The thickness, temperature, and composition studies of spin diffusion length (SDL) and spin Hall angle (SHA) are performed by measuring the spin Hall magnetoresistance in ${\mathrm{Pd}}_{1-x}{\mathrm{Pt}}_x/{\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (=YIG) heterostructures. The SDL is found to be invariant to changes in the electron momentum relaxation time by varying the temperature, the normal metal (NM) thickness, or the alloy composition, while the SHA exhibits a nonmonotonic dependence on temperature. These findings suggest the appearance of D'yakonov-Perel' spin relaxation mechanism and phonon skew scattering in our heterostructures that is associated with strong interfacial Rashba spin-orbit coupling (IRSOC). At last, we employ the ab initio calculations to quantify the IRSOC at the inversion-symmetry-broken NM/YIG interface.

We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.

Intense time-periodic laser fields can transform the electronic structure of a solid into strongly modified Floquet-Bloch bands. While this suggests multiple pathways to induce electronic orders such as superconductivity or charge density waves, the possibility of preparing low-energy phases of Floquet Hamiltonians remains unclear because of the energy absorption at typical experimentally accessible driving frequencies. Here we investigate a realistic pathway towards laser control of electronic orders, which is the transient enhancement of fluctuating orders. Using a conserving Keldysh Green's function formalism, we simulate the buildup of short range Cooper-pair correlations out of a normal metal in the driven attractive Hubbard model. Even for frequencies only slightly above or within the bandwidth, a substantial enhancement of correlations can be achieved before the system reaches a high electronic temperature. This behavior relies on the nonthermal nature of the driven state. The effective temperature of the electrons at the Fermi surface, which more closely determines the superconducting correlations, remains lower than an estimate from the global energy density. Even though short ranged, the fluctuations can have marked signatures in the electronic spectra.

We theoretically investigate photoresponses of a correlated electron system upon stimuli of a pulsed laser light. Real-time dynamics of an interacting spinless fermion model on a one-dimensional chain, as a model of charge order (CO), are numerically simulated using the time-dependent Hartree-Fock method. In particular, we discuss the differences between two situations as the initial state: the homogeneous order and the presence of a domain wall, i.e., a kink structure embedded in the CO bulk. Coherent dynamics are seen in the former case: When the frequency of the pump light ${\omega }_p$ is varied, along with single particle excitations across the CO gap (${\mathrm{\Delta }}_{\mathrm{CO}}$), the resonantly-excited collective phase mode near ${\omega }_p\simeq {\mathrm{\Delta }}_{\mathrm{CO}}/2$ efficiently destabilizes CO. In clear contrast, in the latter case, when ${\omega }_p$ is tuned at such in-gap frequencies and the intensity of light is sufficiently large, inhomogeneity spreads out from the kink to the bulk region through kink creations. Moreover, even stronger intensity induces the inhomogeneous melting of CO where the CO gap is destroyed.

We check the accuracy of the constrained random phase approximation (cRPA) downfolding scheme by considering one-dimensional two- and three-orbital Hubbard models with a target band at the Fermi level and one or two screening bands away from the Fermi level. Using numerically exact quantum Monte Carlo simulations of the full and downfolded model, we demonstrate that depending on filling, the effective interaction in the low-energy theory is either barely screened or antiscreened, in contrast to the cRPA prediction. This observation is explained by a functional renormalization group analysis, which shows that the cRPA contribution to the screening is to a large extent canceled by other diagrams in the direct particle-hole channel. We comment on the implications of this finding for the ab initio estimation of interaction parameters in low-energy descriptions of solids.

By generalizing the Kubo-Streda formula for calculating electrical conductivities to the thermoelectric coefficients, we theoretically study the anomalous Nernst effect (ANE) on the surface of a topological insulator induced by a finite concentration of magnetic impurities. The ANE is found to be modulated by the impurity scattering and thermal fluctuations, simultaneously, and so exhibits rich structures in the energy space. While the anomalous Hall conductivity is half-integer quantized with the Fermi level across the magnetic-impurity-induced gap, the anomalous Nernst signal (ANS) is fully suppressed and the thermopower is linear dependent on the Fermi energy. Around the magnetic-impurity-induced localized levels, the ANS and thermopower are resonant enhanced. The suppression and enhancement of the thermoelectric coefficients will compete with each other as the magnetic impurity potential increases continually. More interestingly, when a finite charge potential is included, the resonant peaks of the ANS and thermopower will be renormalized, making the signs of the ANS and thermopower tunable by the strength of the charge potential.

