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DOE OSTI2022

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Quantum real-time evolution of entanglement and hadronization in jet production: Lessons from the massive Schwinger model

The possible link between entanglement and thermalization, and the dynamics of hadronization are addressed by studying the real-time response of the massive Schwinger model coupled to external sources. This setup mimics the production and fragmentation of quark jets, as the Schwinger model and quantum chromodynamics (QCD) share the properties of confinement and chiral symmetry breaking. By using simulations of quantum dynamics on classical hardware, we study the entanglement between the produced jets, and observe the growth of the corresponding entanglement entropy in time. This growth arises from the increased number of contributing eigenstates of the reduced density matrix with sufficiently large and close eigenvalues. We also investigate the physical nature of these eigenstates, and find that at early times they correspond to fermionic Fock states. We then observe the transition from these fermionic Fock states to mesonlike bound states as a function of time. In other words, we observe how hadronization develops in real time. At late times, the local observables at midrapidity (such as the fermion density and the electric field) approach approximately constant values, suggesting the onset of equilibrium and approach to thermalization. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Extended Lagrangian Density Functional Tight-Binding Molecular Dynamics for Molecules and Solids

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian density functional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent density functional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born–Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materials science, chemistry, and biology.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Efficiency of fermionic quantum distillation

Here, we present a time-dependent density-matrix renormalization group investigation of the quantum distillation process within the Fermi-Hubbard model on a quasi-one-dimensional ladder geometry. The term distillation refers to the dynamical, spatial separation of singlons and doublons in the sudden expansion of interacting particles in an optical lattice, i.e., the release of a cloud of atoms from a trapping potential. Remarkably, quantum distillation can lead to a contraction of the doublon cloud, resulting in an increased density of the doublons in the core region compared to the initial state. As a main result, we show that this phenomenon is not limited to chains that were previously studied. Interestingly, there are additional dynamical processes on the two-leg ladder such as density oscillations and self-trapping of defects that lead to a less efficient distillation process. An investigation of the time evolution starting from product states provides an explanation for this behavior. Initial product states are also considered since in optical lattice experiments, such states are often used as the initial setup. We propose configurations that lead to a fast and efficient quantum distillation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

A unified approach for computing (i) spin-transfer torque in magnetic trilayers like spin valve and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces, and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled material, where injected charge current flows parallel to the interface, was reviewed. The experimentally explored and technologically relevant spin-orbit-coupled materials include 5d heavy metals, topological insulators, Weyl semimetals, and transition metal dichalcogenides. This approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green’s functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. Illustrative examples are provided by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations, as well as by computing spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, it is shown here how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green’s function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. Furthermore, errors made in the calculation of spin-transfer torque are quantified when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

First measurement of prompt and non-prompt D* + vector meson spin alignment in pp collisions at $\sqrt{s}$ = 13 TeV

This letter reports the first measurement of spin alignment, with respect to the helicity axis, for D* + vector mesons and their charge conjugates from charm-quark hadronisation (prompt) and from beauty meson decays (non-prompt) in hadron collisions. The measurements were performed at midrapidity (|y| < 0.8) as a function of transverse momentum (p T ) in proton–proton (pp) collisions collected by ALICE at the centre-of-mass energy $\sqrt{s}$ = 13 TeV. The diagonal spin density matrix element $ρ$00 of D* + mesons was measured from the angular distribution of the D* + → D 0 (→ K - π + )π + decay products, in the D* + rest frame, with respect to the D* + momentum direction in the pp centre of mass frame. The $ρ$00 value for prompt D* + mesons is consistent with 1/3, which implies no spin alignment. However, for non prompt D* + mesons an evidence of $ρ$00 larger than 1/3 is found. The measured value of the spin density element is $ρ$00 = 0.455±0.022(stat.)±0.035(syst.) in the 5 < p T < 20 GeV/c interval, which is consistent with a Pythia 8 Monte Carlo simulation coupled with the EvtGen package, which implements the helicity conservation in the decay of D* + meson from beauty mesons. In non-central heavy-ion collisions, the spin of the D* + mesons may be globally aligned with the direction of the initial angular momentum and magnetic field. Based on the results for pp collisions reported in this letter it is shown that alignment of non-prompt D* + mesons due to the helicity conservation coupled to the collective anisotropic expansion may mimic the signal of global spin alignment in heavy-ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Universal tight binding model for chemical reactions in solution and at surfaces. I. Organic molecules

