Abstract

Many interesting systems in modern condensed matter physics, such as strongly correlated fermions, are too complex to be dealt with by purely analytical methods because of the lack of small parameters. In this talk, I will discuss the power of the diagrammatic technique, which allows us to address problems in many-body physics (and indeed many other areas of physics!) without uncontrolled approximations. I will show how physical quantities can be obtained from the diagrammatic expansion using numerical algorithms, such as quantum Monte Carlo. In this sense, simulations can be viewed as “numerical experiments” probing the system and making quantitative predictions about its properties. In combination with analytical methods they also offer an exciting new way to address fundamental questions. We can test previously uncontrolled assumptions and explicitly check which properties of a model are necessary to produce certain features, and which are irrelevant. I will illustrate the successes and challenges of diagrammatic Quantum Monte Carlo on several examples from atomic physics.