Reactive Many-Body Expansion for a Protonated Water Cluster.

We generalize the standard many-body expansion technique that is used to approximate the total energy of a molecular system to enable the treatment of chemical reactions by quantum chemical techniques. By considering all possible assignments of atoms to monomer units of the many-body expansion and associating suitable weights with each, we construct a potential energy surface that is a smooth function of the nuclear positions. We derive expressions for this reactive many-body expansion energy and describe an algorithm for its evaluation, which scales polynomially with system size, and therefore will make the method feasible for future condensed phase simulations. We demonstrate the accuracy and smoothness of the resulting potential energy surface on a molecular dynamics trajectory of the protonated water hexamer, using the Hartree-Fock method for the many-body term and Møller-Plesset theory for the low order terms of the many-body expansion.

Applying many-body expansion aiming to make ab in initio molecular dynamics more efficient

In this present work we present a methodology that aims to apply the many-body expansion to decrease the computational cost of ab initio molecular dynamics, keeping acceptable accuracy on the results. We implemented this methodology in a program which we called ManBo. In the many-body expansion approach, we partitioned the total energy E of the system in contributions of one body, two bodies, three bodies, etc., until the contribution of the Nth body [1-3]: E = E1 + E2 + E3 + …EN. The E1 term is the sum of the internal energy of the molecules; the term E2 is the energy due to interaction between all pairs of molecules; E3 is the energy due to interaction between all trios of molecules; and so on. In Manbo we chose to truncate the expansion in the contribution of two or three bodies, both for the calculation of the energy and for the calculation of the atomic forces. In order to partially include the many-body interactions neglected when we truncate the expansion, we can include an electrostatic embedding in the electronic structure calculations, instead of considering the monomers, pairs and trios as isolated molecules in space. In simulations we made we chose to simulate water molecules, and use the Gaussian 09 as external program to calculate the atomic forces and energy of the system, as well as reference program for analyzing the accuracy of the results obtained with the ManBo. The results show that the use of the many-body expansion seems to be an interesting approach for reducing the still prohibitive computational cost of ab initio molecular dynamics. The errors introduced on atomic forces in applying such methodology are very small. The inclusion of an embedding electrostatic seems to be a good solution for improving the results with only a small increase in simulation time. As we increase the level of calculation, the simulation time of ManBo tends to largely decrease in relation to a conventional BOMD simulation of Gaussian, due to better scalability of the methodology presented. References [1] E. E. Dahlke and D. G. Truhlar; J. Chem. Theory Comput., 3, 46 (2007). [2] E. E. Dahlke and D. G. Truhlar; J. Chem. Theory Comput., 4, 1 (2008). [3] R. Rivelino, P. Chaudhuri and S. Canuto; J. Chem. Phys., 118, 10593 (2003).

Ultra-sensitive pressure dependence of bandgap of rutile-GeO2 revealed by many body perturbation theory

The reported values of bandgap of rutile GeO2 calculated by the standard density functional theory within local-density approximation (LDA)/generalized gradient approximation (GGA) show a wide variation (similar to 2 eV), whose origin remains unresolved. Here, we investigate the reasons for this variation by studying the electronic structure of rutile-GeO2 using many-body perturbation theory within the GW framework. The bandgap as well as valence bandwidth at Gamma-point of rutile phase shows a strong dependence on volume change, which is independent of bandgap underestimation problem of LDA/GGA. This strong dependence originates from a change in hybridization among O-p and Ge-(s and p) orbitals. Furthermore, the parabolic nature of first conduction band along X-Gamma-M direction changes towards a linear dispersion with volume expansion. (C) 2015 AIP Publishing LLC.

