# VSC School Seminar: Uncovering the Secrets of Strongly Correlated Electron Systems – Algorithms and HPC Implementations

**Abstract:**

With the advancement of HPC, the field of computational physics matured into an independent discipline, alongside experimental- and theoretical physics. Historically, the latter two are considered the basis of physics, while lately computational physics is often referred to as the third pillar of physics.

In material science, strongly correlated electron systems are especially fascinating due to properties emerging from the collective nature of the underlying many-body physics. These include superconductivity in cuprates, topological insulators, correlation driven transistors and others.

The exponential scaling of many-body Hamiltonians with the number of particles and orbitals is intrinsic to the corresponding quantum lattice problems, prohibiting analytic solutions in general. The dynamical mean field theory (DMFT), however, reduces the many-body lattice onto an impurity model, which can be solved numerically.

In this talk I will give an introduction to the many-body problem in the context of strongly correlated electron systems. An intuitive understanding of many-body Green's functions represented in terms of Feynman diagrammatics is presented. Due to their physical relevance and their computational complexity, two-particle response functions will be discussed in more detail. I will then proceed to outline the basic concepts of lattice- and impurity problems in combination with DMFT. For the numerical solution of the impurity problem, continuous-time quantum Monte Carlo (CT-QMC) algorithms are introduced. While the trivial parallelization of Monte Carlo greatly reduces the network communication for HPC systems, speed- and memory requirements become a limiting factor. Optimizations to the Monte Carlo sampling and measurement procedures are discussed from a technical viewpoint ranging from exploiting specialized libraries (e.g. FFTW + NFFT) to CT-QMC specific implementations (see [1], [2]). Overall, optimizations in the implementation and improvements on the algorithmic level outperform performance gains resulting from hardware improvements following Moore's law.

*This talk is based on work supported by the VSC Research Center funded by the Austrian Federal Ministry of Education, Science and Research (BMBWF) and reports about the VSC School Project "Dynamical Vertex Approximation (DΓA)".*

[1] Gunacker, P., et al., Phys. Rev. B. 92, 155102 (2015).

[2] Gunacker, P., et al., Phys. Rev. B. 94, 125153 (2016).

**Speaker:**

Patrik Gunacker

Institute of Solid State Physics, TU Wien

**Language:**

English

**Date, Time, and Location:**

09.04.2018, 15:00 - 17:30, FH Hörsaal 2 (TU Wien, Wiedner Hauptstraße 8-10, 2nd floor, yellow area)

**Registration:**

If you would like to join us for this event, please email to: vsc-seminar@list.tuwien.ac.at

(so we will know how many persons will come)

**Slides:**

The course material will be available for registered attendees only.

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