Many-body Calculations Research Articles

Atomic boson-fermion mixtures in one-dimensional box potentials: Few-body and mean-field many-body analyses

We study binary atomic boson-fermion mixtures confined in one dimensional box potentials by few-body theory with contact interactions and mean-field many-body theory with density-density interactions. A variety of correlations and structures arise as the inter- and intraspecies interactions are tuned. Both few-body and many-body results show that miscible phase and three-chunk phase separation are directly observable in the density profiles. Meanwhile, two-chunk phase separation can be inferred from the few-body correlations and many-body density profiles. We present phase diagrams of selected types of atomic mixtures to show where different structures survive. The few-body analysis demonstrates that two-body correlation functions can reveal information relevant to the results from many-body calculations or experiments. From the many-body density profiles in the phase-separation regime, we extract the healing lengths of both species and explain the scaling behavior by an energy-competition argument.

Empirical Determination of the Bohr-Weisskopf Effect in Cesium and Improved Tests of Precision Atomic Theory in Searches for New Physics.

The finite distribution of the nuclear magnetic moment across the nucleus gives a contribution to the hyperfine structure known as the Bohr-Weisskopf (BW) effect. We have obtained an empirical value of -0.24(18)% for this effect in the ground and excited s states of atomic ^{133}Cs. This value is found from historical muonic-atom measurements in combination with our muonic-atom and atomic many-body calculations. The effect differs by 0.5% in the hyperfine structure from the value found using the uniform magnetization distribution, which has been commonly employed in the precision heavy-atom community over the last several decades. We also deduce accurate values for the BW effect in other isotopes and states of cesium. These results enable cesium atomic wave functions to be tested in the nuclear region at an unprecedented 0.2% level, and are needed for the development of precision atomic many-body methods. This is important for increasing the discovery potential of precision atomic searches for new physics, in particular for atomic parity violation in cesium.

Steering Large Magnetic Exchange Coupling in Nanographenes near the Closed-Shell to Open-Shell Transition

The design of open-shell carbon-based nanomaterials is at the vanguard of materials science, steered by their beneficial magnetic properties like weaker spin-orbit coupling than that of transition metal atoms and larger spin delocalization, which are of potential relevance for future spintronics and quantum technologies. A key parameter in magnetic materials is the magnetic exchange coupling (MEC) between unpaired spins, which should be large enough to allow device operation at practical temperatures. In this work, we theoretically and experimentally explore three distinct families of nanographenes (NGs) (A, B, and C) featuring majority zigzag peripheries. Through many-body calculations, we identify a transition from a closed-shell ground state to an open-shell ground state upon an increase of the molecular size. Our predictions indicate that the largest MEC for open-shell NGs occurs in proximity to the transition between closed-shell and open-shell states. Such predictions are corroborated by the on-surface syntheses and structural, electronic, and magnetic characterizations of three NGs (A[3,5], B[4,5], and C[4,3]), which are the smallest open-shell systems in their respective chemical families and are thus located the closest to the transition boundary. Notably, two of the NGs (B[4,5] and C[4,3]) feature record values of MEC (close to 200 meV) measured on the Au(111) surface. Our strategy for maximizing the MEC provides perspectives for designing carbon nanomaterials with robust magnetic ground states.

Hydrogen-Atom Electronic Basis Sets for Multicomponent Quantum Chemistry.

Multicomponent methods are a conceptually simple way to include nuclear quantum effects into quantum chemistry calculations. In multicomponent methods, the electronic molecular orbitals are described using the linear combination of atomic orbitals approximation. This requires the selection of a one-particle electronic basis set which, in practice, is commonly a correlation-consistent basis set. In multicomponent method studies, it has been demonstrated that large electronic basis sets are required for quantum hydrogen nuclei to accurately describe electron-nuclear correlation. However, as we show in this study, much of the need for large electronic basis sets is due to the correlation-consistent electronic basis sets not being optimized to describe nuclear properties and electron-nuclear correlation. Herein, we introduce a series of correlation-consistent electronic basis sets for hydrogen atoms called cc-pVnZ-mc with additional basis functions optimized to reproduce multicomponent density functional theory protonic densities. These new electronic basis sets are shown to yield better protonic densities with fewer electronic basis functions than the standard correlation-consistent basis sets and reproduce other protonic properties such as proton affinities and protonic excitation energies, even though they were not optimized for these purposes. The cc-pVnZ-mc basis sets should enable multicomponent many-body calculations on larger systems due to the improved computational efficiency they provide for a given level of accuracy.

