Session V2: Explicitly Correlated Methods and Quantum Few-Body Systems

Determinations of physical constants and nuclear properties via few-body atomic systems

Few-body atomic systems provide sources for deriving fundamental physical constants and nuclear properties, such as the fine structure constant, the proton-electron mass ratio, the Rydberg constant, and the nuclear charge radius, provided both theory and experimental measurement can be carried out to a sufficiently high precision. In this talk, I will discuss recent progress along this line and demonstrate the importance of explicitly correlated methods for quantum few-body systems.   

Quantum Monte Carlo study of spin-orbit interaction effects in Tungsten atomic and molecular systems

We study the electronic properties of selected Tungsten molecular systems using averaged and explicit spin-orbit interactions using many-body methods. In particular, we apply recently developed quantum Monte Carlo methods that can treat spin-orbit and other types of spin-dependent interactions explicitly. Our fixed-phase spin-orbital diffusion Monte Carlo (FPSODMC) method is based on a two-component spinor formalism along with a generalization of the fixed-phase approximation and projection of the nonlocal operators with appropriate spinor-based and Jastrow-factor correlated trial wave functions. The determinantal parts of trial wave functions are generated at several levels of accuracy such as single configuration, multi-configuration within the open-shells and large CI expansions. The corresponding impacts on the accuracy of projections and fixed-phase biases are studied on Tungsten molecular systems and the results are compared with the spin-averaged calculations. The binding energies require consistent treatment of spin-orbit and correlations in both atomic and molecular systems. The low symmetry of spinor wave functions increases the multi-reference character of the states and therefore demand appropriate sizes of determinantal expansions.   

Finite temperature properties of strongly correlated systems via variational Monte Carlo

Variational methods are a common approach for computing properties of ground states but have not yet found analogous success in finite temperature calculations. In this talk I present a new variational finite temperature algorithm (VAFT) which combines ideas from maximally entangled thermal states (METTS), variational Monte Carlo optimization (VMC) and path integral Monte Carlo (PIMC) to define an implicit variational finite-temperature density matrix. The algorithm allows us to calculate temperature-averaged observables without ever explicitly representing the full density matrix. On the 2D bipartite Heisenberg lattice, VAFT agrees with exact results at low and intermediate temperatures, and qualitatively reproduces exact results at high temperatures. VAFT is sign-free and works in arbitrary dimensions.   

Path Integral representation of quantum particles in fluids: Convergence of observables .

In previous work the Path Integral Monte Carlo (PIMC) technique was used to simulate a low mass quantum particle (qp) in a dense Lennard-Jones 6-12 fluid having the thermodynamic properties of Xenon. Because of the difference in thermal wavelengths between the qp and the fluid molecules, the fluid molecules can be treated classically. This combination of using quantum mechanics for the qp and classical mechanics for the fluid molecules is known as a hybrid model. In the path integral formulation the qp is represented as a closed chain of P classical particles where the quantum uncertainty in the position of the qp is manifested by the finite spread of the polymer chain. The PIMC technique allows standard classical Monte Carlo techniques to be used to compute quantum mechanical equilibrium values like the ortho-Positronium pick-off decay rate. Here we compare the convergence of PIMC for different thermodynamic states, including one near the liquid-vapor critical point of the fluid. We employ the correlation function of the iterated quantum observables to estimate the number of statistically independent configurations in a run and provide an estimate of the standard error.   

Benchmark calculations of low-lying triplet states of Be atom

Benchmark variational calculations of several lowest triplet states of the beryllium atom are reported. The wave functions of the states were expanded in terms of highly optimized explicitly correlated Gaussian basis sets and accurate energies are deterimed assuming finite nuclear mass of the atom. These wave functions were used to compute various expectation values, including those that appear in the leading relativistic and QED corrections. Density distributions and pair correlation functions are analyzed for both electrons an nucleus.   

