Ab initio determination of model Hamiltonian parameters for strongly correlated materials is a key issue in applying many-particle theoretical tools to real narrow-band materials. We propose a self-contained calculation scheme to construct, with an ab initio approach, and solve such a Hamiltonian. The scheme uses a Wannier-function-basis set, with the Coulomb interaction parameter U obtained specifically for these Wannier functions via constrained Density functional theory (DFT) calculations. The Hamiltonian is solved by Dynamical Mean-Field Theory (DMFT) with the effective impurity problem treated by the Quantum Monte Carlo (QMC) method. Our scheme is based on the pseudopotential plane-wave method, which makes it suitable for developments addressing the challenging problem of crystal structural relaxations and transformations due to correlation effects. We have applied our scheme to the "charge transfer insulator" material nickel oxide and demonstrate a good agreement with the experimental photoemission spectra.
We present a joint implementation of dynamical-mean-field theory (DMFT) with the pseudopotential plane-wave approach, via Wannier functions, for the determination of the electronic properties of strongly correlated materials. The scheme uses, as input for the DMFT calculations, a tight-binding Hamiltonian obtained from the plane-wave calculations by projecting onto atomic-centered symmetry-constrained Wannier functions for the correlated orbitals. We apply this scheme to two prototype systems: a paramagnetic correlated metal, SrVO3, and a paramagnetic correlated system, V2O3, which exhibits a …
Fractional Chern insulators are new realizations of fractional quantum Hall states in lattice systems without orbital magnetic field. These states can be mapped onto conventional fractional quantum Hall states through the Wannier state representation (Phys. Rev. Lett. 107, 126803 (2011)). In this paper, we use the Wannier state representation to construct the pseudopotential Hamiltonians for fractional Chern insulators, which are interaction Hamiltonians with certain ideal model wavefunctions as exact ground states. We show that these pseudopotential Hamiltonians can be approximated by short-r…
The most general way to describe localized atomic-like electronic states in strongly correlated compounds is to utilize Wannier functions. In the present paper we continue the development of widely-spread DFT+U method onto Wannier function basis set and propose the technique to calculate the Hubbard contribution to the forces. The technique was implemented as a part of plane-waves pseudopotential code Quantum-ESPRESSO and successfully tested on a charge transfer insulator NiO.
Recently, generalizations of fractional quantum Hall (FQH) states known as fractional quantum anomalous Hall or, equivalently, fractional Chern insulators states have been realized in lattice models. Ideal wavefunctions such as the Laughlin wavefunction, as well as the corresponding trial Hamiltonians for which the former are exact ground states, have been vital to characterizing FQH phases. The Wannier function representation of fractional Chern insulators proposed in [X.-L. Qi, Phys. Rev. Lett., 126803] defines an approach to generalize these concepts to fractional Chern insulators. In this …
When the first four spectral moments are considered, spectral features missing in standard Kohn-Sham (KS) density-functional theory (DFT), such as upper and lower Hubbard bands, as well as spectral satellite peaks, can be described, and the bandwidths can be corrected. Therefore, we have devised a \textit{moment-functional based spectral density functional theory} (MFbSDFT) recently. However, many computational tools in theoretical solid state physics, such as the construction of maximally localized Wannier functions (MLWFs), have been developed for KS-DFT and require modifications if they are…
Parameterizing DFT+U+V from Hybrid Functionals: A Wannier-Function-Based Approach for Strongly Correlated Materials
M.N. Mikheev Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences（俄罗斯科学院乌拉尔分支 M.N. 米凯耶夫金属物理研究所）；Department of Theoretical Physics and Applied Mathematics, Ural Federal University（乌拉尔联邦大学理论物理与应用数学系）
We present a model example of a quantum critical behavior of renormalized single-particle Wannier function composed of Slater s-orbitals and represented in an adjustable Gaussian STO-7G basis, which is calculated for cubic lattices in the Gutzwiller correlated state near the metal-insulator transition (MIT). The discussion is carried out within the extended Hubbard model and the method of approach proposed earlier [cf. Eur. Phys. J. B {\bf 66}, 385 (2008)]. The component atomic-wave-function size, the Wannier function maximum, as well as the system energy, all scale with the increasing lattice…
