New computational methods in Quantum many-body theory

Description and Aim

New computational methods in quantum many-body theory

Recently a new generation of continuous-time Quantum Monte Carlo (CT-QMC) methods for numerically exact calculation of complicated fermionic path integrals have been proposed for interacting electrons based on the weak-coupling and strong-coupling perturbation expansion. This methodological breakthrough in the quantum many-body theory stimulate a great progress in the electronic calculations of realistic strongly correlated systems within the dynamical mean-field theory (DMFT) where the solution of effective multiband impurity problem is the main point.  The most important achievement of the CT-QMC scheme is related with an opportunity to simulate real systems with arbitrary complex interaction vertex including spin-flip terms and retardation effects. Such progress was impossible with the conventional Hirsch-Fye QMC algorithm based on a time discretization approach.

Such a QMC-revolution makes possible the fast and important developments in the field of strongly correlated materials and results in the recent boom, with numerous applications to a broad circle of many-body problems, such as Kondo problem, cluster DMFT scheme, simulations of magnetic nanosystems on metallic surfaces,  multiorbital Mott transition, correlated electron-phonon systems in the Hubbard-Holstein problem, realistic LDA+DMFT calculation for 14-band case of plutonium, heavy-fermion systems, strongly correlated thermoelectric compounds and novel high-temperature superconducting pnictides. The first attempt to combine the new computational scheme with analytical perturbation approach in correlated fermionic models has been presented recently.

It is highly desirable and timely to discuss a possibility to apply this new idea to other computational methods in various quantum many-body problems. This discussion can bring a new progress, for example, in the field of non-equilibrium transport through correlated nanosystems. Moreover, the new developments in the dynamical density matrix renormalization group (DMRG) community related with the methods of matrix and tensor product states can be very helpful in the calculations of two-particle Green’s functions needed for novel diagrammatic expansion around the DMFT solution.

This workshop brings together people from different many-body communities to discuss a possible synergy of the CT-QMC idea with various quantum many-body methods. Moreover we bring the density functional (DFT) electronic structure community to discuss the optimal many-body impurity solver for realistic DMFT calculations. Computational materials sciences are outstanding growth areas of research. In the future an increasingly larger part of our technological development will depend on computer applications, in particular in materials and nano sciences. Ab-initio calculations based on the density functional theory in combination with the dynamical mean-field theory can make a big progress in the field of nanostructures with d- and f-elements which usually means strong electron correlations. Review lectures of experimental situation in physics of strongly unrelated and non equilibrium systems are planned.