Autumn School on Correlated Electrons: Many-Body Methods for Real Materials

September 16, 2019 ​- September 20, 2019


Forschungszentrum Jülich


  • Eva Pavarini, Institute for Advanced Simulation, Forschungszentrum Jülich, Germany

  • Erik Koch, FZJ, Jülich, Germany

  • Shiwei Zhang, College Williams and Mary, Williamsburg, USA


Emergent many-body phenomena are at the core of the exciting properties of strongly correlated materials. Understanding them requires confronting the many-body problem. While, at first, this appears to be an impossible task, substantial progress has been made by combining physical insights with modern numerical approaches. A successful strategy is to devise methods that use the understanding gained from simple models for constructing physically motivated wave-functions. Results for the ground state of real materials can then be obtained by optimizing them via deterministic or stochastic algorithms. The methods of choice for determining spectra are based on Green functions. A key strategy in these approaches is to map the complex realistic many-body Hamiltonian to a simpler auxiliary model that can be solved numerically.


The goal of this year’s school is to provide students with an overview of the state-of-the art of these techniques, their successes and their limitations. This is the necessary basis for further developments in the field. After introducing fundamental models and key techniques, lectures will focus on quantum Monte Carlo methods for optimizing correlated wave-functions, stochastically sampling series expansions for obtaining Green functions, and renormalization group techniques. Advanced lectures will address approaches to Mott physics, transport phenomena, and out-of-equilibrium dynamics. Applications will cover correlated systems ranging from transition metal compounds, and frustrated spin systems to correlated molecules.

Lecture Topics

Introduction and Basics

  • key questions for strongly correlated materials

  • introduction to the paradigmatic models

  • Green functions, self-energy and Feynman diagrams

  • Luttinger-Ward functional

  • quasi-particles and Fermi liquid theory

Correlated Materials

  • transition-metal compounds

  • correlated molecules

  • Mott insulators

  • heavy fermions

  • frustrated systems

Wave-function Methods

  • variational and diffusion Monte Carlo

  • Jastrow and multi-reference wavefunctions

  • BCS, RVB, Pfaffians

  • Lanczos method

  • density-matrix renormalization group

  • tensor network wavefunction methods

Green functions in and out of equilibrium

  • random-phase approximation

  • linear response functions

  • dynamical mean-field theory


  • Green functions in and out of equilibrium

  • correlated transport through single molecules

QMC for model Hamiltonians

  • Hubbard and Heisenberg models

  • algebraic approaches

  • auxiliary-field QMC at zero and finite temperature

  • diagrammatic Monte Carlo

  • stochastic series expansions