We extend our previous approach (Eur. Phys. J. B, \textbf{74}, 63(2010)) to modeling correlated electronic states and the metal-insulator transition by applying the so-called \emph{statistically consistent Gutzwiller approximation} (SGA) to carry out self-consistent calculations of the renormalized single-particle Wannier functions in the correlated state. The transition to the Mott-Hubbard insulating state at temperature T=0 is of weak first order even if antiferromagnetism is disregarded. The magnitude of the introduced self-consistent magnetic correlation field is calculated and shown to le…
A versatile method for combining density functional theory (DFT) in the local density approximation (LDA) with dynamical mean-field theory (DMFT) is presented. Starting from a general basis-independent formulation, we use Wannier functions as an interface between the two theories. These functions are used for the physical purpose of identifying the correlated orbitals in a specific material, and also for the more technical purpose of interfacing DMFT with different kinds of band-structure methods (with three different techniques being used in the present work). We explore and compare two disti…
The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band like systems described by the Hubbard model and its extensions. The optimized single-particle wave functions contained in the parameters of the Hubbard model (the hopping \textit{t} and the magnitude of the intraatomic interaction \textit{U}) are determined explicitly in the correlated state for the electronic systems of various symmetries and dimensions: Hubbard chain, square and triangular planar lattices, and the three cubic lattices (SC, BCC, FCC). In effect, the evolution of the…
We derive a "Wannier-Hubbard" model consisting of an array of overlapping atomic orbitals interacting via a local Coulomb interaction. Transforming to an orthogonal Wannier basis set, the resulting Hamiltonian displays long range hopping and interactions, with new terms such as correlated hopping and ferromagnetic direct exchange, among others. We numerically study the one-dimensional version of the model at half-filling using the density matrix renormalization group (DMRG) method, unveiling a rich phase diagram as a function of the interaction $U$ and the overlap $s$ with metallic, and ferrom…
We present a new ab initio method for calculating effective onsite Coulomb interactions of itinerant and strongly correlated electron systems. The method is based on constrained local density functional theory formulated in terms of maximally localized Wannier functions. This scheme can be implemented with any basis, and thus allows us to perform the constrained calculation with plane-wave-based electronic-structure codes. We apply the developed method to the evaluation of the onsite interaction of 3d transition-matal series. The results are discussed using a heuristic formula for screened Cou…
We demonstrate how ab initio cluster calculations including the full Coulomb vertex can be done in the basis of the localized, generalized Wannier orbitals which describe the low-energy density functional (LDA) band structure of the infinite crystal, e.g. the transition metal 3d and oxygen 2p orbitals. The spatial extend of our 3d Wannier orbitals (orthonormalized Nth order muffin-tin orbitals) is close to that found for atomic Hartree-Fock orbitals. We define Ligand orbitals as those linear combinations of the O 2p Wannier orbitals which couple to the 3d orbitals for the chosen cluster. The u…
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…
We propose an effective model called the "charge model", for the half-filled one-dimensional Hubbard and extended Hubbard models. In this model, spin-charge separation, which has been justified from an infinite on-site repulsion ($U$) in the strict sense, is compatible with charge fluctuations. Our analyses based on the many-body Wannier functions succeeded in determining the optical conductivity spectra in large systems. The obtained spectra reproduce the spectra for the original models well even in the intermediate $U$ region of $U=5-10T$, with $T$ being the nearest-neighbor electron hopping…
We have implemented recently developed multiple-projector pseudopotentials into the planewave based auxiliary-field quantum Monte Carlo (pw-AFQMC) method. Multiple-projector pseudopotentials can yield smaller planewave cut-offs while maintaining or improving transferability. This reduces the computational cost of pw-AFQMC, increasing its reach to larger and more complicated systems. We discuss the use of non-local pseudopotentials in the separable Kleinman-Bylander form, and the implementation in pw-AFQMC of the multiple-projector optimized norm-conserving pseudopotential ONCVPSP of Hamann. Th…
