Interaction Matrix Elements Research Articles

HOUSEHOLDER TRANSFORMATION IN THE INVERSE PROBLEM FOR A COMPLEX VIBRONIC ANALOGUE OF THE FERMI RESONANCE

In the inverse problem for a complex vibronic analogue of the Fermi resonance, the matrix elements of the electron-vibration interaction should be obtained from experimental data, energies Ek and intensities Ik (k = 1, 2, …, n; n ≥ 3), a “conglomerate” of lines in the spectrum. This problem in the direct-coupling model, where the Hamiltonian HDIR is specified by the energies of the “dark” states Ai and the matrix elements of their coupling with the “bright” state Bi (i = 1, 2, …, n –1), was solved by the author on the basisof algebraic methods. It is shown that the Hamiltonian HDW of the doorway-coupling model, in which the “bright” state has “interaction” with only single distinguished |DW> state, can be obtained from the Hamiltonian HDIR using the Householder triangularization method, namely, by the similarity transformation
 HDW = PHDIRP, where P is the reflection matrix which is constructed from the Bi values. The expressions for main elements of the doorway model, namely, the energy of the |DW> state and the matrix element of its coupling with the "bright" state, are obtained. For pyrazine and acetylene molecules, the matrix elements of the Hamiltonian HDW are calculated using the data of the electronic-vibrational-rotational spectra.

Nuclear superfluidity at finite temperature

The equation of motion for the two-fermion two-time correlation function in the pairing channel is considered at finite temperature. Within the Matsubara formalism, the Dyson-type Bethe-Salpeter equation (Dyson-BSE) with the frequency-dependent interaction kernel is obtained. Similarly to the case of zero temperature, it is decomposed into the static and dynamical components, where the former is given by the contraction of the bare interaction with the two-fermion density and the latter is represented by the double contraction of the four-fermion two-time correlation function, or propagator, with two interaction matrix elements. The dynamical kernel with the four-body propagator, being formally exact, requires approximations to avoid generating prohibitively complicated hierarchy of equations. We focus on the approximation where the dynamical interaction kernel is truncated on the level of two-body correlation functions, neglecting the irreducible three-body and higher-rank correlations. Such a truncation leads to the dynamical kernel with the coupling between correlated fermionic pairs, which can be interpreted as emergent bosonic quasibound states, or phonons, of normal and superfluid nature. The latter ones are, thus, the mediators of the dynamical superfluid pairing. In this framework, we obtained the closed system of equations for the fermionic particle-hole and particle-particle propagators. This allows us to study the temperature dependence of the pairing gap beyond the Bardeen-Cooper-Schrieffer approximation, that is implemented for medium-heavy nuclear systems. The cases of 68Ni and 44,46Ca are discussed in detail.

Microscopic theory of exciton-exciton annihilation in two-dimensional semiconductors

Auger-like exciton-exciton annihilation (EEA) is considered the key fundamental limitation to quantum yield in devices based on excitons in two-dimensional (2d) materials. Since it is challenging to experimentally disentangle EEA from competing processes, guidance of a quantitative theory is highly desirable. The very nature of EEA requires a material-realistic description that is not available to date. We present a many-body theory of EEA based on first-principle band structures and Coulomb interaction matrix elements that goes beyond an effective bosonic picture. Applying our theory to monolayer MoS$_2$ encapsulated in hexagonal BN, we obtain an EEA coefficient in the order of $10^{-3}$ cm$^{2}$s$^{-1}$ at room temperature, suggesting that carrier losses are often dominated by other processes, such as defect-assisted scattering. Our studies open a perspective to quantify the efficiency of intrinsic EEA processes in various 2d materials in the focus of modern materials research.

Microscopic structure of the one-phonon 2+ states of Po208

The lifetimes of the 2 1 + and 4 1 + states of Po 208 were measured in the α -transfer reaction Pb 204 ( C 12 , Be 8 ) Po 208 by γ -ray spectroscopy utilizing the recoil distance Doppler shift method. The newly extracted transition strengths alongside ones of the decay of the 2 2 + state were compared to the results of large-scale shell-model calculations using an effective interaction derived from the realistic CD-Bonn nucleon-nucleon potential. The comparison indicates the importance of the quadrupole isovector excitations in the valence shell for a fine tuning of the two-body matrix elements of the shell-model interaction.

