A computationally efficient workflow for obtaining the low-energy symmetric tight-binding Hamiltonians for twisted multilayer systems is presented in this work. We apply this scheme to twisted bilayer graphene at the first magic angle. As initial step, the full-energy tight-binding Hamiltonian is generated by the Slater-Koster model with parameters fitted to ab-initio data at larger angles. Then, the low-energy symmetric four-band and twelve-band Hamiltonians are constructed using the maximum-localization procedure subjected to crystal and time-reversal-symmetry constraints. Finally, we compute extended Hubbard parameters for both models within the constrained random phase approximation (cRPA) for screening, which again respect the symmetries. The relevant data and results of this work are freely available via an online repository. Our workflow, exemplified in this work on twisted bilayer graphene, is straightforwardly transferable to other twisted multi-layer materials.
We present a theory for charge and heat transport parallel to the interfaces of a multilayer (ML) in which the interfacing gives rise the redistribution of the electronic charges. The ensuing electrical field couples self-consistently to the itinerant electrons, so that the properties of the ML crucially depend on an interplay between the on-site Coulomb forces and the long range electrostatic forces. The ML is described by the Falicov-Kimball model and the self-consistent solution is obtained by iterating simultaneously the DMFT and the Poisson equations. This yields the reconstructed charge …
An effective low-energy model describing magnetic properties of alkali-cluster-loaded sodalites is derived by {\em ab initio} downfolding. We start with constructing an extended Hubbard model for maximally localized Wannier functions. {\em Ab initio} screened Coulomb and exchange interactions are calculated by constrained random phase approximation. We find that the system resides in the strong coupling regime and thus the Heisenberg model is derived as a low-energy model of the extended Hubbard model. We obtain antiferromagnetic couplings $\sim$ $O$(10 K), being consistent with the experiment…
Engineering effective electronic parameters is a major focus in condensed matter physics. Their dynamical modulation opens the possibility of creating and controlling physical properties in systems driven out of equilibrium. In this work, we demonstrate that the Hubbard $U$, the on-site Coulomb repulsion in strongly correlated materials, can be modified on femtosecond time scales by a strong nonresonant laser excitation in the prototypical charge transfer insulator NiO. Using our recently developed time-dependent density functional theory plus self-consistent $U$ (TDDFT+U) method, we demonstra…
We overview the EDABI method developed recently and combining the exact diagonalization and ab initio aspects of electron states in correlated systems and apply it to nanoscopic systems. In particular, we discuss the localization-delocalization transition for the electrons that corresponds to the Mott-Hubbard transition in bulk systems. We show, that, the statistical distribution function for electrons in a nanochain evolves from the Fermi-Dirac-like to the Luttinger-liquid-like with the increasing interatomic distance. The concept of Hubbard subbands is introduced to nanoclusters, and corresp…
Honeycomb structures formed by the growth of perovskite 5d transition metal oxide heteroestructures along the (111) direction in $t_{2g}^5$ configuration can give rise to topological ground states characterized by a topological index $ν$=1. Using a combination of a tight binding model and ab initio calculations we study the multilayers $(\text{SrTiO}_3)_7/(\text{SrIrO}_3)_2$ and $(\text{KTaO}_3)_7/(\text{KPtO}_3)_2$ as a function of parity asymmetry, on-site interaction and uniaxial strain and determine the nature and evolution of the gap. $(\text{SrTiO}_3)_7/(\text{SrIrO}_3)_2$ is found to be…
We derive ab initio local Hubbard models for several optical lattice potentials of current interest, including the honeycomb and Kagomé lattices, verifying their accuracy on each occasion by comparing the interpolated band structures against the originals. To achieve this, we calculate the maximally-localized generalized Wannier basis by implementing the steepest-descent algorithm of Marzari and Vanderbilt [N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)] directly in one and two dimensions. To avoid local minima we develop an initialization procedure that is both robust and require…
We study the electronic structure and magnetic interactions in methylamine-intercalated orthorhombic alkali-doped fullerene (CH3NH2)K3C60 within the density functional theory. As in the simpler ammonia intercalated compound (NH3)K3C60, the orthorhombic crystal-field anisotropy Δlifts the t1u triple degeneracy at the Γpoint and drives the system deep into the Mott-insulating phase. However, the computed Δand conduction electron bandwidth W cannot alone account for the abnormally low experimental Néel temperature, T_N = 11 K of the methylamine compound, compared to the much higher value T_N = 40…