We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states, our results provide a theoretical justification for the use of White's algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics.

The density functional theory $\left(\mathrm{DFT}\right)+U$ method is a pragmatic and effective approach for calculating the ground-state properties of strongly correlated systems, and linear-response calculations are widely used to determine the requisite Hubbard parameters from first principles. We provide a detailed treatment of spin within the linear-response framework, demonstrating that the conventional Hubbard $U$ formula, unlike the conventional $\mathrm{DFT}+U$ corrective functional, incorporates interactions that are off-diagonal in the spin indices and places greater weight on one spin channel over the other. We construct alternative definitions for Hubbard and Hund's parameters that are consistent with the contemporary $\mathrm{DFT}+U$ functional, expanding upon the minimum-tracking linear-response method. This approach allows Hund's $J$ and spin-dependent $U$ parameters to be calculated with the same ease as for the standard Hubbard $U$. Our methods accurately reproduce the experimental band gap, local magnetic moments, and the valence band edge character of manganese oxide, a canonical strongly correlated system. We also apply our approach to a complete series of transition-metal complexes ${\left[M{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{n+}$ (for $M=\text{Ti}$ to Zn), showing that Hubbard corrections on oxygen atoms are necessary for preserving bond lengths, and demonstrating that our methods are numerically well behaved even for near-filled subspaces such as in zinc. However, spectroscopic properties appear to be beyond the reach of standard $\mathrm{DFT}+U$. Collectively, these results shed new light on the role of spin in the calculation of the corrective parameters $U$ and $J$, and point the way toward avenues for further development of $\mathrm{DFT}+U$ and related methods.

We studied the real-space structure of states in twisted bilayer graphene at the magic angle $\theta =1.{08}^{\circ }$. The flat bands close to charge neutrality are composed of a mix of “ring” and “center” orbitals around the AA stacking region. An effective model with localized orbitals is constructed which necessarily includes more than just the four flat bands. Long-range Coulomb interaction causes a charge transfer at half filling of the flat bands from the center to the ring orbitals. Consequently, the Mott phase is a featureless spin-singlet paramagnet. We estimate the effective Heisenberg coupling that favors the singlet coupling to be $J=3.3$ K, consistent with experimental values. The superconducting state depends on the nature of the dopants: hole-doping yields $\left(p+ip\right)$-wave, whereas electron-doping yields $\left(d+id\right)$-wave pairing symmetry.

A detailed analysis of the theoretical x-ray absorption near-edge structures (XANES) for the boron and nitrogen $K$ edge in hexagonal boron nitride ($h$-BN) employing density-functional theory calculations is presented. The supercell core-hole method and the Bethe-Salpeter equation are used for the description of electron-hole interactions. The calculations are carried out with two different codes, the vasp and the wien2k codes, employing the projector augmented-wave and the full-potential linear augmented-plane-wave methods, respectively. We find close agreement between spectra obtained from the two codes and between calculations using the supercell core-hole method and the Bethe-Salpeter approach. All our calculations, as well as previous calculations using the ground-state structure, yield a single $2p_{{\sigma }^{*}}$ peak in the boron $K$-edge spectrum and hence fail to describe the experimental double-peak structure. We find that the inclusion of electron-phonon interactions is crucial to obtain the experimentally observed double-peak structure. We include these effects fully parameter free and ab initio using a one-shot sampling method and obtain excellent agreement with experiment.