Laser-induced torques in metallic antiferromagnets

We study the laser-induced torques in the antiferromagnet (AFM) Mn$_2$Au. We find that even linearly polarized light may induce laser-induced torques in Mn$_2$Au, i.e., the light does not have to be circularly polarized. The laser-induced torques in Mn$_2$Au are comparable in magnitude to those in the ferromagnets Fe, Co and FePt at optical frequencies. We also compute the laser-induced torques at terahertz (THz) frequencies and compare them to the spin-orbit torques (SOTs) excited by THz laser-pulses. We find the SOTs to be dominant at THz frequencies for the laser-field strengths used in experiments. Additionally, we show that the matrix elements of the spin-orbit interaction (SOI) can be used to add SOI only during the Wannier interpolation, which we call Wannier interpolation of SOI (WISOI). This technique allows us to perform the Wannier interpolation conveniently for many magnetization directions from a single set of Wannier functions.

An SYK-inspired model with density–density interactions: Spectral & wave function statistics, Green’s function and phase diagram

The Sachdev–Ye–Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are “randomized” and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density–density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density–density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green’s function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism.

Phonon drag thermopower and energy loss rate in single and bilayer graphene due to piezoelectric surface acoustic phonons in Bloch-Gruneisen regime

In this report, we have both numerically and analytically calculated the phonon drag thermopower, Spz and, energy loss rate, Fpz due to piezoelectric surface acoustic phonons present in the underlying piezoelectric substrate at a distance, d apart from single and bilayer graphene as a function of carrier's temperature, concentration and phonon mean free path. The numerical results are then reduced to analytical results in the Bloch-Gruneisen regime and the corresponding power dependency of the quantities described above are obtained. We have also included the effect of Thomas-Fermi and Random Phase Approximation screening into account in these calculations. The obtained unscreened results are further reduced in much simpler form for a particular case having no distance between the graphene samples and the underlying substrate or at larger values of distances. The temperature dependency in Spz and Fpz for both SLG and BLG systems is found to be one order less than the in-plane acoustic phonons dependency, which is directly related to the matrix element of electron-in plane acoustic phonon interaction having a linear dependence on the phonon wave vector, q. Furthermore, a comparison of these calculations is made between the in-plane and piezoelectric surface acoustic phonon modes. One finds a crossover between these phonons modes depicting these are important in providing effective scattering channels for energy relaxation in typical experimental situations at different temperatures.

Role of hyperfine interaction in Landé [formula omitted]-factors of [formula omitted] clock states

In the weak-magnetic-field approximation, we calculated the hyperfine-induced Landé g-factors of the 3P0o clock states in 27Al+ and 87Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, δghfs(1)(3P0o)=−1.183(6)×10−3 for 27Al+ and δghfs(1)(3P0o)=7.78(30)×10−5 for 87Sr, agree with experimental values very well. The influence of relativistic effects and electron correlations on the involving hyperfine interaction and Zeeman matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the g-factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. Based on these, the computational uncertainties were systematically analyzed for the hyperfine-induced Landé g-factors of the 3P0o clock states in these two atomic systems.

Finite-range separable pairing interaction in Cartesian coordinates

Within a simple SO(8) algebraic model, the coexistence between isoscalar and isovector pairing modes can be successfully described using a mean-field method plus restoration of broken symmetries. In order to port this methodology to real nuclei, we need to employ realistic density functionals in the pairing channel. In this article, we present an analytical derivation of matrix elements of a separable pairing interaction in Cartesian coordinates and we correct errors of derivations available in the literature. After implementing this interaction in the code HFODD, we study evolution of pairing gaps in the chain of deformed Erbium isotopes, and we compare the results with a standard density-dependent contact pairing interaction.

Electron-hole asymmetry in electron systems with orbital degeneracy and correlated hopping

Microscopic models of electronic subsystems with orbital degeneracy of energy states and non-diagonal matrix elements of electron interactions (correlated hopping) are considered within the configuration-operator approach. Equations for arbitrary-temperature numerical calculation of the doublon concentration for the integer band filling $n=1$ at different forms of the model density of states are derived. The energy spectra obtained within the Green function method are discussed with special emphasis on the role of correlated hopping in transition from itinerant to localized behavior observed in vanadium Magneli phases V$_n$O$_{2n-1}$, transition-metal dichalcogenides NiS$_{2-x}$Se$_x$, fulleride A$_n$C$_{60}$ systems.

