Low-energy models for correlated materials: bandwidth renormalization from Coulombic screening

Low-Scaling Algorithms for GW and Constrained Random Phase Approximation Using Symmetry-Adapted Interpolative Separable Density Fitting

We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically, with respect to system size, and linearly with the number of k-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with k-point sampling beyond density functional theory.

Rigorous Screened Interactions for Realistic Correlated Electron Systems

We derive a widely applicable first-principles approach for determining two-body, static effective interactions for low-energy Hamiltonians with quantitative accuracy. The algebraic construction rigorously conserves all instantaneous two-point correlation functions in a chosen model space at the level of the random phase approximation, improving upon the traditional uncontrolled static approximations. Applied to screened interactions within a quantum embedding framework, we demonstrate these faithfully describe the relaxation of local subspaces via downfolding high-energy physics in molecular systems, as well as enabling a systematically improvable description of the long-range plasmonic contributions in extended graphene.

Towards near-term quantum simulation of materials

Determining the ground and excited state properties of materials is considered one of the most promising applications of quantum computers. On near-term hardware, the limiting constraint on such simulations is the requisite circuit depths and qubit numbers, which currently lie well beyond near-term capabilities. Here we develop a quantum algorithm which reduces the estimated cost of material simulations. For example, we obtain a circuit depth improvement by up to 6 orders of magnitude for a Trotter layer of time-dynamics simulation in the transition-metal oxide SrVO3 compared with the best previous quantum algorithms. We achieve this by introducing a collection of connected techniques, including highly localised and physically compact representations of materials Hamiltonians in the Wannier basis, a hybrid fermion-to-qubit mapping, and an efficient circuit compiler. Combined together, these methods leverage locality of materials Hamiltonians and result in a design that generates quantum circuits with depth independent of the system's size. Although the requisite resources for the quantum simulation of materials are still beyond current hardware, our results show that realistic simulation of specific properties may be feasible without necessarily requiring fully scalable, fault-tolerant quantum computers, providing quantum algorithm design incorporates deeper understanding of the target materials and applications.

Correlated Electronic Structure of La_{3}Ni_{2}O_{7} under Pressure

Recently, superconductivity with a T_{c} up to 78 K has been reported in bulk samples of the bilayer nickelate La_{3}Ni_{2}O_{7} at pressures above 14 GPa. Important theoretical tasks are the formulation of relevant low-energy models and the clarification of the normal state properties. Here, we study the correlated electronic structure of the high-pressure phase in a four-orbital low-energy subspace using different many-body approaches: GW, dynamical mean field theory (DMFT), extended DMFT (EDMFT) and GW+EDMFT, with realistic frequency-dependent interaction parameters. The nonlocal correlation and screening effects captured by GW+EDMFT result in an instability toward the formation of charge stripes, with the 3d_{z^{2}} as the main active orbital. We also comment on the potential relevance of the rare-earth self-doping pocket, since hole doping suppresses the ordering tendency.

Interacting chiral electrons at the 2D Dirac points: a review

The pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as the massless Dirac or Weyl fermions, constitute various intriguing issues in modern condensed-matter physics. In particular, the issues linked to the Coulomb interaction between the chiral electrons attract great attentions due to their unusual features, namely, the interaction is not screened and has a long-ranged property near the charge-neutrality point, in clear contrast to its screened and short-ranged properties in the conventional correlated materials. In graphene, this long-range interaction induces an anomalous logarithmic renormalization of the Fermi velocity, which causes a nonlinear reshaping of its Dirac cone. In addition, for strong interactions, it even leads to the predictions of an excitonic condensation with a spontaneous mass generation. The interaction, however, would seem to be not that large in graphene, so that the latter phenomenon appears to have not yet been observed. Contrastingly, the interaction is probably large in the pressurized organic materialα-(BEDT-TTF)₂I₃, where a 2D massless-Dirac-fermion phase emerges next to a correlated insulating phase. Therefore, an excellent testing ground would appear in this material for the studies of both the velocity renormalization and the mass generation, as well as for those of the short-range electronic correlations. In this review, we give an overview of the recent progress on the understanding of such interacting chiral electrons in 2D, by placing particular emphasis on the studies in graphene andα-(BEDT-TTF)₂I₃. In the first half, we briefly summarize our current experimental and theoretical knowledge about the interaction effects in graphene, then turn attentions to the understanding inα-(BEDT-TTF)₂I₃, and highlight its relevance to and difference from graphene. The second half of this review focusses on the studies linked to the nuclear magnetic resonance experiments and the associated model calculations inα-(BEDT-TTF)₂I₃. These studies allow us to discuss the anisotropic reshaping of a tilted Dirac cone together with various electronic correlations, and the precursor excitonic dynamics growing prior to a condensation. We see these provide unique opportunities to resolve the momentum dependence of the spin excitations and fluctuations that are strongly influenced by the long-range interaction near the Dirac points.

