Seminarium Zakładu Mechaniki Kwantowej
W dniu 04. 07. 2013r. (czwartek) o godz. 12.30 w sali 25 prof. So Hirata z Departament of Chemistry, University of Illinois at Urbana-Champaign wygłosi wykład pt."MBPT(2): an eternal frontier".
Second-order many-body perturbation theory or MBPT(2) is the simplest member of the system- atic series of approximations formally convergent to the exact solution of the Schrodinger equa- tion. It thus holds special importance in electronic structure theory and even in quantum dynam- ics. Here, we describe three new advances made in this fundamental theory:
Monte Carlo MBPT(2) (with Soohaeng Willow). With a Laplace transform, the canonical ex- pression of MBPT(2) is converted into the sum of two 13-dimensional integrals, which are evalu- ated by Monte Carlo integration. Weight functions are identified that are analytically integrable, are finite and nonnegative everywhere, and share the same singularities as the integrands. It does away with the integral transformation as the hotspot of the conventional algorithm, displays near linear size dependence of cost even for small molecules, and does not suffer from the sign prob¬lem of quantum Monte Carlo methods. It can also compute MBPT(2) corrections to Dyson self- energies directly and not as small differences between two large, noisy quantities.
Finite-temperature MBPT(2) (with Xiao He). In 1960, Kohn and Luttinger showed that the textbook finite-temperature extension of MBPT(2) had the incorrect zero-temperature limit in a metal and, on this basis, argued that the theory was incorrect. We show that this arises from the noninclusion of temperature effects in the energies of the zeroth-order eigenstates, which also causes another inconsistency, namely, the different rate of divergence of the correlation energy in a metal. We propose a renormalized MBPT(2) derivable from thermal Wick’s theorem, which is shown to have the correct zero-temperature limit and the same rate of divergence in a metal as the zero-temperature counterpart. We assert that this is the correct finite-temperature MBPT(2).
Vibrational MBPT(2) (with Matt Hermes). We develop MBPT(2) for anharmonic vibrational frequencies and zero-point energies. Solving the inverse Dyson equations self-consistently, we obtain from MBPT(2) accurate anharmonic frequencies of not only fundamental but also overtone and combination tones in the presence of strong mode-mode coupling such as Fermi resonances. We also introduce the mathematical constructs of the Dyson coordinates and geometry. The for- mer are a unitary transformation of normal coordinates that bring the self-energy in the diagonal form and are the vibrational analogue of the Dyson orbitals. The latter has no counterparts in electronic structure theory and is a point on the potential energy surface where the sums of the energy gradients and anharmonic vibrational corrections vanish.