Orbital-free density-functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as $\mathcal{O}\left(N\right)$ computation for system size $N$. We here develop a scheme of the OFDFT calculations based on the accurate and transferrable kinetic-energy density-functional (KEDF), which is created in an unprecedented way using appropriately constructed neural network (NN). We show that our OFDFT scheme reproduces the electron density obtained in the state-of-the-art DFT calculations and then provides accurate structural properties of 24 different systems, ranging from atoms, molecules, metals, semiconductors, and an ionic material. The accuracy and the transferability of our KEDF is achieved by our NN training system in which the kinetic-energy functional derivative (KEFD) at each real-space grid point is used. The choice of the KEFD as a set of training data is essentially important, because first it appears directly in the Euler equation, which one should solve, and second, its learning assists in reproducing the physical quantity expressed as the first derivative of the total energy. More generally, the present development of KEDF $T\left[\rho \right]$ is in the line of systematic expansion in terms of the functional derivatives ${\delta }^{{\ell }_1}T/\delta {\rho }^{{\ell }_1}$ through progressive increase of ${\ell }_1$. The present numerical success demonstrates the validity of this approach. The computational cost of the present OFDFT scheme indeed shows the $\mathcal{O}\left(N\right)$ scaling, as is evidenced by the computations of the semiconductor SiC used in power electronics.

We propose a class of tight-binding systems of interacting bosons with a flat band, which are exactly solvable in the sense that one can explicitly write down the unique ground state. The ground state is expressed in terms of local creation operators and apparently resembles that of a Mott insulator. Based on an exact representation in terms of a classical loop-gas model, we conjecture that the ground state may exhibit quasi Bose-Einstein condensation (BEC) and genuine BEC in dimension 2 and in dimension 3 or higher, respectively, still keeping Mott-insulator-like character. Our Monte Carlo simulation of the loop-gas model strongly supports this conjecture, i.e., the ground state undergoes a Kosterlitz-Thouless transition and exhibits quasi-BEC in two dimensions.

The coherent superposition of nonorthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset, Commun. Math. Phys. 356, 451 (2017)]. We propose a practical approach for performing a variational calculation based on such states. Our method is based on approximate imaginary-time equations of motion that decouple the dynamics of each Gaussian state forming the ansatz. It is independent of the lattice connectivity of the model and the implementation is highly parallelizable. To benchmark our variational method, we calculate the spin-spin correlation function and Rényi entanglement entropy of an Anderson impurity, allowing us to identify the screening cloud and compare to density matrix renormalization group calculations. Secondly, we study the screening cloud of the two-channel Kondo model, a problem difficult to tackle using existing numerical tools.

Open-dissipative systems obeying parity-time ($\mathcal{PT}$) symmetry are capable of demonstrating oscillatory dynamics akin to the conservative systems. In contrast to limit cycle solutions characteristic of nonlinear systems, the $\mathcal{PT}$-symmetric oscillations form a continuum of nonisolated orbits. However, precise sculpturing of the real potential and the gain-loss spatial profiles required for establishing of the $\mathcal{PT}$ symmetry is practically challenging. The optical devices, such as lasers, exhibit relaxation dynamics and do not operate as the $\mathcal{PT}$-symmetric systems. Here we demonstrate how these constraints can be overcome. We predict that a pair of optically trapped polariton condensates (a polariton dimer) can be excited and operated in the oscillating regime typical of the isolated systems. This regime can be realized in the presence of both dissipative and conservative coupling between the condensates and can be maintained at an arbitrary external pump intensity. Every orbit is characterized by a frequency comb appearing in the spectrum of a dimer in the presence of the conservative nonlinearity. Our results pave the way for the creation of the optical computing devices operating under the constant-wave external pumping.

