Review of quantum simulation based on Rydberg many-body system

Quantum simulation has been developed extensively over the past decades,widely applied to different models to explore dynamics in the quantum regime.Rydberg atoms have strong dipole-dipole interactions and interact with each other over a long distance,which makes it straightforward to build many-body interacting quantum systems to simulate specific models.Additionally,neutral atoms are easily manipulated due to their weak interactions.These advantages make Rydberg many-body system an ideal platform to implement quantum simulations.This paper reviews several quantum simulations for different models based on Rydberg many-body systems,including quantum Ising models in one dimension and two dimensions mainly for quantum magnetism,XY model for excitation transport,SSH model for symmetry-protected topological phases,and critical self-organized behaviors in many-body systems.Besides,some challenges and promising directions of quantum simulations based on Rydberg many-body system are discussed in this paper.

Fully relativistic many-body perturbation energies,transition properties,and lifetimes of lithium-like iron Fe XXIV

Employing the advanced relativistic configuration interaction(RCI)combined with the many-body perturbation theory(RMBPT)method,we report energies and lifetime values for the lowest 35 energy levels from the(1s^(2))nl configurations(where the principal quantum number n=2–6 and the angular quantum number l=0,...,n-1)of lithium-like iron Fe XXIV,as well as complete data on the transition wavelengths,radiative rates,absorption oscillator strengths,and line strengths between the levels.Both the allowed(E1)and forbidden(magnetic dipole M1,magnetic quadrupole M2,and electric quadrupole E2)ones are reported.Through detailed comparisons with previous results,we assess the overall accuracies of present RMBPT results to be likely the most precise ones to date.Configuration interaction effects are found to be very important for the energies and radiative properties for the ion.The present RMBPT results are valuable for spectral line identification,plasma modeling,and diagnosing.

Fully relativistic energies,transition properties,and lifetimes of lithium-like germanium

Employing two fully relativistic methods,the multi-reference configuration Dirac-Hartree-Fock(MCDHF)methodand the relativistic many-body perturbation theory(RMBPT)method,we report energies and lifetime values for the lowest35 energy levels of the(1s^(2))nl configurations(where the principal quantum number n=2-6 and the angular quantum numberl=0,...,n-1)of lithium-like germanium(Ge XXX),as well as complete data on the transition wavelengths,radiativerates,absorption oscillator strengths,and line strengths between the levels.Both the allowed(E1)and forbidden(magneticdipole M1,magnetic quadrupole M2,and electric quadrupole E2)ones are reported.The results from the two methodsare consistent with each other and align well with previous accurate experimental and theoretical findings.We assess theoverall accuracies of present RMBPT results to be likely the most precise ones to date.The present fully relativistic resultsshould be helpful for soft x-ray laser research,spectral line identification,plasma modeling and diagnosing.The datasetspresented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00135.

From the Green's Function in Tight-Binding Representation to Interatomic Many-body Potentials

In this paper, we deduce the analytical form of many-body interatomic potentials based on the Green's function in tight-binding representation. The many-body potentials are expressed as the functions of the hopping integrals which are the physical origin of cohesion of atoms. For thesimple case of s-valent system, the inversion of the many-body potentials are discussed in detail by using the lattice inversion method.

Understanding many-body physics in one dimension from the Lieb–Liniger model

This article presents an elementary introduction on various aspects of the prototypical integrable model the LiebLiniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe＇s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb-Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang-Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that rbported novel observations of different physical aspects of the Lieb--Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability.

Many-Body-Gravitational Solutions for Galactic Rotational Velocities, Including Possible Negative Mass

The necessary derivation of negative mass in dispersion dynamics suggests cosmic applications. The method analyzes functional relationships between particle angular frequency, wave vector, rest mass and electromagnetic or nuclear potential, f(ω, k, m0, V) = 0. A summary of consequential predictions of the dynamics leads to a calculation of ways in which negative mass might influence such phenomena as the rotational velocities that are observed in spiral galaxies. The velocities are found to be not Newtonian in the simple two body approximations for our solar system;but nearly constant with increasing orbital radii. It has moreover been suggested that the motion is due to halo structures of dark matter or dark energy. However, the motion is simply described by many-body gravitation that is transmitted along elastic spiral arms. In this context, we calculate possible effects of negative mass, but without observational confirmation.