We present a novel treatment of finite temperature properties of the one-dimensional Hubbard model. Our approach is based on a Trotter-Suzuki mapping utilizing Shastry's classical model and a subsequent investigation of the quantum transfer matrix. We derive non-linear integral equations for three auxiliary functions which have a clear physical interpretation of elementary excitations of spin type and charge excitations in lower and upper Hubbard bands. This allows for a transparent analytical study of certain limiting cases as well as for precise numerical investigations. We present data for …
In this article, we propose an energy functional at the level of DFT+U+V that allows us to compute self-consistently the values of the on-site interaction, Hubbard U and Hund J, as well as the intersite interaction V. This functional extends the previously proposed ACBN0 functional [Phys. Rev. X 5, 011006 (2015)] including both on-site and intersite interactions. We show that this ab initio self-consistent functional yields improved electronic properties for a wide range of materials, ranging from $sp$ materials to strongly-correlated materials. This functional can also be seen as an alternati…
\textit{Ab initio} calculations have been performed on hexagonal layers of M$_2$O$_3$ (M being several transition metals of the $5d$ series) sandwiched by a band insulator such as Al$_2$O$_3$ that provides the honeycomb lattice where the $5d$ electrons reside. This corundum-structure-based superlattice is the most obvious way to design a honeycomb lattice with transition metal cations avoiding the use of largely polar surfaces. We obtain that this system supports the presence of Dirac cones at the Fermi level that open up with the introduction of spin-orbit coupling at various fillings of the …
We obtain in a direct and rigorous manner a transition from a stable molecular hydrogen $nH_2$ single chain to the quasiatomic two-chain $2nH$ state. We devise an original method composed of an exact diagonalization in the Fock space combined with an ab initio adjustment of the single-particle wave function in the correlated state. In this approach the well-known problem of double-counting the interparticle interaction does not arise at all. The transition is strongly discontinuous, and appears even for relatively short chains possible to tackle, $n=3\div6$. The signature of the transition as …
We study a minimal Hubbard model for electronically driven superconductivity in a correlated flat mini-band resulting from the superlattice modulation of a twisted graphene multilayer. The valley degree of freedom drastically modifies the nature of thepreferred pairing states, favoring spin triplet $d+id$ order with a valley singlet structure. We identify two candidates in this class, which are both topological superconductors. These states support half-vortices carrying half the usual superconducting flux quantum $hc/(4e)$, and have topologically protected gapless edge states.
Microscopic mechanism of high-temperature superconductivity revealed by ab initio studies on hole-doped multilayer cuprates HgBa$_2$Ca$_2$Cu$_3$O$_8$ under pressure
Sophia University（上智大学）；The University of Tokyo（东京大学）
We used fully correlated ab initio calculations to determine the effective parameters of Hubbard and t - J models for the thermoelectric misfit compound $\rm Ca_3Co_4O_9$. As for the $\rm Na_xCoO_2$ family the Fermi level orbitals are the $a_{1g}$ orbitals of the cobalt atoms ; the $e'_g$ being always lower in energy by more than 240\,meV. The electron correlation is found very large $U/t\sim 26$ as well as the parameters fluctuations as a function of the structural modulation. The main consequences are a partial $a_{1g}$ electrons localization and a fluctuation of the in-plane magnetic exchan…
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio Quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding (AIDMD). For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic bound…
{\it Ab initio} analyses of A$_2$IrO$_4$ (A=Sr, Ba) are presented. Effective Hubbard-type models for Ir 5$d$ $t_{2g}$ manifolds downfolded from the global band structure are solved based on the dynamical mean-field theory. The results for A=Sr and Ba correctly reproduce paramagnetic metals undergoing continuous transitions to insulators below the Néel temperature $T_N$. These compounds are classified not into Mott insulators but into Slater insulators. However, the insulating gap opens by a synergy of the Neel order and significant band renormalization, which is also manifested by a 2D bad met…