We define Wannier functions for interacting systems, and show that the results on the localization of the Wannier functions for non-interacting systems carry over to the Wannier functions for interacting systems. In addition we demonstrate that the characterization of metals and insulators by the decay properties of their respective density matrices does not only apply to non-interacting, but also to interacting systems. As a prototypical example of a correlated system we investigate the one-dimensional Hubbard model. We propose an expression for the density matrix of that model, and derive a …
Tight-binding single-particle models on simple Bravais lattices in space dimension $d \geq 2$, when exposed to commensurate DC fields, result in the complete absence of transport due to the formation of Wannier--Stark flatbands [Phys. Rev. Res. $\textbf{3}$, 013174 (2021)]. The single-particle states localize in a factorial manner, i.e., faster than exponential. Here, we introduce interaction among two such particles that partially lifts the localization and results in metallic two-particle bound states that propagate in the directions perpendicular to the DC field. We demonstrate this effect …
Dynamical Mean Field Theory (DMFT) is a successful method to compute the electronic structure of strongly correlated materials, especially when it is combined with density functional theory (DFT). Here, we present an open-source computational package (and a library) combining DMFT with various DFT codes interfaced through the Wannier90 package. The correlated subspace is expanded as a linear combination of Wannier functions introduced in the DMFT approach as local orbitals. In particular, we provide a library mode for computing the DMFT density matrix. This library can be linked and then inter…
The description of realistic strongly correlated systems has recently advanced through the combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT). This LDA+DMFT method is able to treat both strongly correlated insulators and metals. Several interfaces between LDA and DMFT have been used, such as (N-th order) Linear Muffin Tin Orbitals or Maximally localized Wannier Functions. Such schemes are however either complex in use or additional simplifications are often performed (i.e., the atomic sphere approximation). We present an alt…
Irradiation with light provides a powerful tool to interrogate, control or induce new quantum states of matter out of equilibrium, however a microscopic understanding of light-matter coupling in interacting electron systems remains a profound challenge. Here, we show that light grants a new quantum-geometric handle to steer and probe correlated quantum materials, whereby photons can couple directly to the shape and center of the maximally-localized Wannier functions that comprise the material's interacting bands, dressing both electronic motion and electronic interactions with light. Notably, …
We propose a computational scheme for the ab initio calculation of Wannier functions (WFs) for correlated electronic materials. The full-orbital Hamiltonian H is projected into the WF subspace defined by the physically most relevant partially filled bands. The Hamiltonian H^{WF} obtained in this way, with interaction parameters calculated by constrained LDA for the Wannier orbitals, is used as an ab initio setup of the correlation problem, which can then be solved by many-body techniques, e.g., dynamical mean-field theory (DMFT). In such calculations the self-energy operator Σ(e) is defined in…
We study the low-energy properties of a truncated Haldane pseudopotential with maximal half filling, which describes a strongly correlated system of spinless bosons in a cylinder geometry. For this Hamiltonian with either open or periodic boundary conditions, we prove a spectral gap above the highly degenerate ground-state space which is uniform in the volume and particle number. Our proofs rely on identifying invariant subspaces to which we apply gap-estimate methods previously developed only for quantum spin Hamiltonians. In the case of open boundary conditions, the lower bound on the spectr…
We present an algorithm for the adaptive tetrahedral integration over the Brillouin zone of crystalline materials, and apply it to compute the optical conductivity, dc conductivity, and thermopower. For these quantities, whose contributions are often localized in small portions of the Brillouin zone, adaptive integration is especially relevant. Our implementation, the woptic package, is tied into the wien2wannier framework and allows including a many-body self energy, e.g. from dynamical mean-field theory (DMFT). Wannier functions and dipole matrix elements are computed with the DFT package Wi…
