Many-body Calculations Research Articles

GW band structure of monolayer MoS2 using the SternheimerGW method and effect of dielectric environment

Monolayers of transition-metal dichalcogenides (TMDs) hold great promise as future nanoelectronic and optoelectronic devices. An essential feature for achieving high device performance is the use of suitable supporting substrates, which can affect the electronic and optical properties of these two-dimensional (2D) materials. Here, we perform many-body GW calculations using the SternheimerGW method to investigate the quasiparticle band structure of monolayer ${\mathrm{MoS}}_{2}$ subject to an effective dielectric screening model, which is meant to approximately describe substrate polarization in real device applications. We show that, within this model, the dielectric screening has a sizable effect on the quasiparticle band gap; for example, the gap renormalization is as large as 250 meV for ${\mathrm{MoS}}_{2}$ with model screening corresponding to ${\mathrm{SiO}}_{2}$. Within the ${\mathrm{G}}_{0}{\mathrm{W}}_{0}$ approximation, we also find that the inclusion of the effective screening induces a direct band gap, in contrast to the unscreened monolayer. We also find that the dielectric screening induces an enhancement of the carrier effective masses by as much as 27% for holes, shifts plasmon satellites, and redistributes quasiparticle weight. Our results highlight the importance of the dielectric environment in the design of 2D TMD-based devices.

Many-body calculations for periodic materials via restricted Boltzmann machine-based VQE

A state of the art method based on quantum variational algorithms can be a powerful approach for solving quantum many-body problems. However, the research scope in the field is mainly limited to organic molecules and simple lattice models. Here, we propose a workflow of a quantum variational algorithm for periodic systems on the basis of an effective model construction from first principles. The band structures of the Hubbard model of graphene with the mean-field approximation are calculated as a benchmark, and the calculated eigenvalues obtained by restricted Boltzmann machine-based variational quantum eigensolver (RBM-based VQE) show good agreement with the exact diagonalization results within a few meV. The results show that the present computational scheme has the potential to solve many-body problems quickly and correctly for periodic systems using a quantum computer.

Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations

We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present paper. This development allows us to compute correlation functions, electronic densities, and interatomic forces, paving the way for geometry optimizations and calculations of thermodynamic properties in solids. Finite supercell size effects are considerably more subtle in the many-body framework than in independent-electron calculations. We analyze the convergence of the electronic density, and obtain best estimates for the thermodynamic limit. The densities from several typical density functionals are benchmarked against our near-exact results. The electronic densities we obtained can also be used to help construct improved density functionals.

Proton-induced deuteron knockout reaction as a probe of an isoscalar proton-neutron pair in nuclei

The isoscalar $pn$ pair is expected to emerge in nuclei having the similar proton and neutron numbers but there is no clear experimental evidence for it. We aim to clarify the correspondence between the $pn$ pairing strength in many-body calculation and the triple differential cross section (TDX) of proton-induced deuteron knockout ($p,pd$) reaction on $^{16}$O. The radial wave function of the isoscalar $pn$ pair with respect to the center of $^{16}$O is calculated with the energy density functional (EDF) approach and is implemented in the distorted wave impulse approximation (DWIA) framework. The $pn$ pairing strength $V_0$ in the EDF calculation is varied and the corresponding change in the TDX is investigated. A clear $V_0$ dependence of the TDX is found for the $^{16}$O($p,pd$)$^{14}$N($1_2^+$) at $101.3$ MeV. The nuclear distortion is found to make the $V_0$ dependence stronger. Because of the clear $V_0$-TDX correspondence, the ($p,pd$) reaction will be a promising probe for the isoscalar $pn$ pair in nuclei. For quantitative discussion, further modification of the description of the reaction process will be necessary.

Natural orbitals for many-body expansion methods

The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While various options for the computational basis are available, perturbatively constructed natural orbitals recently have been shown to lead to significant improvement in many-body applications yielding faster model-space convergence and lower sensitivity to basis set parameters in large-scale no-core shell model diagonalizations. This work provides a detailed comparison of single-particle basis sets and a systematic benchmark of natural orbitals in nonperturbative many-body calculations using the in-medium similarity renormalization group approach. As a key outcome we find that the construction of natural orbitals in a large single-particle basis enables for performing the many-body calculation in a reduced space of much lower dimension, thus offering significant computational savings in practice that help extend the reach of ab initio methods towards heavier masses and higher accuracy.