New parameters of many-body potentials: studying the thermal and mechanical properties of noble metals

New parameters of nearest-neighbor EAM (1N-EAM), n-th neighbor EAM (NN-EAM), and the second-moment approximation to the tight-binding (TB-SMA) potentials are obtained by fitting experimental data at different temperatures. In comparison with the available many-body potentials, our results suggest that the 1N-EAM potential with the new parameters is the best description of atomic interactions in studying the thermal expansion of noble metals. For mechanical properties, it is suggested that the elastic constants should be calculated in the experimental zero-stress states for all three potentials. Furthermore, for NNEAM and TB-SMA potentials, the calculated results approach the experimental data as the range of the atomic interaction increases from the first-neighbor to the sixth-neighbor distance.

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Squeezed states phase space representation and semiclassical approximations in many-body systems

We derive an alternative semiclassical approach (to the Wigner-Kirkwood method) for many-body systems using a mapping scheme based on the squeezed states phase space representation. The new expansion is applied to the usual harmonic oscillator case and the differences with the Wigner-Kirkwood results are discussed. © 1990.

Many-body effects in electrochemisorption : Part III. Beyond mean field and hartree-fock

Several channels provided by many-body couplings — both fermion-fermion and fermion-boson — for the evolution of the chemisorption system are discussed. This provides an opportunity of a systematic study of the effects of correlations reflected through the intricate pole structure of the absorbate Green functions. The results of Newns, Anda and others in the context of chemisorption are generalized.

Many-body effects in electrochemisorption : Part IV. Multi-boson formalism

Several boson subsystems may be involved in electrosorption phenomena. To accommodate this possibility, the one-boson formalism described in Parts I–III is extended to this case. The hierarchy in the superoperator scheme, the evaluation of operator averages for closure and several special cases are indicated. As an illustration, some calculations are presented to indicate the trends of many-body corrections in chemisorption.

Landau-Zener problem with waiting at the minimum gap and related quench dynamics of a many-body system

We discuss a technique for solving the Landau-Zener (LZ) problem of finding the probability of excitation in a two-level system. The idea of time reversal for the Schrodinger equation is employed to obtain the state reached at the final time and hence the excitation probability. Using this method, which can reproduce the well-known expression for the LZ transition probability, we solve a variant of the LZ problem, which involves waiting at the minimum gap for a time t(w); we find an exact expression for the excitation probability as a function of t(w). We provide numerical results to support our analytical expressions. We then discuss the problem of waiting at the quantum critical point of a many-body system and calculate the residual energy generated by the time-dependent Hamiltonian. Finally, we discuss possible experimental realizations of this work.

Many-Body Localization in the Presence of a Single-Particle Mobility Edge

In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems.

Conditional independence in quantum many-body systems

In this thesis, I will discuss how information-theoretic arguments can be used to produce sharp bounds in the studies of quantum many-body systems. The main advantage of this approach, as opposed to the conventional field-theoretic argument, is that it depends very little on the precise form of the Hamiltonian. The main idea behind this thesis lies on a number of results concerning the structure of quantum states that are conditionally independent. Depending on the application, some of these statements are generalized to quantum states that are approximately conditionally independent. These structures can be readily used in the studies of gapped quantum many-body systems, especially for the ones in two spatial dimensions. A number of rigorous results are derived, including (i) a universal upper bound for a maximal number of topologically protected states that is expressed in terms of the topological entanglement entropy, (ii) a first-order perturbation bound for the topological entanglement entropy that decays superpolynomially with the size of the subsystem, and (iii) a correlation bound between an arbitrary local operator and a topological operator constructed from a set of local reduced density matrices. I also introduce exactly solvable models supported on a three-dimensional lattice that can be used as a reliable quantum memory.

The interplay of localization and interactions in quantum many-body systems

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.

The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.

The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.

First-principles energetics of water: a many-body analysis

Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for solid, liquid and cluster forms of water. We use a many-body separation of the total energy into its 1-body, 2-body (2B) and beyond-2-body (B2B) components to analyze the deficiencies of two popular DFT approximations. We show how machine-learning methods make this analysis possible for ice structures as well as for water clusters. We find that the crucial energy balance between compact and extended geometries can be distorted by 2B and B2B errors, and that both types of first-principles error are important.