As is now well established, a first order expansion of the Hohenberg–Kohn total energy density functional about a trial input density, namely, the Harris–Foulkes functional, can be used to rationalize a non self consistent tight binding model. If the expansion is taken to second order then the energy and electron density matrix need to be calculated self consistently and from this functional one can derive a charge self consistent tight binding theory. In this paper we have used this to describe a polarizable ion tight binding model which has the benefit of treating charge transfer in point multipoles. This admits a ready description of ionic polarizability and crystal field splitting. It is necessary in constructing such a model to find a number of parameters that mimic their more exact counterparts in the density functional theory. We describe in detail how this is done using a combination of intuition, exact analytical fitting, and a genetic optimization algorithm. Having obtained model parameters we show that this constitutes a transferable scheme that can be applied rather universally to small and medium sized organic molecules. We have shown that the model gives a good account of static structural and dynamic vibrational properties of a library of molecules, and finally we demonstrate the model's capability by showing a real time simulation of an enolization reaction in aqueous solution. In two subsequent papers, we show that the model is a great deal more general in that it will describe solvents and solid substrates and that therefore we have created a self consistent quantum mechanical scheme that may be applied to simulations in heterogeneous catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Global phase diagram of D-wave superconductivity in the square-lattice t-J model

The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.

Chen, Feng (ORCID:000000018196030X)↗

DOE OSTI2023

Plasmon-enhanced optical nonlinearity in graphene nanomeshes

Using the density-matrix formalism, here we show that graphene nanomeshes (GNMs)—graphene sheets patterned with antidots—have large plasmon-enhanced nonlinear optical response. GNMs can be designed to behave as quasi-one-dimensional plasmonic crystals in which plasmons with large propagation lengths are efficiently excited. The associated third-order Kerr and third-harmonic-generation susceptibility can be as high as 10 –7 and 10 –9 m 2 V –2 , respectively, over the mid-to-near-infrared frequency range. Furthermore, carrier-density tuning in GNMs can flip the propagation direction of plasmonic waves and enables bidirectional switching of optical signals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid

We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t–J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ = 0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. In conclusion, our results may be relevant to kagome lattice herbertsmithite upon doping.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport

Based on the complex absorbing potential (CAP) method, a Lorentzian expansion scheme is developed to express the self-energy. The CAP-based Lorentzian expansion of self-energy is employed to solve efficiently the Liouville-von Neumann equation of one-electron density matrix. The resulting method is applicable for both tight-binding and first-principles models and is used to simulate the transient currents through graphene nanoribbons and a benzene molecule sandwiched between two carbon-atom chains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number K=2. In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a nontrivial algebraic vanishing BEC density together with a nonergodic occupation in real space. These peculiar properties can be analytically captured by a simple phenomenological description on the Cayley tree which provides a physical picture of the Bose glass regime.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Use of Spectral Analysis of Singular Values as a Test Metric for IMMAT Trials

One of many challenges in the implementation of multiple exciter testing is establishing a reasonable set of test metrics to measure the quality of testing. This is especially true in the application of Impedance Matched Multi-Axis Testing; in that it is possible to have very large spectral density matrices that serve as reference criteria. While there exist plotting schemes to view a spectral density matrix, it is often necessary to break the overlay of reference and test results into subsections of the matrices to get sufficient resolution to interpret the data. In addition, as one attempts to control multiple locations on a structure, implementation of classical single degree-of freedom test tolerances across all channels and associated cross spectra is simply not feasible. Hence it is challenging to evaluate overall test quality. The use of spectral views of the dominant singular values from the singular value decomposition of the spectral density matrices and metrics based upon them is proposed for establishing a set of compact metrics for evaluating test quality. A laboratory experiment will be included to demonstrate this proposed technique.

Impedance Matched Multi-Axis Testing↗

NASA NTRSDate not supplied

Use of Spectral Analysis of Singular Values as a Test Metric for Impedance Matched Multi-Axis Test Trials

Vibration Testing↗

NASA NTRS2003

Collective Excitations in InAs Well Intersubband Transitions

Intersubband transitions in semiconductor quantum well are studied using a density matrix theory that goes beyond the Hartree-Fock approximation by including the full second order electron-electron scattering terms in the polarization equation for the first time. Even though the spectral features remain qualitatively similar to the results obtained with dephasing rate approximation, significant quantitative changes result from such a more detailed treatment of dephasing. More specifically, we show how the interplay of the two fundamental collective excitations, the Fermi-edge singularity and the intersubband plasmon, leads to significant changes in lineshape as the electron density varies.