In this work, we show that an $N_{\mathrm{C}}$-chain gate potential along the armchair chain (direction $\widehat{y}$) of a graphene sheet gives rise to topological localized states (LSs): one branch for $N_{\mathrm{C}}=1$ and two branches for $N_{\mathrm{C}}\ge 2$. These LSs are shown to form whenever the gate-induced potential $V_0$ is nonzero. The topological nature behind the formation of these LSs is revealed (for $N_{\mathrm{C}}=1,2$) by showing, for $V_0\ne 0$, that the LS-secular equation can be cast into a pseudospin-rotation form on which rotation upon a valley-associated pseudospin is to equate with another valley-associated pseudospin. Both pseudospins are on the same side of the gate potential. That the rotation angle of the pseudospin-rotation operator falls within the range of variation of the relative angle $\mathrm{\Delta }{\theta }_p$ between the two pseudospins, as the energy $E$ varies across the entire energy gap for a given $k_y$, demonstrates the topological nature and the inevitability of the LS branch formation. These topological LS branches exhibit Dirac-point characteristics, with dispersion relations leading out from the Dirac point (at $k_y=0$). For general multiple ($N_{\mathrm{C}}>1$) carbon chain gate-potential cases, the number $N_{\mathrm{LS}}$ of LS branches are found to increase with $V_0$, up to a maximum of $N_{\mathrm{LS},\max }=N_{\mathrm{C}}$. Yet LS branches carrying the Dirac-point characteristics are found to be fixed at two.

We investigate the low-temperature transport in 8-nm-diam Si junctionless nanowire field-effect transistors fabricated by top down techniques with a wraparound gate and two different phosphorus doping concentrations. First we extract the intrinsic gate capacitance of the device geometry from a device that demonstrates Coulomb blockade at 12 mK with over 500 Coulomb peaks across a gate-voltage range of 6 V indicating the formation of an island in the entire 150-nm-long nanowire channel. In two other devices, made from silicon on insulator wafers that were doped to an activated dopant concentration of Si:P $4\times {10}^{19}$ and $2\times {10}^{20}{\text{cm}}^{-3}$, we observe quantum interference and use the extracted gate coupling to determine the mean free paths from the dominant energy scale on the gate-voltage axis. For the higher doped device, the analysis yields a mean free path of $4\pm 2\text{nm}$, which is on the order of the average spacing of phosphorus atoms and suggests scattering on unactivated or activated dopants. For the device with an implanted phosphorus density of $4\times {10}^{19}{\text{cm}}^{-3}$, the quantum interference effects suggest a mean free path of $10\pm 2\text{nm}$, which is comparable to the nanowire width, and thus allows for coherent formation of transversal modes. The results suggest that the low-temperature mobility is limited by scattering on phosphorus dopants rather than the expected surface roughness scattering for nanowires with diameters larger than or comparable to the Fermi wavelength. A temperature-dependent analysis of universal conductance fluctuations indicates a phase-coherence length greater than the nanowire length for temperatures below 1.9 K, and decoherence from one-dimensional electron-electron interactions dominates transport for higher temperatures. Our measurements, therefore, provide insight into scattering and dephasing mechanisms in technologically relevant silicon device geometries, which will help with future design choices with regard to, e.g., doping density.

High-resolution magnetophotoluminescence measurements of strained ${\mathrm{WSe}}_2$ monolayers are reported. At low temperature, a splitting of a few meV in the neutral exciton peak is observed, which is attributed to the theoretically predicted in-plane ($xy$) anisotropy splitting. Measurements in high magnetic fields up to 30 T demonstrate that strain and intervalley electron-hole exchange mix the valley-exciton energy levels, leading to a relaxation of the valley-selective optical selection rules and to strongly modified exciton $g$ factors. Our observation of the bright exciton splitting provides crucial information about the dispersion of valley excitons and paves the way to develop valley functionality for photonic devices.

The half-Heusler compounds YPdBi and TbPdBi, while having a similar band structure, exhibit different magnetic properties. YPdBi is a diamagnet, while TbPdBi shows antiferromagnetic order below 5.5 K. Both are superconductors with $T_c\approx 1$ K for YPdBi and $T_c\approx 1.75$ K for TbPdBi. Such a contrast in properties between these two compounds opens a question about the effects of band structure or magnetic correlations on superconductivity. Using the combination of a tunnel diode oscillator and a commercial dilution refrigerator, we measured the temperature-dependent magnetic penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ in single crystals of YPdBi and TbPdBi, down to temperatures as low as 0.1 K. We found that the penetration depths of both compounds do not show an exponential temperature dependence and saturation at low temperatures, as expected for conventional BCS superconductors. Instead, in both compounds, the penetration depth can be described by a power law $\mathrm{\Delta }\lambda \left(T\right)=A\times T^n$. The coefficient $A$ was found to be about $50\%$ smaller in TbPdBi, but the exponents are very similar, $n=2.76\pm 0.04$ in YPdBi and $n=2.6\pm 0.3$ in TbPdBi, respectively. Our results suggest unconventional superconductivity in both YPdBi and TbPdBi.