The sensitivity of Density Functional Theory plus Dynamical Mean Field Theory calculations to different constructions of the correlated orbitals is investigated via a detailed comparison of results obtained for the quantum material NdNiO$_2$ using different Wannier and projector methods to define the correlation problem. Using the same interaction parameters we find that the different methods produce different results for the orbital and band basis mass enhancements and for the orbital occupancies, with differing implications regarding the importance of multiorbital effects and charge transfer…
An approach to compute exchange parameters of the Heisenberg model in plane-wave-based methods is presented. This calculation scheme is based on the Green's function method and Wannier function projection technique. It was implemented in the framework of the pseudopotential method and tested on such materials as NiO, FeO, Li2MnO3, and KCuF3. The obtained exchange constants are in a good agreement with both the total energy calculations and experimental estimations for NiO and KCuF3. In the case of FeO our calculations explain the pressure dependence of the Néel temperature. Li2MnO3 turns out t…
An efficient computational scheme devised for investigations of ground state properties of the electronically correlated systems is presented. As an example, $(H_{2})_{n}$ chain is considered with the long-range electron-electron interactions taken into account. The implemented procedure covers: (i) single-particle Wannier wave-function basis construction in the correlated state, (ii) microscopic parameters calculation, and (iii) ground state energy optimization. The optimization loop is based on highly effective process-pool solution - specific root-workers approach. The hierarchical, two-lev…
We propose two schemes for interpolation of the one-particle Green's function (GF) calculated within coupled-cluster singles and doubles (CCSD) method for a periodic system. They use Wannier orbitals for circumventing huge cost for a large number of sampled k points. One of the schemes is the direct interpolation, which obtains the GF straightforwardly by using Fourier transformation. The other is the self-energy-mediated interpolation, which obtains the GF via the Dyson equation. We apply the schemes to a LiH chain and trans-polyacetylene and examine their validity in detail. It is demonstrat…
The paper presents the group theory of best localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into best localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M, or to a subgroup of G or M. In this context, the…
We investigate correlated insulating states in magic-angle twisted bilayer graphene (TBG) by the exact diagonalization method applied to the extended Hubbard model with interaction parameters recently evaluated in the realistic effective model. Our model can handle the competing interactions among Wannier orbitals owing to their significant overlap, which is a crucial but overlooked aspect of the magic-angle TBG. We propose two candidates for the correlated insulating states: spin- and valley-ferromagnetic band insulator and the Dirac semimetallic state for two flavors with peculiar renormaliz…
Twisted bilayer graphene (TBLG) has emerged as an important platform for studying correlated phenomena, including unconventional superconductivity, in two-dimensional systems. The complexity of the atomic-scale structures in TBLG has made even the study of single-particle physics at low energies around the Fermi level, quite challenging. Our goal here is to provide a convenient and physically motivated picture of single-particle physics in TBLG using reduced models with the smallest possible number of localized orbitals. The reduced models exactly reproduce the low-energy bands of \textit{ab-i…
We construct a Wannier basis for twisted bilayer graphene that is projected only from the Bloch functions of the twisted bilayer flat bands. The $C_3$ and $C_{2} \mathcal{T}$ symmetries act locally on the Wannier functions while the Wannier function charge density is strongly peaked at the triangular sites and becomes fully sublattice-polarized in the chiral limit. The Wannier functions have a power-law tail, due to the topological obstruction, but most of the charge density is concentrated within one unit cell so that the on-site local Coulomb interaction is much larger than the further neigh…
Examining phase stabilities and phase equilibria in strongly correlated materials asks for a next level in the many-body extensions to the local-density approximation (LDA) beyond mainly spectroscopic assessments. Here we put the charge-self-consistent LDA+dynamical mean-field theory (DMFT) methodology based on projected local orbitals for the LDA+DMFT interface and a tailored pseudopotential framework into action in order to address such thermodynamics of realistic strongly correlated systems. Namely a case study for the electronic phase diagram of the well-known prototype Mott-phenomena syst…