Spectral Theorem of Many-Body Green's Functions When Complex Eigenvalues Appear

In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.

Many-body dissipative particle dynamics with energy conservation:temperature-dependent long-term attractive interaction

Heat and mass transfer during the process of liquid droplet dynamic behaviors has attracted much attention in decades.At mesoscopic scale,numerical simulations of liquid droplets motion,such as impacting,sliding,and coalescence,have been widely studied by using the particle-based method named many-body dissipative particle dynamics(MDPD).However,the detailed information on heat transfer needs further description.This paper develops a modified MDPD with energy conservation(MDPDE)by introducing a temperature-dependent long-term attractive interaction.By fitting or deriving the expressions of the strength of the attractive force,the exponent of the weight function in the dissipative force,and the mesoscopic heat friction coefficient about temperature,we calculate the viscosity,self-diffusivity,thermal conductivity,and surface tension,and obtain the Schmidt number Sc,the Prandtl number P r,and the Ohnesorge number Oh for 273 K to 373 K.The simulation data of MDPDE coincide well with the experimental data of water,indicating that our model can be used to simulate the dynamic behaviors of liquid water.Furthermore,we compare the equilibrium contact angle of droplets wetting on solid surfaces with that calculated from three interfacial tensions by MDPDE simulations.The coincident results not only stand for the validation of Young’s equation at mesoscale,but manifest the reliability of our MDPDE model and applicability to the cases with free surfaces.Our model can be extended to study the multiphase flow withcomplex heat and mass transfer.

A New Many-Body Expansion Scheme for Atomic Clusters:Application to Nitrogen Clusters

Although the many-body expansion(MBE)approach is widely applied to estimate the energy of large systems containing weak interactions,it is inapplicable to calculating the energies of covalent or metal clusters.In this work,we propose an interaction manybody expansion(IMBE)to calculate the energy of atomic clusters containing covalent bonds.In this approach,the energy of a system is expressed as the sum of the energy of atoms and the interaction energy between the atom and its surrounding atoms.The IMBE method is first applied to calculate the energies of nitrogen clusters,in which the interatomic interactions are truncated to four-body terms.The results show that the IMBE approach could significantly reduce the energy error for nitrogen clusters compared with the traditional MBE method.The weak size and structure dependence of the IMBE error with respect to DFT calculations indicates the IMBE method has good potential application in estimating energy of large covalent systems.

Charge oscillation and many-body effect in triangular quantum dots

We study the charge oscillation in the triangular quantum dots symmetrically coupled to the leads. A strong charge oscillation is observed even for a very small level difference. We attribute this oscillation behaviour to the many- body effect in the strongly correlated system instead of the physical scenarios based on the mean-field approach in the previous works for the two-level dot. The level difference induces the difference of the occupations between different dots, while the symmetry of the many-body states favours the homogeneous distribution of the charge density on the three dots. The interplay of these two factors results in the charge oscillation.

THE CORRELATED CROSS SECTION OF THE MANY-BODY SCATTERING

In this paper the tensor probability current and continuity equation is obtained, with this the correlated cross section of many particle scattering can be evaluation.

Facilitation of controllable excitation in Rydberg atomic ensembles

Strongly-interacting Rydberg atomic ensembles have shown intense collective excitation effects due to the inclusion of single Rydberg excitation shared by multiple atoms in the ensemble.In this paper we investigate a counter-intuitive Rydberg excitation facilitation with a strongly-interacting atomic ensemble in the strong probe-field regime,which is enabled by the role of a control atom nearby.Differing from the case of a single ensemble,we show that,the control atom's excitation adds to a second two-photon transition onto the doubly-excited Rydberg state,arising an excitation facilitation for the ensemble atoms.Our numerical studies depending on the method of quantum Monte Carlo wave function,exhibit the observation constraints of this excitation facilitation effect under practical experimental conditions.The results obtained can provide a flexible control for the excitation of Rydberg atomic ensembles and participate further uses in developing mesoscopic Rydberg gates for multiqubit quantum computation.

