Rayleigh-Ritz variation method and connected-moments polynomial approach

We show that the connected-moments polynomial approach proposed recently is equivalent to the well known Rayleigh-Ritz variation method in the Krylov space. We compare the latter with one of the original connected-moments methods by means of a numerical test on an anharmonic oscillato

Solution to the Equations of the Moment Expansions

We develop a formula for matching a Taylor series about the origin and an asymptotic exponential expansion for large values of the coordinate. We test it on the expansion of the generating functions for the moments and connected moments of the Hamiltonian operator. In the former case the formula produces the energies and overlaps for the Rayleigh-Ritz method in the Krylov space. We choose the harmonic oscillator and a strongly anharmonic oscillator as illustrative examples for numerical test. Our results reveal some features of the connected-moments expansion that were overlooked in earlier studies and applications of the approach

Improved tensor-product expansions for the two-particle density matrix

We present a new density-matrix functional within the recently introduced framework for tensor-product expansions of the two-particle density matrix. It performs well both for the homogeneous electron gas as well as atoms. For the homogeneous electron gas, it performs significantly better than all previous density-matrix functionals, becoming very accurate for high densities and outperforming Hartree-Fock at metallic valence electron densities. For isolated atoms and ions, it is on a par with previous density-matrix functionals and generalized gradient approximations to density-functional theory. We also present analytic results for the correlation energy in the low density limit of the free electron gas for a broad class of such functionals.Comment: 4 pages, 2 figure

The heat of atomization of sulfur trioxide, SO3_3 - a benchmark for computational thermochemistry

Calibration ab initio (direct coupled cluster) calculations including basis set extrapolation, relativistic effects, inner-shell correlation, and an anharmonic zero-point energy, predict the total atomization energy at 0 K of SO$_3$ to be 335.96 (observed 335.92$\pm$0.19) kcal/mol. Inner polarization functions make very large (40 kcal/mol with $spd$, 10 kcal/mol with $spdfg$ basis sets) contributions to the SCF part of the binding energy. The molecule presents an unusual hurdle for less computationally intensive theoretical thermochemistry methods and is proposed as a benchmark for them. A slight modification of Weizmann-1 (W1) theory is proposed that appears to significantly improve performance for second-row compounds.Comment: Chem. Phys. Lett., in pres

Shell Structure of Confined Charges at Strong Coupling

A theoretical description of shell structure for charged particles in a harmonic trap is explored at strong coupling conditions of $\Gamma$ = 50 and 100. The theory is based on an extension of the hypernetted chain approximation to confined systems plus a phenomenological representation of associated bridge functions. Predictions are compared to corresponding Monte Carlo simulations and quantitative agreement for the radial density profile is obtained.Comment: 9 pages, 5 figures. Presented at the 13th International Conference on the Physics of Non-Ideal Plasmas (PNP 13) held in Chernogolovka, Russia (September 13-18, 2009). Proceedings to be published in "Contributions to Plasma Physics" (Dec. 2009-Jan. 2010

Correlations in excited states of local Hamiltonians

Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix)

High--order connected moments expansion for the Rabi Hamiltonian

We analyze the convergence properties of the connected moments expansion (CMX) for the Rabi Hamiltonian. To this end we calculate the moments and connected moments of the Hamiltonian operator to a sufficiently large order. Our large--order results suggest that the CMX is not reliable for most practical purposes because the expansion exhibits considerable oscillations.Comment: 12 pages, 5 figures, 1 tabl

The on-shell self-energy of the uniform electron gas in its weak-correlation limit

The ring-diagram partial summation (or RPA) for the ground-state energy of the uniform electron gas (with the density parameter $r_s$) in its weak-correlation limit $r_s\to 0$ is revisited. It is studied, which treatment of the self-energy $\Sigma(k,\omega)$ is in agreement with the Hugenholtz-van Hove (Luttinger-Ward) theorem $\mu-\mu_0= \Sigma(k_{\rm F},\mu)$ and which is not. The correlation part of the lhs h as the RPA asymptotics $a\ln r_s +a'+O(r_s)$ [in atomic units]. The use of renormalized RPA diagrams for the rhs yields the similar expression $a\ln r_s+a''+O(r_s)$ with the sum rule $a'= a''$ resulting from three sum rules for the components of $a'$ and $a''$. This includes in the second order of exchange the sum rule $\mu_{2{\rm x}}=\Sigma_{2{\rm x}}$ [P. Ziesche, Ann. Phys. (Leipzig), 2006].Comment: 19 pages, 10 figure

Reducible Correlations in Dicke States

We apply a simple observation to show that the generalized Dicke states can be determined from their reduced subsystems. In this framework, it is sufficient to calculate the expression for only the diagonal elements of the reudced density matrices in terms of the state coefficients. We prove that the correlation in generalized Dicke states $|GD_N^{(\ell)}>$ can be reduced to $2\ell$-partite level. Application to the Quantum Marginal Problem is also discussed.Comment: 12 pages, single column; accepted in J. Phys. A as FT

The high-density electron gas: How its momentum distribution n(k) and its static structure factor S(q) are mutually related through the off-shell self-energy Sigma(k,omega)

It is shown {\it in detail how} the ground-state self-energy $\Sigma(k,\omega)$ of the spin-unpolarized uniform electron gas (with the density parameter $r_s$) in its high-density limit $r_s\to 0$ determines: the momentum distribution $n(k)$ through the Migdal formula, the kinetic energy $t$ from $n(k)$, the potential energy $v$ through the Galitskii-Migdal formula, the static structure factor $S(q)$ from $e=t+v$ by means of a Hellmann-Feynman functional derivative. The ring-diagram partial summation or random-phase approximation is extensively used and the results of Macke, Gell-Mann/Brueckner, Daniel/Vosko, Kulik, and Kimball are summarized in a coherent manner. There several identities were brought to the light.Comment: 34 pages, 6 figure