There have been extensive recent developments on kagome metals, such as T$_m$X$_n$ (T= Fe, Co and X= Sn, Ge) and $A$V$_3$Sb$_5$ ($A=$ Cs, K, Rb). An emerging issue is the nature of correlated phases when topologically \textit{non-trivial} bands cross the Fermi level. Here, we consider an extended Hubbard model on the kagome lattice in the presence of spin-orbit couplings, involving a Kramer's pair of bands that have opposite Chern numbers and are isolated in the band structure. We construct an effective model in a time-reversal (T) symmetric lattice description. We determine the correlated pha…
We discuss physical properties of strongly correlated electron states for a linear chain obtained with the help of the recently proposed new method combining the exact diagonalization in the Fock space with an ab initio readjustment of the single-particle orbitals in the correlated state. The method extends the current discussion of the correlated states since the properties are obtained with varying lattice spacing. The finite system of N atoms evolves with the increasing interatomic distance from a Fermi-liquid-like state into the Mott insulator. The criteria of the localization are discusse…
A novel hybrid scheme is proposed. The {\it ab initio} LDA calculation is used to construct the Wannier functions and obtain single electron and Coulomb parameters of the multiband Hubbard-type model. In strong correlation regime the electronic structure within multiband Hubbard model is calculated by the Generalized Tight-Binding (GTB) method, that combines the exact diagonalization of the model Hamiltonian for a small cluster (unit cell) with perturbation treatment of the intercluster hopping and interactions. For undoped La$_2$CuO$_4$ and Nd$_2$CuO$_4$ this scheme results in charge transfer…
We present a quantum critical behavior of the renormalized single-particle Wannier function, calculated in the Gutzwiller correlated state near the insulator-metal transition (IMT) for cubic lattices. The wave function size and its maximum, as well as the system energy scale with increasing lattice parameter $R$ as $R^{n}$. Such scaling is interpreted as the evidence of a dominant role of the Coulomb repulsion. Relation of the insulator-metal transition lattice-parameter value $R=R_{C}$ to the original {\em Mott criterion\} is obtained. The method is tested by comparing our results with the ex…
We present a first-principles method for deriving effective low-energy models of electrons in solids having entangled band structure. The procedure starts with dividing the Hilbert space into two subspaces, the low-energy part ("$d$ space'') and the rest of the space ("$r$ space''). The low-energy model is constructed for the $d$ space by eliminating the degrees of freedom of the $r$ space. The thus derived model contains the strength of electron correlation expressed by a partially screened Coulomb interaction, calculated in the constrained random-phase-approximation (cRPA) where screening ch…
RESPACK is a first-principles calculation software for evaluating the interaction parameters of materials and is able to calculate maximally localized Wannier functions, response functions based on the random phase approximation and related optical properties, and frequency-dependent electronic interaction parameters. RESPACK receives its input data from a band-calculation code using norm-conserving pseudopotentials with plane-wave basis sets. Automatic generation scripts that convert the band-structure results to the RESPACK inputs are prepared for xTAPP and Quantum ESPRESSO. An input file fo…
We review recent results on the properties of materials with correlated electrons obtained within the LDA+DMFT approach, a combination of a conventional band structure approach based on the local density approximation (LDA) and the dynamical mean-field theory (DMFT). The application to four outstanding problems in this field is discussed: (i) we compute the full valence band structure of the charge-transfer insulator NiO by explicitly including the p-d hybridization, (ii) we explain the origin for the simultaneously occuring metal-insulator transition and collapse of the magnetic moment in MnO…
The realistic description of correlated electron systems has taken an important step forward a few years ago as the combination of density functional methods and the dynamical mean-field theory was conceived. This framework allows access to both high and low energy physics and is capable of the description of the specific physics of strongly correlated materials, like the Mott metal-insulator transition. A very important step in the procedure is the interface between the band structure method and the dynamical mean-field theory and its impurity solver. We present a general interface between a …