We use a functional renormalization group (fRG) approach to investigate potential interaction-induced instabilities in a two-dimensional model for the Dirac nodal-line materials ZrSiS and ZrSiSe employing model parameters derived from ab initio calculations. Our results characterize the excitonic instability recently found in random-phase approximation for ZrSiS as an on-site spin-charge-degenerate exciton. Beyond this, we show that the fRG analysis produces an energy scale for the onset of the instability, in good agreement with the experimentally observed mass enhancement. Additionally, by exploring the parameter space of the model, we find that reducing the band splitting increases the instability scale and gives the chance to drive the system into an unconventional superconducting pairing state. The model parameters for the case of the structurally similar material ZrSiSe suggest the $d$-wave superconducting state as the leading instability with a very small critical scale.

Entanglement, which quantifies nonlocal correlations in quantum mechanics, is the fascinating concept behind much of the aspiration towards quantum technologies. Nevertheless, directly measuring the entanglement of a many-particle system is very challenging. Here, we show that via supervised machine learning using a convolutional neural network, we can infer the entanglement from a measurable observable for a disordered interacting quantum many-particle system. Several structures of neural networks were tested and a convolutional neural network akin to structures used for image and speech recognition performed the best. After training on a set of 500 realizations of disorder, the network was applied to 200 new realizations and its results for the entanglement entropy were compared to a direct computation of the entanglement entropy. Excellent agreement was found, except for several rare regions which in a previous study were identified as belonging to an inclusion of a Griffiths-like quantum phase. Training the network on a test set with different parameters (in the same phase) also works quite well.

We report strong electron-phonon coupling in magic-angle twisted bilayer graphene (MA-TBG) obtained from atomistic description of the system including more than 10 000 atoms in the moiré supercell. Electronic structure, phonon spectrum, and electron-phonon coupling strength $\lambda$ are obtained before and after atomic-position relaxation both in and out of plane. Obtained $\lambda$ is very large for MA-TBG, with $\lambda >1$ near the half-filling energies of the flat bands, while it is small ($\lambda \sim 0.1$) for monolayer and unrotated bilayer graphene. Significant electron-hole asymmetry occurs in the electronic structure after atomic-structure relaxation, so $\lambda$ is much stronger with hole doping than electron doping. Obtained electron-phonon coupling is nearly isotropic and depends very weakly on electronic band and momentum, indicating that electron-phonon coupling prefers single-gap $s$-wave superconductivity. Relevant phonon energies are much larger than electron energy scale, going far beyond adiabatic limit. Our results provide a fundamental understanding of the electron-phonon interaction in MA-TBG, highlighting that it can contribute to rich physics of the system.

An efficient $\mathrm{O}(N$) divide-conquer (DC) method based on localized single-particle natural orbitals (LNOs) is presented for large-scale density functional theory (DFT) calculations of gapped and metallic systems. The LNOs are noniteratively calculated by a low-rank approximation via a local eigendecomposition of a projection operator for the occupied space. Introducing LNOs to represent the long-range region of a truncated cluster reduces the computational cost of the DC method while keeping computational accuracy. A series of benchmark calculations and high parallel efficiency in a multilevel parallelization clearly demonstrate that the $\mathrm{O}(N$) method enables us to perform large-scale simulations for a wide variety of materials including metals with sufficient accuracy in accordance with development of massively parallel computers.

Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is $if$ any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo approach. By comparing with density-matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t\text{−}J$ model, which is kinetic-energy driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.

A numerical verification of Luttinger's theorem, based on a recently developed many-body approach, is given for the Kondo-lattice model. For a two-dimensional lattice the completely localized spins $(S=1/2)$ are found to contribute to the Fermi sea volume as if they were electrons, which is in agreement with Oshikawa's topological proof of Luttinger's theorem. Underpinning this result we explicitly calculate the momentum-resolved one-particle spectral function showing nearly dispersionless excitations clearly below the Fermi level for different values of the conduction electron filling. Numerical integration over momentum and energy always leads to the correct particle number of the localized spins according to the well-accepted picture of a large Fermi surface. In this paper, a first many-body approach is shown, which is able to reproduce the correct value of Luttinger's theorem for this model.