Quasiparticle band structure of SrTiO3 and BaTiO3 : A combined LDA+U and G0W0 approach

We present the quasiparticle band structures of prototypical oxide perovskites ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$, two seemingly simple oxides for which accurate calculations of the electronic structure have been met with significant (and somewhat unexpected) challenges. Previous ${G}^{0}{W}^{0}$ calculations predicted a band gap ranging from 3.36 to 3.82 eV for ${\mathrm{SrTiO}}_{3}$, with a majority of the studies giving a band gap around 3.7 $\ensuremath{\sim}$ 3.8 eV, to be compared with the experimental value of 3.25 eV. A similar discrepancy between theory and experiment is also observed for ${\mathrm{BaTiO}}_{3}$. We show that the ${G}^{0}{W}^{0}$ approach can predict reasonably accurate band gaps of ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$, provided that the calculations are carried out on top of the local density approximation (LDA) plus $U$ ($\mathrm{LDA}+U$) solutions and are fully converged. The deficiency of the LDA in describing the localized $3d$ states, although not particularly critical in this case, still results in a poor mean-field starting point for subsequent many-body perturbation calculations. ${G}^{0}{W}^{0}$ calculations starting from the $\mathrm{LDA}+U$ solutions, on the other hand, give significantly improved results for both systems. Our work demonstrates the accuracy and applicability of the combined ${G}^{0}{W}^{0}$ and $\mathrm{LDA}+U$ approach in calculating the quasiparticle band structures for materials involving localized $3d$ states, not only for systems with fully occupied $3d$ semicore states as has been shown before, but also for systems in which the $3d$ states are nominally unoccupied.

Direct formation of interlayer exciton in two-dimensional van der Waals heterostructures.

In atomically thin two-dimensional van der Waals (2D vdW) heterostructures, spatially separated interlayer excitons play an important role in the optoelectronic performance and show great potential for the exploration of many-body quantum phenomena. A commonly accepted formation mode for interlayer excitons is via a two-step intralayer exciton transfer mechanism, namely, photo-excited intralayer excitons are initially generated in individual sublayers, and photogenerated electrons and holes are then separated into opposite sublayers based on the type-II band alignment. Herein, we expand the concept of interlayer exciton formation and reveal that bright interlayer excitons can be generated in one step by direct interlayer photoexcitation in 2D vdW heterostructures that have strong interlayer coupling and a short photoexcitation channel. First-principles and many-body perturbation theory calculations demonstrate that indium selenide/antimonene and indium selenide/black phosphorus heterostructures are two promising systems that show an exceptionally large interlayer transition probability (>500 Debye2). This study enriches the understanding of interlayer exciton formation and provides a new avenue to acquiring strong interlayer excitons in artificial 2D vdW heterostructures.

Excitonic Effects on the Linear and Nonlinear Optical Properties of Solid C60 Fullerene, Insights from Many-Body First-Principles Calculations

We perform the many-body Bethe-Salpeter equation eigenstates based sum-over-states calculations for the linear and nonlinear optical properties of solid C 60 fullerene. Excitonic and local field effects are included in the calculations. We calculate the one-photon absorption (OPA), third harmonic generation (THG), degenerate four-wave mixing (DFWM), and electric-field-induced second harmonic generation (ESHG) spectra of solid C 60 fullerene. The overall agreement between the theoretical and experimental results is good for all calculated spectra. The OPA spectrum shows that the solid C 60 fullerene has a large excitonic binding energy of 0.35 eV. The position and intensity of spectral peaks are modified significantly. By tracing the sum-over-states progress, we determine the type of nonlinear polarization resonances for the characteristic peaks of the THG process, which may clear up a discrepancy in two experimental results. The calculated DFWM spectrum is in excellent agreement with the available experimental results in terms of line shape and peak positions, and thus the two-photon absorption peaks can be well understood on the basis of the excitonic states of solid C 60 fullerene. The dynamic ESHG spectrum is given as a reference for the future experiment.