Benchmarking calculations of excitation energies and transition properties with spectroscopic accuracy of highly charged ions used for the fusion plasma and astrophysical plasma

Atomic radiative data such as excitation energies, transition wavelengths, radiative rates, and level lifetimes with high precision are the essential parameters for the abundance analysis, simulation, and diagnostics in fusion and astrophysical plasmas. In this work, we mainly focus on reviewing our two projects performed in the past decade. One is about the ions with Z■30 that are generally of astrophysical interest, and the other one is about the highly charged krypton(Z = 36)and tungsten(Z = 74) ions that are relevant in research of magnetic confinement fusion. Two different and independent methods, namely, multiconfiguration Dirac–Hartree–Fock(MCDHF) and the relativistic many-body perturbation theory(RMBPT) are usually used in our studies. As a complement/extension to our previous works for highly charged tungsten ions with open M-shell and open N-shell, we also mainly focus on presenting and discussing our complete RMBPT and MCDHF calculations for the excitation energies, wavelengths, electric dipole(E1), magnetic dipole(M1), electric quadrupole(E2), and magnetic quadrupole(M2) transition properties, and level lifetimes for the lowest 148 levels belonging to the 3l3configurations in Al-like W61+. We also summarize the uncertainties of our systematical theoretical calculations, by cross-checking/validating our datasets from our RMBPT and MCDHF calculations, and by detailed comparisons with available accurate observations and other theoretical calculations. The data are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.10569.

Backflow Transformation for A=3 Nuclei with Artificial Neural Networks

A novel variational wave function defined as a Jastrow factor multiplying a backflow transformed Slater determinant was developed for A=3 nuclei.The Jastrow factor and backflow transformation were represented by artificial neural networks.With this newly developed wave function,variational Monte Carlo calculations were carried out for3H and3He nuclei starting from a nuclear Hamiltonian based on the leadingorder pionless effective field theory.The obtained ground-state energy and charge radii were successfully benchmarked against the results of the highly-accurate hypersphericalharmonics method.The backflow transformation plays a crucial role in improving the nodal surface of the Slater determinant and,thus,providing accurate ground-state energy.

Generalized Toda Mechanics Associated with Loop Algebras L（Cr） and L（Dr） and Their Reductions

We construct a class of integrable generalization of Toda mechanics withlong-range interactions. These systems are associated with the loop algebras L(C_r) and L(D_r) inthe sense that their Lax matrices can he realized in terms of the c = 0 representations of theaffine Lie algebras C_r~((1)) and D_r~((1)) and the interactions pattern involved bears the typicalcharacters of the corresponding root systems. We present the equations of motion and the Hamiltoninnstructure. These generalized systems can be identified unambiguously by specifying the underlyingloop algebra together with an ordered pair of integers (n, m). It turns out that different systemsassociated with the same underlying loop algebra but with different pairs of integers (n_1, m_1) and(n_2, m_2) with n_2 【 n_1 and m_2 【 m_2 can be related by a nested Hamiltonian reduction procedure.For all nontrivial generalizations, the extra coordinates besides the standard Toda variables arePoisson non-commute, and when either n or m ≥ 3, the Poisson structure for the extra coordinatevariables becomes some Lie algebra (i.e. the extra variables appear linearly on the right-hand sideof the Poisson brackets). In the quantum case, such generalizations will become systems withnoncommutative variables without spoiling the integrability.

High‑accuracy measurement of Compton scattering in germanium for dark matter searches

Compton scattering with bound electrons contributes to a significant atomic effect in low-momentum transfer,yielding background structures in direct light dark matter searches as well as low-energy rare event experiments.We report the measurement of Compton scattering in low-momentum transfer by implementing a 10-g germanium detector bombarded by a^(137)Cs source with a radioactivity of 8.7 mCi and a scatter photon captured by a cylindrical NaI(Tl)detector.A fully relativistic impulse approximation combined with multi-configuration Dirac–Fock wavefunctions was evaluated,and the scattering function of Geant4 software was replaced by our calculation results.Our measurements show that the Livermore model with the modified scattering function in Geant4 is in good agreement with the experimental data.It is also revealed that atomic many-body effects significantly influence Compton scattering for low-momentum transfer(sub-keV energy transfer).