Magnetoelectric multipoles, which are odd under both space-inversion $\mathcal{I}$ and time-reversal $\mathcal{T}$ symmetries, are fundamental in understanding and characterizing magnetoelectric materials. However, the detection of these magnetoelectric multipoles is often not straightforward as they remain “hidden” in conventional experiments in part since many magnetoelectrics exhibit combined $\mathcal{IT}$ symmetry. In this paper, we show that the antisymmetric Compton profile is a unique signature for all the magnetoelectric multipoles, since the asymmetric magnetization density of the magnetoelectric multipoles couples to space via spin-orbit coupling, resulting in an antisymmetric Compton profile. We develop the key physics of the antisymmetric Compton scattering using symmetry analysis and demonstrate it using explicit first-principles calculations for two well-known representative materials with magnetoelectric multipoles, insulating ${\mathrm{LiNiPO}}_4$ and metallic ${\mathrm{Mn}}_2\mathrm{Au}$. Our work emphasizes the crucial roles of the orientation of the spin moments, the spin-orbit coupling, and the band structure in generating the antisymmetric Compton profile in magnetoelectric materials.

Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge, and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localization transitions and mobility edges, and find the expressions of Lyapunov exponents for some models. We further introduce topological winding numbers of Floquet quasienergies to distinguish non-Hermitian quasicrystalline phases with different localization nature. Our discovery thus extend the study of quasicrystals to non-Hermitian Floquet systems, and provide an efficient way of modulating the topological and transport properties of these unique phases.

We investigate a polaronic excitation in a one-dimensional spin-1/2 Fermi gas with contact attractive interactions, using the complex Langevin method, which is a promising approach to evade a possible sign problem in quantum Monte Carlo simulations. We found that the complex Langevin method works correctly in a wide range of temperature, interaction strength, and population imbalance. The Fermi polaron energy extracted from the two-point imaginary Green's function is not sensitive to the temperature and the impurity concentration in the parameter region we considered. Our results show a good agreement with the solution of the thermodynamic Bethe ansatz at zero temperature.

The chiral hinge modes are the key feature of a second-order topological insulator in three dimensions. Here we propose a quadrupole index in combination of a slab Chern number in the bulk to characterize the flowing pattern of chiral hinge modes along the hinges at the intersection of the surfaces of a sample. We further utilize the topological field theory to present a picture of three-dimensional quantum anomalous Hall effect as a consequence of chiral hinge modes. The two bulk topological invariants can be measured in electric transport and magneto-optical experiments. In this way we establish the bulk-hinge correspondence in a three-dimensional second-order topological insulator.

A high-pressure phase of solid iodine is identified in the pressure range of 16–23 GPa at room temperature by reanalyzing the previous powder x-ray diffraction data. The phase VI has a four-dimensional (4D) incommensurately modulated structure, in which ${\mathrm{I}}_2$ molecules and zigzag chains of three iodine atoms coexist. This structural model can successfully explain the Raman scattering data previously reported. Furthermore, our method clarifies that the structure of phase V, which was once analyzed as a 4D incommensurately modulated structure, can be better described by a five-dimensional incommensurately modulated tetragonal lattice wherein two modulation waves run in orthogonal directions. Our findings show that the pressure-induced molecular dissociation proceeds in multiple stages that are more complex than previously thought. In addition, it has become necessary to describe the molecular dissociation pressure separately for the starting pressure $P_s$ of 16 GPa and the finishing pressure $P_f$ of 29 GPa. This transition process has finally resolved the contradiction with the Mössbauer experiment.