Intense experimental and theoretical studies have demonstrated that the anisotropic triangular lattice as realized in the kappa-(BEDT-TTF)2X family of organic charge transfer (CT) salts yields a complex phase diagram with magnetic, superconducting, Mott insulating and even spin liquid phases. With extensive density functional theory (DFT) calculations we refresh the link between manybody theory and experiment by determining hopping parameters of the underlying Hubbard model. This leads us to revise the widely used semiempirical parameters in the direction of less frustrated, more anisotropic t…
We present ab initio results for the electron-phonon interaction of the Γ-point phonons in the tetragonal high-temperature phase of La2CuO4. Eigenfrequencies and eigenvectors for the symmetry-allowed phonon modes are calculated with the full-potential augmented plane wave+local orbitals method using the frozen phonon approach. It is found that the Γ-point phonons with the strongest electron-phonon interaction are the A{2u} modes with 236 cm^{-1}, 131 cm^{-1} and 476 cm^{-1}. To take effect of strong electron on-site interaction into account we use generalized tight-binding method that results …
Accurate high-energy electron diffraction measurements of structure factors of NiO have been carried out to investigate how strong correlations in the Ni 3d shell affect electron charge density in the interior area of nickel ions and whether the new ab-initio approaches to the electronic structure of strongly correlated metal oxides are in accord with experimental observations. The generalized gradient approximation (GGA) and the local spin density approximation corrected by the Hubbard U term (LSDA+U) are found to provide the closest match to experimental measurements. The comparison of calcu…
We discuss a general approach to a realistic theory of the electronic structure in materials containing correlated d- or f- electrons. The main feature of this approach is the taking into account the energy dependence of the electron self-energy with the momentum dependence being neglected (local approximation). In the case of strong interactions (U/W>>1 - rare-earth system) the Hubbard-I approach is the most suitable. Starting from an exact atomic Green function with the constrained density matrix the band structure problem is formulated as the functional problem on Nmm' for f-electrons and t…
Metallic Néel order stabilized by coupling between inequivalent Hubbard layers
Institute for Advanced Study in Physics, Zhejiang University（浙江大学前沿物理研究院）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Physics, Stanford University（斯坦福大学物理系）
The electronic properties of paramagnetic V_2O_3 are investigated by the ab-initio computational scheme LDA+DMFT(QMC). This approach merges the local density approximation (LDA) with dynamical mean-field theory (DMFT) and uses numerically exact quantum Monte Carlo simulations (QMC) to solve the effective Anderson impurity model of DMFT. Starting with the crystal structure of metallic V_2O_3 and insulating (V_{0.962}Cr_{0.038})_2O_3 we find a Mott-Hubbard metal-insulator-like transition at a Coulomb interaction U\approx 5eV. The calculated spectrum is in very good agreement with experiment. Fur…
We derive effective Hubbard-type Hamiltonians of $κ$-(ET)$_2X$, using an {\em ab initio} downfolding technique, for the first time for organic conductors. They contain dispersions of the highest occupied Wannier-type molecular orbitals with the nearest neighbor transfer $t$$\sim$0.067 eV for a metal $X$=Cu(NCS)$_2$ and 0.055 eV for a Mott insulator $X$=Cu$_2$(CN)$_3$, as well as screened Coulomb interactions. It shows unexpected differences from the conventional extended Hückel results, especially much stronger onsite interaction $U$$\sim$0.8 eV ($U/t$$\sim$12-15) than the Hückel estimates ($U…
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is transformed into a correlated form. In order to elucidate the microscopical origin of the parameters of the periodical Hubbard-Anderson model (PHAM) the terms of the full Hamiltonian which have the operator structure of PHAM are separated. It is found that the matrix element of mixing interaction includes ion-configuration and number-of-particles dependent contribut…
We derive an effective low-energy Hamiltonian for potassium loaded zeolite A, a unique ferromagnet from non-magnetic elements. We perform ab initio density functional calculations and construct maximally localized Wannier functions for low-energy states made from potassium s electrons. The resulting Wannier orbitals, spreading widely in the alminosilicate cage, are found to be the superatomic s and p orbitals in the confining potential formed by the host cage. We then make a tight-binding model for these superatomic orbitals and introduce interaction parameters such as the Hubbard U. After mea…
The optimized single-particle wave functions contained in the parameters of the Hubbard model (t and U) were determined for an infinite atomic chain. In effect, the electronic properties of the chain as a function of interatomic distance R were obtained and compared for the Lieb - Wu exact solution (LW), the Gutzwiller-Wave-Function approximation (GWF), and the Gutzwiller-ansatz case (GA). The ground state energy and other characteristics for the infinite chain were also compared with those obtained earlier for a nanoscopic chain within the Exact Diagonalization combined with an Ab Initio adju…