Interlayer and excited-state exciton transitions in bulk 2H−MoS2

Photoreflectance (PR) spectrum of bulk $2H\text{\ensuremath{-}}{\mathrm{MoS}}_{2}$ at energies around its direct band gap is shown to have at least three distinct spectral features over a certain temperature range, although only two are seen in absorption and reflectance spectra. These observations are compared with results from many-body perturbation theory band structure calculations that include exciton formation through the Bethe-Salpeter equation. Apart from the ground state $A\phantom{\rule{4pt}{0ex}}(n=1)$ exciton transition around 1.92 eV at 25 K, the next spectral feature around 1.96 eV, whose origin has been much debated, is identified here with a transition $I$ with strong interlayer contributions. Its greater sensitivity to electric fields is established through electroreflectance measurements. The third one around 1.99 eV, which is prominent only in PR, is shown to arise from the first excited state $A\phantom{\rule{4pt}{0ex}}(n=2)$ exciton transition. We discuss the previously unexplained observation as to why the $A\phantom{\rule{4pt}{0ex}}(n=2)$ feature dominates the PR spectrum at high temperatures. The $A$ exciton is shown to have a quasi-two-dimensional (2D) nature with binding energy of $77\ifmmode\pm\else\textpm\fi{}3$ meV under a 2D hydrogenic exciton model.

RESPACK: An ab initio tool for derivation of effective low-energy model of material

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 for specifying the RESPACK calculation conditions is designed pursuing simplicity and is given in the Fortran namelist format. RESPACK supports hybrid parallelization using OpenMP and MPI and can treat large systems including a few hundred atoms in the calculation cell. Program summaryProgram Title: RESPACKCPC Library link to program files:https://dx.doi.org/10.17632/3cxb7474nj.1Developer’s repository link:https://sites.google.com/view/kazuma7k6rLicensing provisions: GNU General Public Licence v3.0Programming language:Fortran, PythonExternal routines:LAPACK, BLAS, MPINature of problem: Ab initio calculations for maximally localized Wannier function, response function with random-phase approximation, and matrix-element evaluations of frequency-dependent screened direct and exchange interactions. With this code, an effective low-energy model of materials is derived from first principles.Solution method: Our method is based on ab initio many-body perturbation calculation and the maximally localized Wannier function calculation. The program employs the plane-wave basis set, and evaluations of matrix elements are performed with the fast Fourier transformation. The generalized tetrahedron method is used for the Brillouin Zone integral.Additional comments including restrictions and unusual features: RESPACK supports xTAPP and Quantum ESPRESSO packages, and automatic generation scripts for converting the band-calculation results to the RESPACK inputs are prepared for these software. The current RESPACK only supports band-calculation codes using norm-conserving pseudopotentials with plane-wave basis sets. RESPACK supports hybrid parallelization using OpenMP and MPI to treat large systems in which a few hundred atoms are contained in unit cell.

Probing quantum materials

Spectroscopy Unraveling the functionalities of quantum materials such as spin-valley-electronic, topological, and many-body effects provides a route to exploiting these materials for applications. Borsch et al. introduce a spectroscopic technique based on the concept of crystal-momentum combs. By extending the ideas of frequency combs of metrology and superresolution imaging, they demonstrate the ability to directly map out the properties of quantum electronic structures under ambient conditions. Using this technique combined with accurate many-body computations, they were able to reveal tomographic images of two-dimensional quantum materials. Science , this issue p. [1204][1] [1]: /lookup/doi/10.1126/science.abe2112

Super-resolution lightwave tomography of electronic bands in quantum materials.