Within a Dirac model in $1+1$ dimensions, a prototypical model to describe low-energy physics for a wide class of lattice models, we propose a field-theoretical version for the representation of Wannier functions, the Zak-Berry connection, and the geometric tensor. In two natural Abelian gauges we present universal scaling of the Dirac Wannier functions in terms of four fundamental scaling functions that depend only on the phase $\gamma$ of the gap parameter and the charge correlation length $\xi$ in an insulator. The two gauges allow for a universal low-energy formulation of the surface charge and surface fluctuation theorem, relating the boundary charge and its fluctuations to bulk properties. Our analysis describes the universal aspects of Wannier functions for the wide class of one-dimensional generalized Aubry-André-Harper lattice models. In the low-energy regime of small gaps we demonstrate universal scaling of all lattice Wannier functions and their moments in the corresponding Abelian gauges. In particular, for the quadratic spread of the lattice Wannier function, we find the universal result $Za\xi /8$, where $Za$ is the length of the unit cell. This result solves a long-standing problem providing further evidence that an insulator is only characterized by the two fundamental length scales $Za$ and $\xi$. Finally, we discuss also non-Abelian lattice gauges and find that lattice Wannier functions of maximal localization show universal scaling and are uniquely related to the Dirac Wannier function of the lower band. In addition, via the winding number of the determinant of the non-Abelian transformation, we establish a bulk-boundary correspondence for the number of edge states up to the bottom of a certain band, which requires no symmetry constraints. Our results present evidence that universal aspects of Wannier functions and of the boundary charge are uniquely related and can be elegantly described within universal low-energy theories.

We develop a microscopic theory of multipole interactions and orderings in $5d^2$ transition metal ion compounds. In a cubic environment, the ground state of $5d^2$ ions is a non-Kramers $E_g$ doublet, which is nonmagnetic but hosts quadrupole and octupole moments. We derive low-energy pseudospin one-half Hamiltonians describing various spin-orbital exchange processes between these ions. Direct overlap of the $t_{2g}$ orbitals results in bond-dependent pseudospin interactions similar to those for $e_g$ orbitals in manganites, except for different orientations of the pseudospin easy axes. On the other hand, the superexchange process, where two different $t_{2g}$ orbitals communicate via oxygen ions, generates new types of pairwise interactions. In perovskites with ${180}^{\circ }$ bonding, we find nearly equal mixture of Heisenberg and $e_g$ orbital compass-type couplings. The ${90}^{\circ }$ superexchange in compounds with edge-shared octahedra is most unusual: Despite highly anisotropic shapes of the $E_g$ wave functions, the pseudospin interactions have no bond dependence. We consider the $E_g$ pseudospin models on various lattices and obtain their ground state properties using analytical and numerical methods. On the honeycomb lattice, we observe a duality with the extended Kitaev model, and use it to uncover a critical point where the quadrupole and octupole states are exactly degenerate. On the triangular lattice, an exotic pseudospin state, corresponding to the coherent superposition of vortex-type quadrupole and ferri-type octupole orders, is realized due to geometrical frustration. This state breaks both spatial and time-reversal symmetries, but possesses no dipolar magnetism. We also consider Jahn-Teller coupling effects and lattice mediated interactions between $E_g$ pseudospins, and find that they support quadrupole order. Possible implications of the results for recent experiments on double perovskite osmates are discussed, including effects of local distortions on the pseudospin wave functions and interactions.

In a noncentrosymmetric system, an intrinsic electric polarization is allowed and may lead to unusual nonreciprocal charge transport phenomena. As a result, a current-dependent resistance, arising from the magnetoelectric anisotropy term of $k·\vec{E}\times \vec{B}$, appears and acts as a current rectifier with the amount of rectification being linearly proportional to the magnitude of both current and applied magnetic field. In this work, a different type of nonreciprocal transport effect was demonstrated in a graphene-based device, which requires no external magnetic field. Due to the unique pseudospin (valley) degree of freedom in chiral fermions with trigonal warping, a large nonreciprocal transport effect was uncovered in a gapped bilayer graphene, where electric-field tunabilities of the band gap and valley polarization play an important role. The exact cancellation of nonreciprocal effect between two different valleys is effectively removed by breaking the inversion symmetry via electric gatings. The magnitude of the current rectification appears to be at a maximum when the Fermi surface undergoes a Lifshitz transition near the band edges, which is proportional to the current and the displacement field strength. The full electric-field tuning of the nonreciprocal transport effect without a magnetic field opens up a new direction for valleytronics in two-dimensional-based devices.

