. The magnitude of the nonlinear spin current peaks enhances with the strength of Zeeman interaction. The linear spin current is polarized out-of-plane, while the nonlinear ones are polarized in-plane. We witness pure anomalous nonlinear spin current with spin polarization along the direction of propagation. In 3D noncentrosymmetric metals, background and linear spin currents are monotonically increasing functions of Fermi energy, while nonlinear spin currents vary nonmonotonically as a function of Fermi energy and are independent of the Berry curvature. These findings may provide useful information to manipulate spin currents in Rashba spin-orbit coupled systems.

Ensembles with long-range interactions between particles are promising for revealing strong quantum collective effects and many-body phenomena. Here we study the ground-state phase diagram of a two-dimensional Bose system with quadrupolar interactions using a diffusion Monte Carlo technique. We predict a quantum phase transition from a gas to a solid phase. The Lindemann ratio and the condensate fraction at the transition point are $\gamma =0.269\left(4\right)$ and $n_0/n=0.031\left(4\right)$, correspondingly. We observe the strong rotonization of the collective excitation branch in the vicinity of the phase transition point. Our results can be probed using state-of-the-art experimental systems of various nature, such as quasi-two-dimensional systems of quadrupolar excitons in transition metal dichalcogenide trilayers, quadrupolar molecules, and excitons or Rydberg atoms with quadrupole moments induced by strong magnetic fields.

The development of nanomaterials with a large nonlinear susceptibility is essential for nonlinear nanophotonics. We show that transition metal dichalcogenide (TMD) nanotriangles have a large effective second-order susceptibility $\left[{\chi }^{\left(2\right)}\right]$ at midinfrared to near-infrared frequencies owing to their broken centrosymmetry. ${\chi }^{\left(2\right)}$ is calculated within the density-matrix formalism that accounts for dissipation and screening. ${\chi }^{\left(2\right)}$ peaks in the vicinity of both two-photon resonances (specified by the geometry) and plasmon resonances (tunable via the carrier density). Aligning the resonances yields the values of ${\chi }^{\left(2\right)}$ as high as ${10}^{-6}\mathrm{m}/\mathrm{V}$. These findings underscore the potential of TMD nanotriangles for nonlinear nanophotonics, particularly second-harmonic generation.

We use dispersion-corrected density functional theory to determine the relative energies of competing polytypes of bulk layered hexagonal post transition metal chalcogenides to search for the most stable structures of these potentially technologically important semiconductors. We show that there is some degree of consensus among dispersion-corrected exchange-correlation functionals regarding the energetic orderings of polytypes, but we find that for each material there are multiple stacking orders with relative energies of less than 1 meV per monolayer unit cell, implying that stacking faults are expected to be abundant in all post transition metal chalcogenides. By fitting a simple model to all our energy data, we predict that the most stable hexagonal structure has the $P{6}_3/mmc$ space group in each case but that the stacking order differs between GaS, GaSe, GaTe, and InS, on the one hand, and InSe and InTe, on the other. At zero pressure, the relative energies obtained with different functionals disagree by around 1–5 meV per monolayer unit cell, which is not sufficient to identify the most stable structure unambiguously; however, multigigapascal pressures reduce the number of competing phases significantly. At higher pressures, an ${\mathrm{AB}}^{\prime }$-stacked structure of the most stable monolayer polytype is found to be the most stable bulk structure.

We have investigated the spin and oxidation states of Co in ${\mathrm{Co}}_3{\mathrm{BO}}_5$ using x-ray magnetic circular dichroism (XMCD) and dc magnetic susceptibility measurements. At low temperatures, XMCD experiments have been performed at the Co $K$-edge in ${\mathrm{Co}}_3{\mathrm{BO}}_5$ and ${\mathrm{Co}}_2{\mathrm{FeBO}}_5$ single crystals in the fully ferrimagnetically ordered phase. The Co ($K$-edge) XMCD signal is found to be related to the ${\mathrm{Co}}^{2+}$ magnetic sublattices in both compounds, providing strong experimental support for the low-spin (LS) ${\mathrm{Co}}^{3+}$ scenario. The paramagnetic susceptibility is highly anisotropic. An estimation of the effective magnetic moment in the temperature range 100–250 K correlates well with two ${\mathrm{Co}}^{2+}$ ions in the high-spin (HS) state and some orbital contribution, while ${\mathrm{Co}}^{3+}$ remains in the LS state. The crystal structure of the ${\mathrm{Co}}_3{\mathrm{BO}}_5$ single crystal has been solved in detail at the $T$ range 296–703 K. The unit cell parameters and volume show anomalies at 500 and 700 K. The octahedral environment of the Co4 site strongly changes with heating. The generalized gradient approximation with Hubbard $U$ correction calculations have revealed that, at low-temperatures, the system is insulating with a band gap of 1.4 eV, and the ${\mathrm{Co}}^{2+}$ ions are in the HS state, while ${\mathrm{Co}}^{3+}$ are in the LS state. At high temperatures ($T$ > 700 K), the charge ordering disappears, and the system becomes metallic with all Co ions in $3d^7$ electronic configuration and HS state.

