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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Finite-temperature many-body perturbation theory in the grand canonical ensemble

A finite-temperature many-body perturbation theory is presented, which expands in power series the electronic grand potential, chemical potential, internal energy, and entropy on an equal footing. Sum-over-states and sum-over-orbitals analytical formulas for the second-order perturbation corrections to these thermodynamic properties are obtained in a time-independent, nondiagrammatic, algebraic derivation, relying on the sum rules of the Hirschfelder–Certain degenerate perturbation energies in a degenerate subspace as well as nine algebraic identities for the zeroth-order thermal averages of one- through four-indexed quantities and products thereof. Lastly, they reproduce numerically exactly the benchmark data obtained as the numerical derivatives of the thermal-full-configuration-interaction results for a wide range of temperatures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Low-temperature breakdown of many-body perturbation theory for thermodynamics

It is shown analytically and numerically that the finite-temperature many-body perturbation theory in the grand canonical ensemble has zero radius of convergence at zero temperature when the energy ordering or degree of degeneracy for the ground state changes with the perturbation strength. When the degeneracy of the reference state is partially or fully lifted at the first-order Hirschfelder-Certain degenerate perturbation theory, the grand potential and internal energy diverge as T → 0. Contrary to earlier suggestions of renormalizability by the chemical potential μ, this nonconvergence, first suspected by W. Kohn and J. M. Luttinger, is caused by the nonanalytic nature of the Boltzmann factor e –E/k e T at T = 0, also plaguing the canonical ensemble, which does not involve chemical potential. The finding reveals a fundamental flaw in perturbation theory, which is deeply rooted in the mathematical limitation of power-series expansions and is unlikely to be removed within its framework.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Many-body perturbation theory with hybrid density functional theory starting points accelerated by adaptively compressed exchange

We report on the use of the adaptively compressed exchange (ACE) operator to accelerate many-body perturbation theory (MBPT) calculations, including G 0 W 0 and the Bethe–Salpeter equation (BSE), for hybrid density functional theory starting points. We show that by approximating the exact exchange operator with the low-rank ACE operator, substantial computational savings can be achieved with systematically controllable errors in the quasiparticle energies computed with full-frequency G 0 W 0 and the optical absorption spectra and vertical excitation energies computed by solving the BSE within density matrix perturbation theory. Our implementation makes use of the ACE-accelerated electronic Hamiltonian to carry out both G 0 W 0 and BSE without explicitly computing empty states. We show the robustness of the approach and present the computational gains obtained on both the central processing unit and graphics processing unit nodes. In conclusion, our work will facilitate the exploration and evaluation of fine-tuned hybrid starting points aimed at enhancing the accuracy of MBPT calculations without involving computationally demanding self-consistency in Hedin’s equations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Relativistic configuration-interaction and many-body-perturbation-theory calculations of U i hyperfine constants

Neutral uranium (U i) is a very difficult atom for theoretical calculations due to a large number (six) of valence electrons, strong valence-valence and valence-core correlations, high density of states, and relativistic effects. Configuration-interaction many-body perturbation theory (CI-MBPT) can efficiently treat valence-core correlations and relativistic effects, but because the formalism was developed for a Dirac-Hartree-Fock (DHF) starting potential that does not contain valence electrons, quite large CI space is needed to compensate for the + 6 charge of such a potential. Much more efficient is the relativistic configuration-interaction (RCI) approach, which uses a relatively accurate starting DHF potential that includes some valence electrons to make the valence-electron Hamiltonian diagonally dominated for some states. Here we report calculations of U i hyperfine constants of several low-energy states using the RCI method with the starting potential that includes four f valence electrons. With this starting potential, it is possible to use the single-configuration approximation or small basis sets to obtain quite accurate results for hyperfine-structure constants. In fact, by scaling the nuclear magnetic moment, the agreement for five levels was within 5% and a new magnetic moment can be recommended, 0.43(2). When two states are mixed, it is difficult to predict the exact mixing fractions, so in this case we proposed a method in which the mixing fraction is found by optimization of one parameter in the MBPT correction to obtain correct g factors. The resulting hyperfine constants are significantly improved. Finally, the CI-MBPT approach was also tested, with some success for low-energy states, with the limited basis set. The methods investigated here can be further developed to include more extensive data sets to improve accuracy and can be applied to other atoms and for calculations of other properties, for example, relevant to fundamental symmetry tests.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

A Many-Body Perturbation Theory Approach to Energy Band Alignment at the Crystalline Tetracene–Silicon Interface

Hybrid inorganic–organic semiconductor (HIOS) interfaces are of interest for new photovoltaic devices operating above the Shockley–Queisser limit. Predicting energy band alignment at the interfaces is crucial for their design, but represents a challenging problem due to the large scales of the system, the energy precision required and a wide range of physical phenomena that occur at the interface. To tackle this problem, many-body perturbation theory in the non-self-consistent GW approximation, orbital relaxation corrections for organic semiconductors, and line-up potential method for inorganic semiconductors which allows for tractable and accurate computing of energy band alignment in crystalline van-der-Waals hybrid inorganic–organic semiconductor interfaces are used. In this work, crystalline tetracene physisorbed on the clean hydrogen-passivated 1 × 2 reconstructed (100) silicon surface is studied. Using this computational approach, it is found that the energy band alignment is determined by an interplay of the mutual dynamic dielectric screening of two materials and the formation of a dipole layer due to a weak hybridization of atomic/molecular orbitals at the interface. The significant role of the exchange-correlation effects in predicting band offsets for the hybrid inorganic–organic semiconductor interfaces is also emphasized.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Computational Discovery of Intermolecular Singlet Fission Materials Using Many-Body Perturbation Theory