Theoretical Investigation of Exchange Bias in Compensated Cases

The exchange bias （EB） of the ferromagnetic （FM）/antiferromagnetic （AFM） bilayers in a compensated case is studied by use of the many-body Green＇s function method of quantum statistical theory. The so-called compensated case is that there is no net magnetization on the AFM side of the interface. Our conclusion is that the EB in this case is primarily from the asymmetry of the interracial exchange coupling strengths between the FM and the two sublattices of the AFM. The effects of the layer thickness, temperature and the interracial coupling strength oi2 the exchange bias HE are investigated. The dependence of HE on the FM layer thickness and temperature is qualitatively in agreement with experimental results. HE is nearly inversely proportional to FM thickness. When temperature varies, both HE and He decrease with temperature increasing. The anisotropy of the FM layer only slightly influence He, but does not influence HE.

Statistical Average of Spin Operators for Calculation of Three-Component Magnetization （II）： Solution of Equation

In this paper, the solution of Chebyshev equation with its argument being greater than 1 is obtained. The initial value of the derivative of the solution is the expression of magnetization, which is valid for any spin quantum number S. The Chebyshev equation is transformed from an ordinary differential equation obtained when we dealt with Heisenberg model, in order to calculate all three components of magnetization, by many-body Green＇s function under random phase approximation. The Chebyshev functions with argument being greater than 1 are discussed. This paper shows that the Chebyshev polynomials with their argument being greater than 1 have their physical application.

Effects of Coverage,Water,and Defects on Catechol/TiO2 Interface

Catechol adsorbed on TiO_(2)is one of the simplest models to explore the relevant properties of dye-sensitized solar cells.However,the effects of water and defects on the electronic levels and the excitonic properties of the catechol/TiO_(2)interface have been rarely explored.Here,we investigate four catechol/TiO_(2)interfaces aiming to study the influence of coverage,water,and defects on the electronic levels and the excitonic properties of the catechol/TiO_(2)interface through the first-principles many-body Green’s function theory.We find that the adsorption of catechol on the rutile(110)surface increases the energies of both the TiO_(2)valence band maximum and conduction band minimum by approximately 0.7 eV.The increasing coverage and the presence of water can reduce the optical absorption of charge-transfer excitons with maximum oscillator strength.Regarding the reduced hydroxylated TiO_(2)substrate,the conduction band minimum decreases greatly,resulting in a sub-bandgap of 2.51 eV.The exciton distributions in the four investigated interfaces can spread across several unit cells,especially for the hydroxylated TiO2substrate.Although the hydroxylated TiO_(2)substrate leads to a lower open-circuit voltage,it may increase the separation between photogenerated electrons and holes and may therefore be beneficial for improving the photovoltaic efficiency by controlling its concentration.Our results may provide guidance for the design of highly efficient solar cells in future.

Theoretical study of the structure and analytic potential energy function for the ground state of the PO_2 molecule

In this paper, the energy, equilibrium geometry, and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP, B3P86, CCSD（T）, and QCISD（T） methods in conjunction with the 6-311＋＋G（3df, 3pd） and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311＋＋G（3df, 3pd） method can give better energy calculation results for the PO2 molecule. It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2A1. The equilibrium parameters of the structure are Rp-o = 0.1465 am, ZOPO = 134.96°, and the dissociation energy is Ed = 19.218 eV. The bent vibrational frequency Ul = 386 cm-1, symmetric stretching frequency v2 = 1095 cm-1, and asymmetric stretching frequency ua = 1333 em-1 are obtained. On the basis of atomic and molecular reaction statics, a reasonable dissociation limit for the ground state of the PO2 molecule is determined. Then the analytic potential energy function of the PO2 molecule is derived using many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO2 molecule.