Energy levels of radium monofluoride RaF in external electric and magnetic fields to search for P - and T,P -violation effects

The RaF molecule is considered to be a potential candidate to search for the electron electric dipole moment and other effects of the time-reversal $(T)$ and spatial parity $(P)$ symmetries violation of fundamental interactions as well as $T$-even, $P$-odd effects. Recently, the existence of a suitable laser-cooling scheme for this molecule was proven experimentally, R. F. Garcia Ruiz et al. [Nature (London) 581, 396 (2020)]. In the present paper, we study energy levels, $g$-factors, and sensitivities to the electron electric dipole moment as functions of the external electric field for the lowest rotational levels of $^{224,226,228}\mathrm{RaF}$ molecules. The state with zero sensitivity to the electron electric dipole moment suitable to test systematic effects is found. Also energy levels of $^{223,225}\mathrm{RaF}$ as functions of the external magnetic field are calculated for the lowest rotational levels. The values of magnetic fields corresponding to the crossing of the levels of opposite parity are found. For these values of the magnetic field, the off-diagonal matrix element of the nuclear spin-dependent parity violation interaction is calculated. The obtained data can be used to design experiments to search for the $T,P$- and $P$-violating effects using the RaF molecule.

Tribaryons in a constituent quark model

We calculate the matrix elements of the color-spin interaction for all possible multi-quark states of tribaryons in flavor SU(3) broken case. For that purpose, we construct the flavor$\otimes$color$\otimes$spin wave functions of the tribaryons, which are taken to be antisymmetric to satisfy the Pauli exclusion principle. Furthermore, we analyze the diquark structure of the tribaryon configurations using the symmetric and antisymmetric basis set of flavor, color and spin states.

Extension of the LDA-1/2 method to the material class of bismuth containing III–V semiconductors

The local density approximation-1/2 method is employed in density functional theory calculations for the electronic structure of III–V dilute bismide systems. For the representative example of Ga(SbBi) with Bi concentrations below 10%, it is shown that this method works very efficiently, especially due to its reasonably low demand on computer memory. The resulting band structure and wavefunctions are used to compute the interaction matrix elements that serve as input to the microscopic calculations of the optical properties and intrinsic losses relevant for the optoelectronic applications of dilute bismides.

Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

The aim of this work is to present an overview of the derivation of the effective shell-model Hamiltonian and decay operators within many-body perturbation theory, and to show the results of selected shell-model studies based on their utilisation. More precisely, we report some technical details that are needed by non-experts to approach the derivation of shell-model Hamiltonians and operators starting from realistic nuclear potentials, in order to provide some guidance to shell-model calculations where the single-particle energies, two-body matrix elements of the residual interaction, effective charges and decay matrix elements, are all obtained without resorting to empirical adjustments. On the above grounds, we will present results of studies of double-beta decay of heavy-mass nuclei where shell-model ingredients are derived from theory, so to assess the reliability of such a way to shell-model investigations. Attention will be also focussed on the relevant aspects that are connected to the behavior of the perturbative expansion, whose knowledge is needed to establish limits and perspectives of this approach to nuclear structure calculations.

Engineering quantum Hall phases in a synthetic bilayer graphene system

Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diagonalization (ED), we show that the system exhibits a non-abelian bilayer Fibonacci phase at filling fraction $\nu = 2/3$. Moreover, at integer filling $\nu = 1$, the SQHB exhibits quantum Hall ferromagnetism. Using Hartree-Fock theory and exact diagonalization, we show that excitations of the quantum Hall ferromagnet are topological textures known as skyrmions.

Fluctuational electrodynamics in atomic and macroscopic systems: van der Waals interactions and radiative heat transfer

We present an approach to describing fluctuational electrodynamic (FED) interactions, particularly van der Waals (vdW) interactions as well as radiative heat transfer (RHT), between material bodies of vastly different length scales, allowing for going between atomistic and continuum treatments of the response of each of these bodies as desired. Any local continuum description of electromagnetic (EM) response is compatible with our approach, while atomistic descriptions in our approach are based on effective electronic and nuclear oscillator degrees of freedom, encapsulating dissipation, short-range electronic correlations, and collective nuclear vibrations (phonons). While our previous works using this approach have focused on presenting novel results, this work focuses on the derivations underlying these methods. First, we show how the distinction between "atomic" and "macroscopic" bodies is ultimately somewhat arbitrary, as formulas for vdW free energies and RHT look very similar regardless of how the distinction is drawn. Next, we demonstrate that the atomistic description of material response in our approach yields EM interaction matrix elements which are expressed in terms of analytical formulas for compact bodies or semianalytical formulas based on Ewald summation for periodic media; we use this to compute vdW interaction free energies as well as RHT powers among small biological molecules in the presence of a metallic plate as well as between parallel graphene sheets in vacuum, showing strong deviations from conventional macroscopic theories due to the confluence of geometry, phonons, and EM retardation effects. Finally, we propose formulas for efficient computation of FED interactions among material bodies in which those that are treated atomistically as well as those treated through continuum methods may have arbitrary shapes, extending previous surface-integral techniques.