Li, Jian-Zhong↗

DOE OSTI2020

Prediction of exotic magnetic states in the alkali-metal quasi-one-dimensional iron selenide compound Na 2 FeSe 2

The magnetic and electronic phase diagram of a model for the quasi-one-dimensional alkali-metal iron selenide compound Na 2 FeSe 2 is presented. The novelty of this material is that the valence of iron is Fe 2+ , contrary to most other iron-chain compounds with valence Fe 3+ . Using first-principles techniques, we developed a three-orbital tight-binding model that reproduces the ab initio band structure near the Fermi level. Including Hubbard and Hund couplings and studying the model via the density-matrix renormalization group and Lanczos methods, we constructed the ground-state phase diagram. A robust region where the block state ↑↑↓↓↑↑↓↓ is stabilized was unveiled. The analog state in iron ladders, employing 2×2 ferromagnetic blocks, is by now well established, but in chains a block magnetic order has not been observed yet in real materials. The phase diagram also contains a large region of canonical staggered spin order ↑↓↑↓↑↓↑ at very large Hubbard repulsion. At the block-to-staggered transition region, an exotic phase is stabilized with a mixture of both states: an inhomogeneous orbital-selective charge density wave with the exotic spin configuration ↑↑↓↑↓↓↑↓. Our predictions for Na 2 FeSe 2 may guide crystal growers and neutron-scattering experimentalists towards the realization of block states in one-dimensional iron selenide chain materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Cost-effective description of strong correlation: Efficient implementations of the perfect quadruples and perfect hextuples models

Novel implementations based on dense tensor storage are presented here for the singlet-reference perfect quadruples (PQ) [J. A. Parkhill et al., J. Chem. Phys. 130, 084101 (2009)] and perfect hextuples (PH) [J. A. Parkhill and M. Head-Gordon, J. Chem. Phys. 133, 024103 (2010)] models. The methods are obtained as block decompositions of conventional coupled-cluster theory that are exact for four electrons in four orbitals (PQ) and six electrons in six orbitals (PH), but that can also be applied to much larger systems. PQ and PH have storage requirements that scale as the square, and as the cube of the number of active electrons, respectively, and exhibit quartic scaling of the computational effort for large systems. Applications of the new implementations are presented for full-valence calculations on linear polyenes (C n H n+2 ), which highlight the excellent computational scaling of the present implementations that can routinely handle active spaces of hundreds of electrons. The accuracy of the models is studied in the π space of the polyenes, in hydrogen chains (H 50 ), and in the π space of polyacene molecules. In all cases, the results compare favorably to density matrix renormalization group values. With the novel implementation of PQ, active spaces of 140 electrons in 140 orbitals can be solved in a matter of minutes on a single core workstation, and the relatively low polynomial scaling means that very large systems are also accessible using parallel computing.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Selection of active spaces for multiconfigurational wavefunctions

The efficient and accurate description of the electronic structure of strongly correlated systems is still a largely unsolved problem. The usual procedures start with a multiconfigurational (usually a Complete Active Space, CAS) wavefunction which accounts for static correlation and add dynamical correlation by perturbation theory, configuration interaction, or coupled cluster expansion. This procedure requires the correct selection of the active space. Intuitive methods are unreliable for complex systems. The inexpensive black-box unrestricted natural orbital (UNO) criterion postulates that the Unrestricted Hartree-Fock (UHF) charge natural orbitals with fractional occupancy (e.g., between 0.02 and 1.98) constitute the active space. UNOs generally approximate the CAS orbitals so well that the orbital optimization in CAS Self-Consistent Field (CASSCF) may be omitted, resulting in the inexpensive UNO-CAS method. A rigorous testing of the UNO criterion requires comparison with approximate full configuration interaction wavefunctions. This became feasible with the advent of Density Matrix Renormalization Group (DMRG) methods which can approximate highly correlated wavefunctions at affordable cost. We have compared active orbital occupancies in UNO-CAS and CASSCF calculations with DMRG in a number of strongly correlated molecules: compounds of electronegative atoms (F{sub 2}, ozone, and NO{sub 2}), polyenes, aromatic molecules (naphthalene, azulene, anthracene, and nitrobenzene), radicals (phenoxy and benzyl), diradicals (o-, m-, and p-benzyne), and transition metal compounds (nickel-acetylene and Cr{sub 2}). The UNO criterion works well in these cases. Other symmetry breaking solutions, with the possible exception of spatial symmetry, do not appear to be essential to generate the correct active space. In the case of multiple UHF solutions, the natural orbitals of the average UHF density should be used. The problems of the UNO criterion and their potential solutions are discussed: finding the UHF solutions, discontinuities on potential energy surfaces, and inclusion of dynamical electron correlation and generalization to excited states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