Entanglement in three-flavor collective neutrino oscillations

Extreme conditions present in the interiors of the core-collapse supernovae make neutrino-neutrino interactions not only feasible but dominant in specific regions, leading to the nonlinear evolution of the neutrino flavor. Results obtained when such collective neutrino oscillations are treated in the mean-field approximation deviate from the results using the many-body picture because of the ignored quantum correlations. We present the first three-flavor many-body calculations of the collective neutrino oscillations. The entanglement is quantified in terms of the entanglement entropy and the components of the polarization vector. We propose a qualitative measure of entanglement in terms of flavor-lepton number conserved quantities. We find that in the cases considered in the present work, the entanglement can be underestimated in the two-flavor approximation. The dependence of the entanglement on mass ordering is also investigated. We also explore the mixing of mass eigenstates in different mass orderings.

0νββ decay to the first 2+ state with a two-nucleon mechanism for a L−R symmetric model

We develop the formalism for calculating the decay rate of neutrinoless double $\ensuremath{\beta}$ decay to the ${2}^{+}$ excited states within the L-R symmetric model. We consider the effects from induced hadronic currents up to next to leading order. The quasiparticle random phase approximation method in a spherical basis is adopted for the nuclear many-body calculation and the corresponding nuclear matrix elements are given. Also, the phase space factors are obtained with numerical electron wave functions. Our results suggest that the nuclear matrix elements are nucleus dependent and they are generally smaller than that of the decay to the ground states. And finally, we give a naive analysis of how current experiment data constrains the L-R symmetric model.

Nonequilibrium spectral moment sum rules of the Holstein–Hubbard model

We derive a general procedure for evaluating the nth derivative of a time-dependent operator in the Heisenberg representation and employ this approach to calculate the zeroth to third spectral moment sum rules of the retarded electronic Green’s function and self-energy for a system described by the Holstein–Hubbard model allowing for arbitrary spatial and time variation of all parameters (including spatially homogeneous electric fields and parameter quenches). For a translationally invariant (but time-dependent) Hamiltonian, we also provide sum rules in momentum space. The sum rules can be applied to various different phenomena like time-resolved angle-resolved photoemission spectroscopy and benchmarking the accuracy of numerical many-body calculations. This work also corrects some errors found in earlier work on simpler models.

High-performance lead-free quaternary antiperovskite photovoltaic candidate Ca6N2AsSb.

Accurate many-body perturbation theory-based calculations were used to study the electronic and excitonic properties of lead-free quaternary antiperovskite Ca6N2AsSb; large quasiparticle band gap renormalization, strong optical absorption, and low exciton binding energy, as well as high efficiency of >32% with a thickness of 500 nm were predicted.

Electron correlation and relativistic effects on the electronic properties of a plutonium and americium mixed oxide (PuAmO4): from single-particle approximation to dynamical mean-field theory.

First-principles calculations were performed on a plutonium and americium mixed oxide (PuAmO4), aiming at revealing the effects of electron correlation, Pu/Am 5f-conduction electrons' hybridization, and relativity on its electronic properties. The many-body calculation suggests that the spin-orbit-coupling (SOC)-splitting of j = 5/2 and j = 7/2 manifolds are both in the weakly and moderately correlated states, respectively, implying that the jj coupling scheme is more appropriate for Pu/Am 5f electrons. The density of states, 5f occupation numbers, and Green's functions all suggest that both Pu and Am 5f electrons exhibit the coexistence of the localized and delocalized states. The admixture of 5fn atomic configurations, Pu/Am 5f-conduction electrons' hybridization, and dual characteristics of 5f electrons yield average occupation numbers of 5f electrons n5f = 4.78 and 5.86 for Pu and Am ions, respectively. Within the DFT+DMFT calculation, the weighted-summation-derived occupation numbers in terms of 5f4/5f5/5f6 and 5f5/5f6 configurations for Pu and Am 5f electrons, respectively, are in reasonable agreement with those of other DFT-based calculations.

Parameter-free analytic continuation for quantum many-body calculations

We develop a reliable parameter-free analytic continuation method for quantum many-body calculations. Our method is based on a kernel grid, a causal spline, a regularization using the second-derivative roughness penalty, and the L-curve criterion. We also develop the L-curve averaged deviation to estimate the precision of our analytic continuation. To deal with statistically obtained data more efficiently, we further develop a bootstrap-averaged analytic continuation method. In the test using the exact imaginary-frequency Green's function with added statistical error, our method produces the spectral function that converges systematically to the exact one as the statistical error decreases. As an application, we simulate the two-orbital Hubbard model for various electron numbers with the dynamical-mean field theory in the imaginary time and obtain the real-frequency self-energy with our analytic continuation method, clearly identifying a non-Fermi liquid behavior as the electron number approaches the half filling from the quarter filling. Our analytic continuation can be used widely and it will facilitate drawing clear conclusions from imaginary-time quantum many-body calculations.