We present ab initio two-dimensional extended Hubbard-type multiband models for EtMe_3Sb[Pd(dmit)_2]_2 and κ-(BEDT-TTF)_2Cu(NCS)_2, after a downfolding scheme based on the constrained random phase approximation (cRPA) and maximally-localized Wannier orbitals, together with the dimensional downfolding. In the Pd(dmit)_2 salt, the antibonding state of the highest occupied molecular orbital (HOMO) and the bonding/antibonding states of the lowest unoccupied molecular orbital (LUMO) are considered as the orbital degrees of freedom, while, in the κ-BEDT-TTF salt, the HOMO-antibonding/bonding states …
We present a general framework for deriving effective spin Hamiltonians of correlated magnetic systems based on a combination of relativistic ab initio density functional theory calculations (DFT), exact diagonalization of a generalized Hubbard Hamiltonian on finite clusters and spin projections onto the low-energy subspace. A key motivation is to determine anisotropic bilinear exchange couplings in materials of interest. As an example, we apply this method to the pyrochlore Lu$_2$V$_2$O$_7$ where the vanadium ions form a lattice of corner-sharing spin-1/2 tetrahedra. In this compound, anisotr…
We derive an effective three-orbital model for the infinite-layer nickelates based on the band structure obtained by the GW approximation (GWA), where we consider the Ni 3$d_{x^2-y^2}$ and O 2$p$ orbitals forming the $σ$-bond. In the GWA, the self-energy correction to the local density approximation (LDA) increases the energy difference between Ni $3d_{x^2-y^2}$ and O $2p$, which reduces the bandwidth of the antibonding 3$d_{x^2-y^2}$ orbitals. The isolation of the Ni $3d_{x^2-y^2}$ around the Fermi level suppresses the screening effect. As a result, the correlation effect becomes more signifi…
Correlation computations on multiband Hubbard Hamiltonians are presented. It is shown why the proper degeneracy is of vital importance and that the atomic exchange interaction plays a particular role. The different methods are connected, and their results are discussed. Many experimental properties for the elemental solids can be explained by single closely related sets of parameters each. There is an exception, Tc of Fe. Here, a novel feature of longer-range interactions enters, as demonstrated on ab-initio results of the Local Ansatz for Fe. Connections are made to LSDA-calculations; and the…
We present an \textit{ab initio} auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the \textit{ab initio} phaseless auxiliary field quantum Monte Carlo algorithm known to produce high accuracy ground state energies of molecules and solids with its finite temperature variant, long used by condensed matter physicists for studying model Hamiltonian phase diagrams, to yield a phaseless, \textit{ab initio} finite temperature method. We demonstrate that the method produces interna…
We analyze the pressure-induced metal-insulator transition in a two-dimensional vertical stack of $H_2$ molecules in x-y plane, and show that it represents a striking example of the Mott-Hubbard-type transition. Our combined exact diagonalization approach, formulated and solved in the second quantization formalism, includes also simultaneous ab initio readjustment of the single-particle wave functions, contained in the model microscopic parameters. The system is studied as a function of applied side force (generalized pressure), both in the $H_2$-molecular and $H$-quasiatomic states. Extended …
We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin polarized, $C_{3z}$-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin polarized, nematic insulator states are in the quantum valley Hall phase by virtue of the nontrivial…
Using the newly developed VASP2WANNIER90 interface we have constructed maximally localized Wannier functions (MLWFs) for the e_g states of the prototypical Jahn-Teller magnetic perovskite LaMnO3 at different levels of approximation for the exchange-correlation kernel. These include conventional density functional theory (DFT) with and without additional on-site Hubbard U term, hybrid-DFT, and partially self-consistent GW. By suitably mapping the MLWFs onto an effective e_g tight-binding (TB) Hamiltonian we have computed a complete set of TB parameters which should serve as guidance for more el…
We perform an ab-initio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we…
Correlation effects play an important role in the electronic structure of half-metallic (HM) magnets. In particular, they give rise to non-quasiparticle states above (or below) the Fermi energy at finite temperatures that reduce the spin polarization and, as a consequence, the efficiency of spintronics devices. Employing the constrained random-phase approximation (cRPA) within the full-potential linearized augmented-plane-wave (FLAPW) method using maximally localized Wannier functions, we calculate the strength of the effective on-site Coulomb interaction (Hubbard $U$ and Hund exchange $J$) be…