Topological nodal line semimetals offer an attractive platform to investigate exotic phenomena related to spintronics. Herein, we discover the existence of topological nodal-net semimetal states in metal dihydrides $M{\mathrm{H}}_2$ ($M=\mathrm{Hf}$, Th), a class of well-known hydrogen storing and superconducting materials. These materials host a fascinating nodal-net-like band degeneracy around the Fermi level, including triply degenerate points and multiple Dirac nodal lines (DNLs) in three mirror planes. Importantly, the inclusion of spin-orbit coupling breaks the degeneracy of DNLs, contributing to giant spin Hall conductivity values that are robust against large concentrations of charge doping. Furthermore, due to the rather small intrinsic electronic conductivities, large spin Hall angles can be achieved in $M{\mathrm{H}}_2$ for practice applications.

The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the $k$ space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the $c$ axis and magnetic field rotating in the $ab$ plane. The extremal orbits identified through the field orientation dependence of the QOs interlock with the nodal line, leading to a nonzero Berry phase. Most importantly, the Berry phase shows a significant dependence on the magnetic field orientation, which we argue to be due to the finite spin-orbit coupling gap. Our results demonstrate the importance of the spin-orbit coupling and the nodal-line dispersion in understanding the quantum transport of NLSMs.

Matrix product states (MPS) and “dressed” ground states of quadratic mean fields (e.g., Gutzwiller projected Slater determinants) are both important classes of variational wave functions. This latter class has played important roles in understanding superconductivity and quantum spin liquids. We present a method to obtain both the finite and infinite MPS (iMPS) representation of the ground state of an arbitrary fermionic quadratic mean-field Hamiltonian (which in the simplest case is a Slater determinant and in the most general case is a Pfaffian). We also show how to represent products of such states (e.g., determinants times Pfaffians). From this representation one can project to single occupancy and evaluate the entanglement spectra after Gutzwiller projection. We then obtain the MPS and iMPS representation of Gutzwiller projected mean-field states that arise from the variational slave-fermion approach to the $S=1$ bilinear-biquadratic quantum spin chain. To accomplish this, we develop an approach to orthogonalize degenerate iMPS to find all the states in the degenerate ground-state manifold. We find the energies of the MPS and iMPS states match the variational energies closely, indicating the method is accurate and there is minimal loss due to truncation error. We then present an exploration of the entanglement spectra of projected slave-fermion states, exploring their qualitative features and finding good qualitative agreement with the respective exact ground-state spectra found from density matrix renormalization group.

The intrinsic anomalous Hall effect is one of the most exciting manifestations of the geometric properties of the electronic wave function. The electronic wave-function's geometric nature also gives rise to a purely quantum-mechanical intrinsic (scattering time-independent) Hall conductivity in the presence of a magnetic field. Here, we demonstrate that the orbital magnetic moment and the anomalous Hall velocity can combine to generate a scattering time-independent contribution to the thermoelectric and thermal Hall effects in addition to the Lorentz force-induced scattering time-dependent “classical” contribution. Considering specific examples of two-dimensional and three-dimensional systems, we explicitly: (i) show that neglecting the intrinsic charge Hall conductivity leads to an underestimation of the charge-carrier density in Hall measurement, and (ii) explore the implications of intrinsic thermoelectric Hall conductivity on the Nernst coefficient and the magneto-Seebeck effect.

When spin-polarized electrons flow through a magnetic texture a transfer torque is generated. We examine the effect of this torque on skyrmions and skyrmion bags, skyrmionic structures of arbitrary integer topological degree, in thin ferromagnetic films. Using micromagnetic simulations and analysis from the well-known Thiele equation, we explore the potential for sorting or binning skyrmions of varying degrees mechanically. We investigate the applicability of the Thiele equation to problems of this nature and derive a theory of skyrmion deflection ordered by topological degree. We show that skyrmions and skyrmion bags have the potential to move in different directions under a constant current, which has significant potential for technical applications.

The vibrational properties of the Si(553)-Au surface are studied by Raman spectroscopy and ab initio calculations. A multitude of surface localized phonon modes with wave number below 200 ${\mathrm{cm}}^{-1}$ is experimentally observed, along with two modes at about 400 ${\mathrm{cm}}^{-1}$. Atomistic models within density functional theory allow to assign the low-energy spectral features to vibrations within the Au chain, while the Raman signatures at higher energies are mostly localized at the Si step edge. The Raman activity of nominally silent modes associated with a large charge transfer between Au chain and Si step edge states is explained by scattering at charge density fluctuations. Temperature-dependent measurements reveal specific mode shifts that are discussed in terms of a recently proposed order-disorder phase transition. The presence of model-specific displacement patterns allows us to identify the structural models compatible with the measured spectra at low and at room temperature.