A structural optimization algorithm with stochastic forces and stresses.

We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such as quantum Monte Carlo or neural network states, or are performed on quantum devices that have intrinsic noise. Our proposed algorithm is based on the combination of two ingredients: an update rule derived from the steepest-descent method, and a staged scheduling of the targeted statistical error and step size, with position averaging. We compare it with commonly applied algorithms, including some of the latest machine learning optimization methods, and show that the algorithm consistently performs efficiently and robustly under realistic conditions. Applying this algorithm, we achieve full-degree optimizations in solids using ab initio many-body computations, by auxiliary-field quantum Monte Carlo with plane waves and pseudopotentials. A potential metastable structure in Si is discovered using density-functional calculations with synthetic noisy forces.

Relation between crystal structure and optical properties in the correlated blue pigment YIn1−xMnxO3

A material's properties and functionalities are determined by its chemical constituents and the atomic arrangement in which they crystallize. For the recently discovered pigment YIn$_{1-x}$Mn$_x$O$_3$, for instance, it had been surmised that its bright blue color owes to an unusual, trigonal bipyramidal, oxygen coordination of the manganese impurities. Here, we demonstrate that, indeed, a direct correspondence between details of the local Mn environment and the pigment's blue color holds: Combining realistic many-body calculations (dynamical mean-field theory to treat the quasi-atomic Mn-multiplets at low doping x=0.08) with an effective medium description (Kubelka-Munk model to describe scattering in a milled pigment sample), we find that only a Mn-coordination polyhedra consisting of two distorted oxygen pyramids results in a diffuse reflectance commensurate with the experimental blue color. We motivate that the distortion of the bipyramid helps circumventing atomic selection rules, allowing for dipolar $d$-$d$ transitions and creating the desired two-peak absorption profile.

Spin-triplet pairing induced by near-neighbor attraction in the extended Hubbard model for cuprate chain

In quantum materials, the electronic interaction and the electron-phonon coupling are, in general, two essential ingredients, the combined impact of which may drive exotic phases. Recently, an anomalously strong electron-electron attraction, likely mediated by phonons, has been proposed in one-dimensional copper-oxide chain Ba2−xSrxCuO3+δ. Yet, it is unclear how this strong near-neighbor attraction V influences the superconductivity pairing in the system. Here we perform accurate many-body calculations to study the extended Hubbard model with on-site Coulomb repulsion U > 0 and near-neighbor attraction V < 0 that could well describe the cuprate chain and likely other similar transition-metal materials with both strong correlations and lattice effects. We find a rich quantum phase diagram containing an intriguing Tomonaga-Luttinger liquid phase — besides the spin density wave and various phase separation phases — that can host dominant spin-triplet pairing correlations and divergent superconductive susceptibility. Upon doping, the spin-triplet superconducting regime can be further broadened, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate chains.

Band gaps of halide perovskites from a Wannier-localized optimally tuned screened range-separated hybrid functional

The accurate prediction of the band gaps of halide perovskites within density functional theory is known to be challenging. The recently developed Wannier-localized optimally tuned screened range-separated hybrid functional was shown to be highly accurate for fundamental band gaps of standard semiconductors and insulators. This was achieved by selecting the parameters of the functional to satisfy an ansatz that generalizes the ionization potential theorem to the removal of charge from a state that corresponds to a Wannier function. Here, we present applications of the method to the band gaps of typical halide perovskites. We find a satisfyingly small formal mean absolute error of $\ensuremath{\sim}$0.1 eV with respect to experimental band gaps and very good agreement with previous many-body perturbation theory calculations.

Attosecond clocking of correlations between Bloch electrons.

Delocalized Bloch electrons and the low-energy correlations between them determine key optical1, electronic2 and entanglement3 functionalitiesof solids, all the way through to phase transitions4,5. To directly capture how many-body correlations affect the actual motion of Bloch electrons, subfemtosecond (1 fs = 10-15 s) temporal precision6-15 is desirable. Yet, probing with attosecond (1 as = 10-18 s) high-energy photons has not been energy-selective enough to resolve the relevant millielectronvolt-scale interactions of electrons1-5,16,17 near the Fermi energy. Here, we use multi-terahertz light fields to force electron-hole pairs in crystalline semiconductors onto closed trajectories, and clock the delay between separation and recollision with 300 as precision, corresponding to 0.7% of the driving field's oscillation period. We detect that strong Coulomb correlations emergent in atomically thin WSe2 shift the optimal timing of recollisions by up to 1.2 ± 0.3 fs compared to the bulk material. A quantitative analysis with quantum-dynamic many-body computations in a Wigner-function representation yields a direct and intuitive view on how the Coulomb interaction, non-classical aspects, the strength of the driving field and the valley polarization influence the dynamics. The resulting attosecond chronoscopy of delocalized electrons could revolutionize the understanding of unexpected phase transitions and emergent quantum-dynamic phenomena for future electronic, optoelectronic and quantum-information technologies.