Searching for quantum functionalities requires access to the electronic structure, constituting the foundation of exquisite spin-valley-electronic, topological, and many-body effects. All-optical band-structure reconstruction could directly connect electronic structure with the coveted quantum phenomena if strong lightwaves transported localized electrons within preselected bands. Here, we demonstrate that harmonic sideband (HSB) generation in monolayer tungsten diselenide creates distinct electronic interference combs in momentum space. Locating these momentum combs in spectroscopy enables super-resolution tomography of key band-structure details in situ. We experimentally tuned the optical-driver frequency by a full octave and show that the predicted super-resolution manifests in a critical intensity and frequency dependence of HSBs. Our concept offers a practical, all-optical, fully three-dimensional tomography of electronic structure even in microscopically small quantum materials, band by band.

Wave Function Based Analysis of Dynamics versus Yield of Free Triplets in Intramolecular Singlet Fission.

Experiments in several intramolecular singlet fission materials have indicated that the triplet-triplet spin biexciton has a much longer lifetime than believed until recently, opening up loss mechanisms that can annihilate the biexciton prior to its dissociation to free triplets. We have performed many-body calculations of excited state wave functions of hypothetical phenylene-linked anthracene molecules to better understand linker-dependent behavior of dimers of larger acenes being investigated as potential singlet fission candidates. The calculations reveal unanticipated features that we show carry over to the real covalently linked pentacene dimers. Dissociation of the correlated triplet-triplet spin biexciton and free triplet generation may be difficult in acene dimers where the formation of the triplet-triplet spin biexciton is truly ultrafast. Conversely, relatively slower biexciton formation may indicate smaller spin biexciton binding energy and greater yield of free triplets. Currently available experimental results appear to support this conclusion. Whether or not the two distinct behaviors are consequences of distinct mechanisms of triplet-triplet generation from the optical singlet is an interesting theoretical question.

How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties.

We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory (χEFT). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as χEFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the χEFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density, the predicted symmetry energy and its slope are consistent with experimental constraints.

Quantifying uncertainties and correlations in the nuclear-matter equation of state

We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($\chi$EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $\chi$EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $\chi$EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.

LISA sources from young massive and open stellar clusters

I study the potential role of young massive (YMCs) and open star clusters (OCs) in assembling stellar-mass binary black holes (BBHs) which would be detectable as persistent gravitational-wave (GW) sources by the forthcoming LISA mission. The energetic dynamical interactions inside star clusters make them factories of assembling BBHs and other types of double-compact binaries that undergo general-relativistic (GR) inspiral and merger. The initial phase of such inspirals would, typically, sweep through the LISA GW band. Here, such LISA sources are studied from a set of evolutionary models of star clusters with masses ranging over $10^4M_\odot-10^5M_\odot$ that represent YMCs and intermediate-aged OCs in metal-rich and metal-poor environments of the Local Universe. These models are evolved with long-term, direct, relativistic many-body computations incorporating state-of-the-art stellar-evolutionary and remnant-formation models. Based on models of Local Universe constructed with such model clusters, it is shown that YMCs and intermediate-aged OCs would yield several 10s to 100s of LISA BBH sources at the current cosmic epoch with GW frequency within $10^{-3}{\rm~Hz} - 10^{-1}{\rm~Hz}$ and signal-to-noise-ratio (S/N) $>5$, assuming a mission lifetime of 5 or 10 years. Such LISA BBHs would have a bimodal distribution in total mass, be generally eccentric ($\lesssim0.7$), and typically have similar component masses although mass-asymmetric systems are possible. Intrinsically, there would be 1000s of present-day, LISA-detectable BBHs from YMCs and OCs. That way, YMCs and OCs would provide a significant and the dominant contribution to the stellar-mass BBH population detectable by LISA. A small fraction, $<5$%, of these BBHs would undergo GR inspiral to make it to LIGO-Virgo GW frequency band and merge, within the mission timespan; $<15$% would do so within twice the timespan.

