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Quantum many-body systems in thermal equilibrium can be described by the imaginary time Green's function formalism. However, the treatment of large molecular or solid ab initio problems with a fully realistic Hamiltonian in large basis sets is hampered by the storage of the Green's function and the precision of the solution of the Dyson equation. We present a Legendre-spectral algorithm for solving the Dyson equation that addresses both of these issues. By formulating the algorithm in Legendre coefficient space, our method inherits the known faster-than-exponential convergence of the Green's function's Legendre series expansion. In this basis, the fast recursive method for Legendre polynomial convolution enables us to develop a Dyson equation solver with quadratic scaling. We present benchmarks of the algorithm by computing the dissociation energy of the helium dimer He2 within dressed second-order perturbation theory. For this system, the application of the Legendre spectral algorithm allows us to achieve an energy accuracy of 10−9Eh with only a few hundred expansion coefficients. [ABSTRACT FROM AUTHOR]

We present a numerically exact study of charge transport and its fluctuations through a molecular junction driven out of equilibrium by a bias voltage, using the inchworm quantum Monte Carlo method. After showing how the technique can be used to address any lead geometry, we concentrate on one dimensional chains as an example. The finite bandwidth of the leads is shown to affect transport properties in ways that cannot be fully captured by quantum master equations: in particular, we reveal an interaction-induced broadening of transport channels that is visible at all voltages and show how fluctuations of the current are a more sensitive probe of this effect than the mean current. [ABSTRACT FROM AUTHOR]

REFERENCE 1 X. Dong, D. Zgid, E. Gull, and H. U. R. Strand, "Legendre-spectral dyson equation solver with super-exponential convergence", J. Chem. Phys. This erratum corrects three equation misprints and the equation reference numbering in Fig. Erratum: "Legendre-spectral Dyson equation solver with super-exponential convergence" [J. Chem. Phys. [Extracted from the article]

We apply the recently developed adaptive ensemble optimization technique to simulate dense Lennard-Jones fluids and a particle-solvent model by broad-histogram Monte Carlo techniques. Equilibration of the simulated fluid is improved by sampling an optimized histogram in radial coordinates that shifts statistical weight towards the entropic barriers between the shells of the liquid. Interstitial states in the vicinity of these barriers are identified with unprecedented accuracy by sharp signatures in the quickly converging histogram and measurements of the local diffusivity. The radial distribution function and potential of mean force are calculated to high precision. [ABSTRACT FROM AUTHOR]