High-accuracy optical clocks based on group-16-like highly charged ions

We identify laser-accessible transitions in group 16-like highly charged ions as candidates for high-accuracy optical clocks, including S-, Se-, and Te-like systems. For this class of ions, the ground $^{3}P_{J}$ fine structure manifold exhibits irregular (nonmonotonic in $J$) energy ordering for large enough ionization degree. We consider the $|^3P_2\rangle \longleftrightarrow |^3P_0\rangle$ (ground to first-excited state) electric quadrupole transition, performing relativistic many-body calculations of several atomic properties important for optical clock development. All ions discussed are suitable for production in small-scale ion sources and lend themselves to sympathetic cooling and quantum-logic readout with singly charged ions.

Magnetic couplings in edge-sharing high-spin d 7 compounds

High-spin d 7 Co(II) compounds have recently been identified as possible platforms for realizing highly anisotropic and bond-dependent couplings featured in quantum-compass models such as the celebrated Kitaev model. In order to evaluate this potential, we consider all symmetry-allowed contributions to the magnetic exchange for ideal edge-sharing bonds. Though a combination of ab-initio and cluster many-body calculations we conclude that bond-dependent couplings are generally suppressed in favor of Heisenberg exchange for real materials. Consequences for several prominent materials including Na2Co2TeO6 and BaCo2(AsO4)2 are discussed.

Trie-based ranking of quantum many-body states

Ranking bit patterns -- finding the index of a given pattern in an ordered sequence -- is a major bottleneck scaling up numerical quantum many-body calculations, as fermionic and hard-core bosonic states translate naturally to bit patterns. Traditionally, ranking is done by bisectioning search, which has poor cache performance on modern machines. We instead propose to use tries (prefix trees), thereby achieving a two- to ten-fold speed-up in numerical experiments with only moderate memory overhead. For the important problem of ranking permutations, the corresponding tries can be compressed. These compressed "staggered" lookups allow for a considerable speed-up while retaining the memory requirements of prior algorithms based on the combinatorial number system.

Orbital-selective Mott and Peierls transition in HxVO2

Materials displaying metal-insulator transitions (MITs) as a function of external parameters such as temperature, pressure, or composition are most intriguing from the fundamental point of view and also hold high promise for applications. Vanadium dioxide (VO2) is one of the most prominent examples of MIT having prospective applications ranging from intelligent coatings, infrared sensing, or imaging, to Mott memory and neuromorphic devices. The key aspects conditioning possible applications are the controllability and reversibility of the transition. Here we present an intriguing MIT in hydrogenated vanadium dioxide, HxVO2. The transition relies on an increase of the electron occupancy through hydrogenation on the transition metal vanadium, driving the system insulating by a hybrid of two distinct MIT mechanisms. The insulating phase observed in HVO2 with a nominal d2 electronic configuration contrasts with other rutile d2 systems, most of which are metallic. Using spectroscopic tools and state-of-the-art many-body electronic structure calculations, our investigation reveals a correlation-enhanced Peierls and a Mott transition taking place in an orbital-selective manner cooperate to stabilize an insulating phase. The identification of the hybrid mechanism for MIT controlled by hydrogenation opens the way to radically design strategies for future correlated oxide devices by controlling phase reversibly while maintaining high crystallinity.

Efficient ab initio many-body calculations based on sparse modeling of Matsubara Green's function

This lecture note reviews recently proposed sparse-modeling approaches for efficient ab initio many-body calculations based on the data compression of Green's functions. The sparse-modeling techniques are based on a compact orthogonal basis, an intermediate representation (IR) basis, for imaginary-time and Matsubara Green's functions. A sparse sampling method based on the IR basis enables solving diagrammatic equations efficiently. We describe the basic properties of the IR basis, the sparse sampling method and its applications to ab initio calculations based on the GW approximation and the Migdal--Eliashberg theory. We also describe a numerical library for the IR basis and the sparse sampling method, sparse-ir, and provide its sample codes. This lecture note follows the Japanese review article [H. Shinaoka et al., Solid State Physics 56(6), 301 (2021)].