Schrödinger and Dirac solutions to few-body problems

\\ We elaborate on the variational solution of the Schr\"odinger and Dirac equations for small atomic and molecular systems without relying on the Born-Oppenheimer approximation. The all-particle equations of motion are solved in a numerical procedure that relies on the variational principle, Cartesian coordinates and parametrized explicitly correlated Gaussians functions. A stochastic optimization of the variational parameters allows the calculation of accurate wave functions for ground and excited states. Expectation values such as the radial and angular distribution functions or the dipole moment can be calculated. We developed a simple strategy for the elimination of the global translation that allows to generally adopt laboratory-fixed cartesian coordinates. Simple expressions for the coordinates and operators are then preserved throughout the formalism. For relativistic calculations we devised a kinetic-balance condition for explicitly correlated basis functions. We demonstrate that the kinetic-balance condition can be obtained from the row reduction process commonly applied to solve systems of linear equations. The resulting form of kinetic balance establishes a relation between all components of the spinor of an N-fermion system.   

Embedding four-body correlation into antisymmetrized geminal power wave function

We extend the Coleman's antisymmetrized geminal power (AGP) to develop a variational wave function theory that can incorporate up to four-body correlation in a region of strong correlation. AGP has been used in the variational Monte Carlo (VMC) simulation by multiplying a Jastrow-type correlation factor, but here we develop a formalism to determistically obtain the total energy and its derivatives in order to avoid the statistical fluctuation that hampers evaluation of the atomic force for geometry optimization and molecular dynamics simulation. For this purpose, we developed a total energy formula in terms of the traces of geminal powers. This novel trace formula is applied to a simple Hubbard ring model to test its numerical accuracy and robustness. The result shows a promising step toward development of a first-principles wave function theory for a strongly correlated point defect or adsorbate embedded in an AGP-based mean-field medium.   

Sympathetic cooling of antiprotons with laser cooling of molecular anions

Molecular anions play a central role in a wide range of fields: from atmospheric and interstellar science, anionic superhalogens to the chemistry of highly correlated systems. However, up to now the synthesis of negative ions in a controlled manner at ultracold temperatures relevant for the processes in which they are involved is currently limited to a few kelvin by supersonic beam expansion followed by resistive, buffer gas or electron cooling in cryogenic environments. We present a realistic scheme for the laser cooling of C2- molecules to subkelvin temperatures, which has been so far only achieved for neutral diatomics. The generation of a pulsed source of C2- and the subsequent laser cooling techniques of C2- confined in a Penning trap are reviewed. Further, laser cooling one anions species would allow to sympathetically cool other molecular anions, electrons and antiprotons that are confined in the same trapping potential. The latter are especially relevant for the potential generation of ultracold antihydrogen atoms for precision experiments of the WEP and spectroscopy for CPT symmetry tests. In this presentation the status of the experiment and the feasibility of C2- sympathetic Doppler laser cooling, photo-detachment cooling and AC Stark Sisyphus cooling will be reviewed.   

Using Monte Carlo Methods to Calculate Some Properties of Finite Mass Helium

If one is interested in evaluating atomic properties to high precision then the finite mass of the atom needs to be explicitly incorporated. We have developed a simple method that includes the kinetic energy of the nucleus into atomic calculations and does not increase the time or the complexity of these calculations. To test this method we have optimized compact, explicitly correlated trial wave functions for the three lowest states of the helium atom with symmetry $^{1}$S, $^{1}$P, $^{1}$D, $^{3}$S, $^{3}$P, and $^{3}$D. With these wavefunctions we then calculated a variety of properties to illustrate some of the advantages of our method.   

Momentum and mass in the covariant theory of light in a medium

We have recently developed a novel covariant theory of light in a medium by considering a light wave simultaneously with the dynamics of the medium driven by the optomechanical forces between the induced dipoles and the electromagnetic field. One of the most fundamental consequences of our theory following directly from the covariance principle and the fundamental conservation laws of nature is that a light pulse having a total electromagnetic energy $\hbar\omega$ propagating in a nondispersive medium transfers a mass equal to $\delta m=(n^2-1)\hbar\omega/c^2$, where $n$ is the refractive index. This mass is made of atoms, which are more dense inside the light pulse due to the optomechanical forces. The predicted photon mass drag effect leads to dissipation of photon energy and it also gives an essential contribution to the total momentum of the light wave, which becomes equal to the Minkowski momentum $p=n\hbar\omega/c$. Therefore, our theory also gives a unique resolution to the centenary Abraham-Minkowski controversy. For the experimental verification of the covariant state of light in a medium, both the total momentum and the transferred mass of the coupled state of the field and matter have to be measured.