Starting-point-independent quantum Monte Carlo calculations of iron oxide

Quantum Monte Carlo (QMC) methods are useful for studies of strongly correlated materials because they are many body in nature and use the physical Hamiltonian. Typical calculations assume as a starting point a wave function constructed from single-particle orbitals obtained from one-body methods, e.g., density functional theory. However, mean-field-derived wave functions can sometimes lead to systematic QMC biases if the mean-field result poorly describes the true ground state. Here, we study the accuracy and flexibility of QMC trial wave functions using variational and fixed-node diffusion QMC estimates of the total spin density and lattice distortion of antiferromagnetic iron oxide (FeO) in the ground state $B1$ crystal structure. We found that for relatively simple wave functions the predicted lattice distortion was controlled by the choice of single-particle orbitals used to construct the wave function, rather than by subsequent wave function optimization techniques within QMC. By optimizing the orbitals with QMC, we then demonstrate starting-point independence of the trial wave function with respect to the method by which the orbitals were constructed by demonstrating convergence of the energy, spin density, and predicted lattice distortion for two qualitatively different sets of orbitals. The results suggest that orbital optimization is a promising method for accurate many-body calculations of strongly correlated condensed phases.

Quadruply Ionized Barium as a Candidate for a High-Accuracy Optical Clock

We identify Ba^{4+} (Te-like) as a promising candidate for a high-accuracy optical clock. The lowest-lying electronic states are part of a ^{3}P_{J} fine structure manifold with anomalous energy ordering, being nonmonotonic in J. We propose a clock based on the 338.8THz electric quadrupole transition between the ground (^{3}P_{2}) and first-excited (^{3}P_{0}) electronic states. We perform relativistic many-body calculations to determine relevant properties of this ion. The lifetime of the excited clock state is found to be several seconds, accommodating low statistical uncertainty with a single ion for practical averaging times. The differential static scalar polarizability is found to be small and negative, providing suppressed sensitivity to blackbody radiation while simultaneously allowing cancellation of Stark and excess micromotion shifts. With the exception of Hg^{+} and Yb^{+}, sensitivity to variation of the fine structure constant is greater than other optical clocks thus far demonstrated.

Spin-polarized β -stable neutron star matter: The nuclear symmetry energy and GW170817 constraint

Magnetic field of rotating pulsar might be so strong that the equation of state (EOS) of neutron star (NS) matter is significantly affected by the spin polarization of baryons. In the present work, the EOS of the spin-polarized nuclear matter is investigated in the nonrelativistic Hartree-Fock formalism, using a realistic density dependent nucleon-nucleon interaction with its spin and spin-isospin dependence accurately adjusted to the Brueckner-Hartree-Fock results for the spin-polarized nuclear matter. The nuclear symmetry energy and proton fraction are found to increase significantly with the increasing spin polarization of baryons, leading to a larger probability of the direct Urca process in the cooling of magnetar. The EOS of the $\beta$-stable np$e\mu$ matter obtained at different spin polarizations of baryons is used as the input for the Tolman-Oppenheimer-Volkov equations to determine the hydrostatic configuration of NS. Based on the GW170817 constraint on the radius $R_{1.4}$ of NS with $M\approx 1.4_\odot$, our mean-field results show that up to $60~\%$ of baryons in the NS merger might be spin-polarized. This result supports the magnetar origin of the blue kilonova ejecta of GW170817 suggested by Metzger et al., and the spin polarization of baryons needs, therefore, to be properly treated in the many-body calculation of the EOS of NS matter before comparing the calculated NS mass and radius with those constrained by the multi-messenger GW170817 observation.

Effect of silicon doping on the electronic and optical properties of phosphorous nanotubes

Using many-body ab initio calculations, the direction-dependent electronic and the optical properties of silicon doped phosphorene nanotubes are investigated in the DFT framework. Both pure armchair (APNT) and zigzag phosphorene nanotubes (ZPNT) are estimated to be semi-conductor with a direct bandgap in which their valance band maximum and conduction band minimum are placed at the Г-Z zone, while all doped by silicon nanotubes represent metallic behavior. In addition, due to the weaker sp3 hybridization of phosphorus atoms through zigzag phosphorene nanotubes, they have narrower bandgaps than the APNTs. For all simulated APNTs except those with 2% silicon, the atomic configuration is symmetrical respect to the z axis. Moreover, by parallel to the tube axis polarization, for all APNTs, the first intra-band optical band gap is less than 1 eV. The silicon dopant decreases the gap between the highest valence and the lowest conduction bands which leads to smaller inter-band optical transition as well.