Bandwidth renormalization due to the intersite Coulomb interaction

The theory of correlated electrons is currently moving beyond the paradigmatic Hubbard U, towards the investigation of intersite Coulomb interactions. Recent investigations have revealed that these interactions are relevant for the quantitative description of realistic materials. Physically, intersite interactions are responsible for two rather different effects: screening and bandwidth renormalization. We use a variational principle to disentangle the roles of these two processes and study how appropriate the recently proposed Fock treatment of intersite interactions is in correlated systems. The magnitude of this effect in graphene is calculated based on cRPA values of the intersite interaction. We also apply the variational principle to benzene and find effective parameters comparable to those obtained by ab initio density matrix downfolding.

Electronic correlations in dense iron: from moderate pressure to Earth's core conditions

We discuss the role of dynamical many-electron effects in the physics of iron and iron-rich solid alloys under applied pressure on the basis of recent ab initio studies employing the dynamical mean-field theory (DMFT). We review in detail two particularly interesting regimes: first, a moderate pressure range up to 60 GPa and, second, the ultra-high pressure of about 360 GPa expected inside the solid inner core of Earth. Electronic correlations in iron under the moderate pressure of several tens GPa are discussed in the first section. DMFT-based methods predict an enhancement of electronic correlations at the pressure-induced body-centered cubic α to hexagonal close-packed [Formula: see text] phase transition. In particular, the electronic effective mass, scattering rate and electron-electron contribution to the electrical resistivity undergo a step-wise increase at the transition point. One also finds a significant many-body correction to the [Formula: see text]-Fe equation of state, thus clarifying the origin of discrepancies between previous DFT studies and experiment. An electronic topological transition is predicted to be induced in [Formula: see text]-Fe by many-electron effects; its experimental signatures are analyzed. The next section focuses on the geophysically relevant pressure-temperature regime of the Earth's inner core (EIC) corresponding to the extreme pressure of 360 GPa combined with temperatures up to 6000 K. The three iron allotropes ([Formula: see text], [Formula: see text] and face-centered-cubic [Formula: see text]) previously proposed as possible stable phases at such conditions are found to exhibit qualitatively different many-electron effects as evidenced by a strongly non-Fermi-liquid metallic state of [Formula: see text]-Fe and an almost perfect Fermi liquid in the case of [Formula: see text]-Fe. A recent active discussion on the electronic state and transport properties of [Formula: see text]-Fe at the EIC conditions is reviewed in details. Estimations for the dynamical many-electron contribution to the relative phase stability are presented. We also discuss the impact of a Ni admixture, which is expected to be present in the core matter. We conclude by outlining some limitation of the present DMFT-based framework relevant for studies of iron-base systems as well as perspective directions for further development.

Towards a First-Principles Determination of Effective Coulomb Interactions in Correlated Electron Materials: Role of Intershell Interactions

The determination of the effective Coulomb interactions to be used in low-energy Hamiltonians for materials with strong electronic correlations remains one of the bottlenecks for parameter-free electronic structure calculations. We propose and benchmark a scheme for determining the effective local Coulomb interactions for charge-transfer oxides and related compounds. Intershell interactions between electrons in the correlated shell and ligand orbitals are taken into account in an effective manner, leading to a reduction of the effective local interactions on the correlated shell. Our scheme resolves inconsistencies in the determination of effective interactions as obtained by standard methods for a wide range of materials, and allows for a conceptual understanding of the relation of cluster model and dynamical mean field-based electronic structure calculations.