Prompt-delayed γ -ray spectroscopy of neutron-rich In119,121 isotopes

The fusion and transfer induced fission reaction $^{9}$Be($^{238}$U,~f) with 6.2 MeV/u beam energy, using a unique setup consisting of AGATA, VAMOS++ and EXOGAM detectors, was used to populate through the fission process and study the neutron-rich $^{119,121}$In isotopes. This setup enabled the prompt-delayed $\gamma$-ray spectroscopy of isotopes in the time range of $100~\rm{ns} - 200~\mu\rm{s}$. In the odd-$A$ $^{119,121}$In isotopes, indications of a short half-life $19/2^{-}$ isomeric state, in addition to the previously known $25/2^{+}$ isomeric state, were observed from the present data. Further, new prompt transitions above the $25/2^{+}$ isomer in $^{121}$In were identified along with reevaluation of its half-life. The experimental data were compared with the theoretical results obtained in the framework of large-scale shell-model calculations in a restricted model space. The $\langle \pi g_{9/2} \nu h_{11/2};I \arrowvert \hat{\mathcal{H}}\arrowvert \pi g_{9/2} \nu h_{11/2};I\rangle$ two-body matrix elements of residual interaction were modified to explain the excitation energies and the $B(E2)$ transition probabilities in the neutron-rich In isotopes. The (i) decreasing trend of $E(29/2^{+}) - E(25/2^{+})$ in odd-In (with dominant configuration $\pi g_{9/2}^{-1}\nu h_{11/2}^{-2}$ and maximum aligned spin of $29/2^{+}$) and (ii) increasing trend of $E(27/2^{+}) - E(23/2^{+})$ in odd-Sb (with dominant configuration $\pi g_{7/2}^{+1}\nu h_{11/2}^{-2}$ and maximum aligned spin of $27/2^{+}$) with increasing neutron number could be understood as a consequence of hole-hole and particle-hole interactions, respectively.

Phonon-limited mobility for novel two-dimensional semiconductors of [formula omitted] and [formula omitted]: First-principles calculation

BC3 and C3N are all novel two-dimensional (2D) semiconductors with excellent thermodynamic stability and high lattice thermal conductivity. To obtain accurate results, phonon-limited carrier mobility is investigated by an iterative Boltzmann transport equation (IBTE) including electron–phonon interaction (EPI) matrix elements for each scattering process. The piezoelectricity (PE) and polar optical phonon (POP) are not the main scattering sources. The mobility is mainly dominated by the short-range interaction between electrons and phonons. At 300 K, the electron mobility for BC3 and C3N is predicted to be 6.56×102 and 8.54×102cm2V-1s-1, while the hole mobility is estimated to be 9.60×101 and 3.26×103cm2V-1s-1. High mobility suggests that C3N is a promising material in nanoelectronic device. Furthermore, the deformation potential theory (DPT) based on longitudinal acoustic phonon (LAP) and optical phonon (OP) scattering is used to investigate mobility. The contribution of three valleys, light and heavy electrons or holes to mobility is considered in the calculation, which can effectively avoid overestimation of mobility. The carrier mobility calculated from DPT is lower than that from IBTE. Too many assumptions make the semiempirical models unable to correctly describe the complex EPI.

Nuclear shell model and level density

The accurate knowledge of the nuclear level density is crucial for understanding the nuclear structure and for numerous applications including astrophysical reactions. In this review paper, we discuss the shell-model description of the nuclear level density, the use of the statistical moments method and underlying physics. The level density found with the moments method is shown to agree with the results of the exact diagonalization of the Hamiltonian matrix. The statistical approach is also compared to other standard methods for deriving level densities. The role of specific interaction matrix elements is reviewed in connection to the behavior of the level densities as these evolve. Chaotization and thermalization processes, collective enhancement and phase transitions are discussed with changing strengths of specific groups of two-body interaction matrix elements. The popular phenomenological constant temperature model is compared to the moments method and the effective temperature parameter of the model for different isotopes is discussed.

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Recent investigations have emphasized the importance of uncertainty quantification (UQ) to describe errors in nuclear theory. We carry out UQ for configuration-interaction shell model calculations in the $1s$-$0d$ valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing the Hessian yields the principal components of the interaction: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical error propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark matter-nucleus scattering matrix elements.