Developing realistic and precise models of the electronic properties of organic molecular crystals is crucial for understanding the full range of strongly correlated phases that they exhibit. By using \textit{ab initio} model construction methods, one can obtain unbiased non-interacting models of such systems from density functional theory, upon which one can base further (many-body) models. We will discuss the utility and advantages of \textit{ab initio} model construction using Wannier orbitals. We will briefly review the approach, and then explain why it is so well suited to molecular cryst…
We present the TRIQS/DFTTools package, an application based on the TRIQS library that connects this toolbox to realistic materials calculations based on density functional theory (DFT). In particular, TRIQS/DFTTools together with TRIQS allows an efficient implementation of DFT plus dynamical mean-field theory (DMFT) calculations. It supplies tools and methods to construct Wannier functions and to perform the DMFT self-consistency cycle in this basis set. Post-processing tools, such as band-structure plotting or the calculation of transport properties are also implemented. The package comes wit…
An expression is derived for angle-resolved photocurrent from a semi-infinite correlated system. Within the sudden approximation, the photocurrent is proportional to the spectral function of a one-particle two-time retarded Green's function $\mathcal{G}$ of an operator that creates an electron in a special quantum state $χ$ localized at the surface. For a system described by a many-body single-band model we present an analytical expression that relates the Green's function $\mathcal{G}$ with the Green's function of an infinite crystal $G_{b,\mathbf{k}}(ω)$ in Wannier representation. The role o…
LDA+DMFT (Local Density Approximation combined with Dynamical Mean-Field Theory) computation scheme has been used to calculate spectral properties of LaFeAsO -- the parent compound of the new high-T_c iron oxypnictides. The average Coulomb repulsion U=3-4 eV and Hund's exchange J=0.8 eV parameters for iron 3d electrons were calculated using the first principles constrained density functional theory scheme in the Wannier functions formalism. DMFT calculations using these parameters result in moderately correlated electronic structure with effective electron mass enhancement m^*~2 that is in agr…
We discuss the construction of low-energy tight-binding Hamiltonians for condensed matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given set of Wannier orbitals. However, different representations of the continuum theory lead to different low-energy formulations, because different representations may entangle light and matter, transforming orbitals into light-matter hybrid states before the projection. In particular, a multi-center Power-Zienau-Woolley transformation yields a dipolar Hamiltoni…
We analyze the strongly correlated regime of a two-component trapped ultracold fermionic gas in a synthetic non-Abelian U(2) gauge potential, that consists of both a magnetic field and a homogeneous spin-orbit coupling. This gauge potential deforms the Landau levels (LLs) with respect to the Abelian case and exchanges their ordering as a function of the spin-orbit coupling. In view of experimental realizations, we show that a harmonic potential combined with a Zeeman term, gives rise to an angular momentum term, which can be used to test the stability of the correlated states obtained through …
We present an approach that combines the local density approximation (LDA) and the dynamical mean-field theory (DMFT) in the framework of the full-potential linear augmented plane waves (FLAPW) method. Wannier-like functions for the correlated shell are constructed by projecting local orbitals onto a set of Bloch eigenstates located within a certain energy window. The screened Coulomb interaction and Hund's coupling are calculated from a first-principle constrained RPA scheme. We apply this LDA+DMFT implementation, in conjunction with continuous-time quantum Monte-Carlo, to study the electroni…
The possible discovery of $s_\pm$ superconducting gaps in the moderately correlated iron-based superconductors has raised the question of how to properly treat $s_\pm$ gaps in strongly correlated superconductors. Unlike the d-wave cuprates, the Coulomb repulsion does not vanish by symmetry, and a careful treatment is essential. Thus far, only the weak correlation approaches have included this Coulomb pseudopotential, so here we introduce a symplectic N treatment of the t-J model that incorporates the strong Coulomb repulsion through the complete elimination of on-site pairing. Through a proper…