Interfacial defects induced electronic property transformation at perovskite SrVO3/SrTiO3 and LaCrO3/SrTiO3 heterointerfaces

Unravelling the atomic structure and chemical species of interfacial defects is critical to understanding the origin of interfacial properties in many heterojunctions.

Dynamical screening in correlated electron systems-from lattice models to realistic materials

Recent progress in treating the dynamical nature of the screened Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We discuss approximate and exact methods for the solution of impurity models with retarded interactions, and explain how these models appear as auxiliary problems in various extensions of the dynamical mean field formalism. The current state of the field is illustrated with results from recent applications of these schemes to U-V Hubbard models and correlated materials.

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.

Interaction-Driven Metal-Insulator Transition in Strained Graphene

The question of whether electron-electron interactions can drive a metal to insulator transition in graphene under realistic experimental conditions is addressed. Using three representative methods to calculate the effective long-range Coulomb interaction between π electrons in graphene and solving for the ground state using quantum Monte Carlo methods, we argue that, without strain, graphene remains metallic and changing the substrate from SiO_{2} to suspended samples hardly makes any difference. In contrast, applying a rather large-but experimentally realistic-uniform and isotropic strain of about 15% seems to be a promising route to making graphene an antiferromagnetic Mott insulator.

Dynamical correlations and screened exchange on the experimental bench: spectral properties of the cobalt pnictide BaCo2As2

Understanding the Fermi surface and low-energy excitations of iron or cobalt pnictides is crucial for assessing electronic instabilities such as magnetic or superconducting states. Here, we propose and implement a new approach to compute the low-energy properties of correlated electron materials, taking into account both screened exchange beyond the local density approximation and local dynamical correlations. The scheme allows us to resolve the puzzle of BaCo2As2, for which standard electronic structure techniques predict a ferromagnetic instability not observed in nature.

Dynamical mean field theory-based electronic structure calculations for correlated materials

We give an introduction to dynamical mean field approaches to correlated materials. Starting from the concept of electronic correlation, we explain why a theoretical description of correlations in spectroscopic properties needs to go beyond the single-particle picture of band theory.We discuss the main ideas of dynamical mean field theory and its use within realistic electronic structure calculations, illustrated by examples of transition metals, transition metal oxides, and rare-earth compounds. Finally, we summarise recent progress on the calculation of effective Hubbard interactions and the description of dynamical screening effects in solids.

Dynamical screening effects in correlated electron materials-a progress report on combined many-body perturbation and dynamical mean field theory: 'GW + DMFT'

We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed 'LDA + DMFT'. It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(ω) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency dependence leads to effects that cannot be neglected in a truly first principles description. We review the recently introduced extension of LDA + DMFT to dynamical local Coulomb interactions 'LDA + U(ω) + DMFT' (Casula et al 2012 Phys. Rev. B 85 035115, Werner et al 2012 Nature Phys. 1745-2481). A reliable description of dynamical screening effects is also a central ingredient of the 'GW + DMFT' scheme (Biermann et al 2003 Phys. Rev. Lett. 90 086402), a combination of many-body perturbation theory in Hedin's GW approximation and dynamical mean field theory. Recently, the first GW + DMFT calculations including dynamical screening effects for real materials have been achieved, with applications to SrV O3 (Tomczak et al 2012 Europhys. Lett. 100 67001, Tomczak et al Phys. Rev. B submitted (available electronically as arXiv:1312.7546)) and adatom systems on surfaces (Hansmann et al 2013 Phys. Rev. Lett. 110 166401). We review these and comment on further perspectives in the field. This review is an attempt to put elements of the original works into the broad perspective of the development of truly first principles techniques for correlated electron materials.