In the 35 years since the discovery of cuprate superconductors, we have not yet reached a unified understanding of their properties, including their material dependence of the superconducting transition temperature $T_{\text{c}}$. The preceding theoretical and experimental studies have provided an overall picture of the phase diagram, and some important parameters for the $T_{\text{c}}$, such as the contribution of the Cu $d_{z^2}$ orbital to the Fermi surface and the site-energy difference ${\mathrm{\Delta }}_{dp}$ between the Cu $d_{x^2-y^2}$ and O $p$ orbitals. However, they are somewhat empirical and limited in scope, always including exceptions, and do not provide a comprehensive view of the series of cuprates. Here we propose a four-band $d\text{−}p$ model as a minimal model to study material dependence in cuprates. Using the variational Monte Carlo method, we theoretically investigate the phase diagram for the ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{HgBa}}_2{\mathrm{CuO}}_4$ systems and the correlation between the key parameters and the superconductivity. Our results comprehensively account for the empirical correlation between $T_{\text{c}}$ and model parameters, and thus can provide a guideline for new material design. We also show that the effect of the nearest-neighbor $d\text{−}d$ Coulomb interaction $V_{dd}$ is actually quite important for the stability of superconductivity and phase competition.

We develop a formalism to describe the scattering of dark matter (DM) particles by electrons bound in crystals for a general form of the underlying DM-electron interaction. Such a description is relevant for direct-detection experiments of DM particles lighter than a nucleon, which might be observed in operating DM experiments via electron excitations in semiconductor crystal detectors. Our formalism is based on an effective theory approach to general nonrelativistic DM-electron interactions, including the anapole, and magnetic and electric dipole couplings, combined with crystal response functions defined in terms of electron wave function overlap integrals. Our main finding is that, for the usual simplification of the velocity integral, the rate of DM-induced electronic transitions in a semiconductor material depends on at most five independent crystal response functions four of which are distinct from the usual scalar response. We identify these crystal responses and evaluate them using density functional theory for crystalline silicon and germanium, which are used in operating DM direct-detection experiments. Our calculations allow us to set 90% confidence level limits on the strength of DM-electron interactions from data reported by the SENSEI and EDELWEISS experiments. The crystal response functions discovered in this paper encode properties of crystalline solids that do not interact with conventional experimental probes, suggesting the use of the DM wind as a probe to reveal new kinds of hidden order in materials.

We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization, are fragile and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs those that depend on local trajectories.

We study the Hall effect in square, planar type-II superconductors using numerical simulations of time dependent Ginzburg-Landau (TDGL) equations. The Hall field in some type-II superconductors displays sign-change behavior at some magnetic fields due to the induced field of vortex flow when its contribution is strong enough to reverse the field direction. In this paper, we use modified TDGL equations which couple an externally applied current, and also incorporate normal-state and flux-flow Hall effects. We obtain the profile of Hall angle as a function of applied magnetic field for six different sizes $(l\times l)$ of the superconductor: $l/\xi \in \{3,5,15,20,100,200\}$. We obtain vastly different profiles for different size regimes, proving that size is an important parameter that determines Hall behavior. We find that electric field dynamics provide an insight into several anomalous features including a sign change of the Hall angle, and leads us to the precise transient behavior of the order parameter responsible for them.

The concept of generalized Gibbs ensembles (GGEs) has been introduced to describe steady states of integrable models. Recent advances show that GGEs can also be stabilized in nearly integrable quantum systems when driven by external fields and open. Here, we present a weakly dissipative dynamics that drives towards a steady-state GGE and is realistic to implement in systems of trapped ions. We outline the engineering of the desired dissipation by a combination of couplings which can be realized with ion-trap setups and discuss the experimental observables needed to detect a deviation from a thermal state. We present a mixed-species motional mode engineering technique in an array of microtraps and demonstrate the possibility to use sympathetic cooling to construct many-body dissipators. Our paper provides a blueprint for experimental observation of GGEs in open systems and opens an avenue for quantum simulation of driven-dissipative quantum many-body problems.