We examine whether essence and quantitative aspects of electronic excitation spectra are correctly captured by an effective low-energy model constructed from an {\em ab initio} downfolding scheme. A global electronic structure is first calculated by {\em ab initio} density-functional calculations with the generalized gradient approximation. With the help of constrained density functional theory, the low-energy effective Hamiltonian for bands near the Fermi level is constructed by the downfolding procedure in the basis of maximally localized Wannier functions. The excited states of this low-ene…
We propose an electron-phonon parameterization which reliably reproduces the geometry and harmonic frequencies of a real system. With respect to standard electron-phonon models, it adds a "double-counting" correction, which takes into account the lattice deformation as the system is dressed by low-energy electron-phonon processes. We show the importance of this correction by studying potassium-doped picene (K$_3$Picene), recently claimed to be a superconductor with a $T_c$ of up to 18 K. The Hamiltonian parameters are derived from ab-initio density functional theory, and the lattice model is s…
Electron correlation effects in the half-metallic ferromagnet NiMnSb are investigated within a combined density functional and many-body approach. Starting from a realistic multi-orbital Hubbard-model including Mn and Ni-d orbitals, the many-body problem is addressed via the Variational Cluster Approach. The density of states obtained in the calculation shows a strong spectral weight transfer towards the Fermi level in the occupied conducting majority spin channel with respect to the uncorrelated case, as well as states with vanishing quasiparticle weight in the minority spin gap. Although the…
The molecular solids $β^\prime$-$X$[Pd(dmit)$_2$]$_2$ (where $X$ represents a cation) are typical compounds whose electronic structures are described by single-orbital Hubbard-type Hamiltonians with geometrical frustration. Using the $ab$ $initio$ downfolding method, we derive the low-energy effective Hamiltonians for $β^\prime$-$X$[Pd(dmit)$_2$]$_2$ with available room- and low-temperature structures. We find that the amplitudes of the Coulomb interactions and the anisotropy of the hopping parameters in the effective Hamiltonians are sensitive to the changes in the lattice constants induced b…
We show how an accurate first-principles treatment of the antiferromagnetic (AFM) ground state of La$_2$CuO$_4$ can be obtained without invoking any free parameters such as the Hubbard $U$. The magnitude and orientation of our theoretically predicted magnetic moment of $0.495 μ_{B}$ on Cu-sites along the (100) direction are in excellent accord with experimental results. The computed values of the band gap (1.00 eV) and the exchange-coupling (-138 meV) match the corresponding experimental values. We identify interesting band splittings below the Fermi energy, including an appreciable Hund's spl…
Using {\it ab initio} approaches for extended Hubbard interactions coupled to phonons, we reveal that the intersite Coulomb interaction plays important roles in determining various distinctive phases of the paradigmatic charge ordered materials of Ba$_{1-x}$K$_x A$O$_3$ ($A=$ Bi and Sb). We demonstrated that all their salient doping dependent experiment features such as breathing instabilities, anomalous phonon dispersions, and transition between charge-density wave and superconducting states can be accounted very well if self-consistently obtained nearest neighbor Hubbard interaction are incl…
The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and accurate model of the systems is of vital importance for the further study. Here, we construct the symmetry-adapted localized Wannier functions and the corresponding $\textit{ab initio}$ minimal two-valley four-band effective tight-binding models for generic twisted graphene systems with small twist angle. Such two-valley model evades the Wannier obstruction caused…
These lecture notes introduce some simple effective Hamiltonians (also known as semi-empirical models) that have widespread applications to solid state and molecular systems. They are aimed as an introduction to a beginning graduate student. I also hope that it may help to break down the divide between the physics and chemistry literatures. After a brief introduction to second quantisation notation, which is used extensively, I focus of the "four H's": the Huckel (or tight binding), Hubbard, Heisenberg and Holstein models. Some other related models, such as the Pariser-Parr-Pople model, the ex…
Ab initio spin Hamiltonians and magnetism of Ce and Yb triangular-lattice compounds
École polytechnique, Institut Polytechnique de Paris（巴黎综合理工学院，巴黎理工学院）；Collège de France, Université PSL（法兰西公学院，巴黎文理研究大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）