Intermolecular singlet fission (SF) is the conversion of a photogenerated singlet exciton into two triplet excitons residing on different molecules. SF has the potential to enhance the conversion efficiency of solar cells by harvesting two charge carriers from one high-energy photon, whose surplus energy would otherwise be lost to heat. The development of commercial SF-augmented modules is hindered by the limited selection of molecular crystals that exhibit intermolecular SF in the solid state. Computational exploration may accelerate the discovery of new SF materials. The GW approximation and Bethe–Salpeter equation (GW+BSE) within the framework of many-body perturbation theory is the current state-of-the-art method for calculating the excited-state properties of molecular crystals with periodic boundary conditions. In this Review, we discuss the usage of GW+BSE to assess candidate SF materials as well as its combination with low-cost physical or machine learned models in materials discovery workflows. We demonstrate three successful strategies for the discovery of new SF materials: (i) functionalization of known materials to tune their properties, (ii) finding potential polymorphs with improved crystal packing, and (iii) exploring new classes of materials. In addition, three new candidate SF materials are proposed here, which have not been published previously.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Finite-temperature many-body perturbation theory in the canonical ensemble

Benchmark data are presented for the zeroth- through third-order many-body perturbation corrections to the electronic Helmholtz energy, internal energy, and entropy in the canonical ensemble in a wide range of temperature. They are determined as numerical λ-derivatives of the respective quantities computed by thermal full configuration interaction with a perturbation-scaled Hamiltonian, $\hat{H} = \hat{H}_0 + λ\hat{V}$. Sum-over-states analytical formulas for up to the third-order corrections to these properties are also derived as analytical λ-derivatives. These formulas, which are verified by exact numerical agreement with the benchmark data, are given in terms of the Hirschfelder–Certain degenerate perturbation energies and should be valid for both degenerate and nondegenerate reference states at any temperature down to zero. Further, the results in the canonical ensemble are compared with the same in the grand canonical ensemble.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Mixed Stochastic-Deterministic Approach for Many-Body Perturbation Theory Calculations

Here, we present an approach for GW calculations of quasiparticle energies with quasi-quadratic scaling by approximating high-energy contributions to the Green's function in its Lehmann representation with effective stochastic vectors. The method is easy to implement without altering the GW code, converges rapidly with stochastic parameters, and treats systems of various dimensionality and screening response. Our calculations on a 5.75° twisted MoS 2 bilayer show how large-scale GW methods include geometry relaxations and electronic correlations on an equal basis in structurally nontrivial materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Chiral Effective Field Theory and the High-Density Nuclear Equation of State

Born in the aftermath of core-collapse supernovae, neutron stars contain matter under extraordinary conditions of density and temperature that are difficult to reproduce in the laboratory. In recent years, neutron star observations have begun to yield novel insights into the nature of strongly interacting matter in the high-density regime where current theoretical models are challenged. At the same time, chiral effective field theory has developed into a powerful framework to study nuclear matter properties with quantified uncertainties in the moderate-density regime for modeling neutron stars. In this article, we review recent developments in chiral effective field theory and focus on many-body perturbation theory as a computationally efficient tool for calculating the properties of hot and dense nuclear matter. We also demonstrate how effective field theory enables statistically meaningful comparisons among nuclear theory predictions, nuclear experiments, and observational constraints on the nuclear equation of state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Electronic Properties of Ultra‐Wide Bandgap B x Al 1− x N Computed from First‐Principles Simulations

Abstract Ultra‐wide bandgap (UWBG) materials such as AlN and BN hold great promise for future power electronics due to their exceptional properties. They exhibit large bandgaps, high breakdown fields, high thermal conductivity, and high mechanical strengths. AlN and BN have been extensively researched, however, their alloys, B x Al 1− x N, are much less studied despite their ability to offer tunable properties by adjusting x . In this article, the electronic properties of 17 recently predicted ground states of B x Al 1− x N in the x = 0 − 1 range are predicted using first‐principles density functional theory and many‐body perturbation theory within GW approximation. All the B x Al 1− x N structures are found to be UWBG materials and have bandgaps that vary linearly from that of wurtzite‐phase ( w ) AlN (6.19 eV) to that of w ‐BN (7.47 eV). The bandstructures of B x Al 1− x N show that a direct‐to‐indirect bandgap crossover occurs near x = 0.25. Furthermore, it is found that B x Al 1− x N alloys have much larger dielectric constants than the constituent bulk materials (AlN = 9.3 ɛ 0 or BN = 7.3 ɛ 0 ), with values reaching as high as 12.1 ɛ 0 . These alloys are found to exhibit large dielectric breakdown fields in the range 9–35 MV cm −1 with a linear dependence on x . This work provides the much needed advancement in the understanding of the properties of B x Al 1− x N to aid their application in next‐generation devices.

Milne, Cody L.↗