## Why quantum many-body physics?

Quantum many-body physics is the study of quantum systems that consist of, you have probably guessed it, many particles. Examples of such systems in nature include various materials, liquids, gases. The area of physics concerned with such systems is called condensed matter physics. In many cases, the fact that we have a large number of particles does not matter much, namely if the particles (atoms in a gas, electrons in a conductor, etc.) do not interact strongly with each other. A number of exact and approximate methods are available for such systems. But many interesting phenomena can only be observed if the interactions between the particles are very strong. High-temperature superconductivity is one famous example of such a phenomenon. In such cases we need to come up with more intricate methods.

## What is special about fermions?

In quantum physics we distinguish between two classes of particles: fermions and bosons. The basic particles that make up matter (electrons, protons, neutrons, and also quarks) are all fermions. Two identical fermions can never be in the same quantum state. This property of fermions, called Pauli exclusion principle, is why we have different chemical elements — the electrons have to fill successive energy shells around the atomic nucleus. Many other properties of solids are a consequence of this principle. Understanding properties of electrons, and fermions in general, is therefore important for understanding fundamental properties of matter.

## What can computers do?

Most strongly interacting quantum many-body systems are too complex to be described exactly. This is why researchers are developing powerful computational techniques to study such systems. This is more computationally expensive for quantum systems than for classical systems. Fermions are particularly difficult due to Pauli’s exclusion principle, which leads to cancellations in the numerical sampling process and strongly amplifies statistical noise. But there are powerful numerical methods, called Diagrammatic Monte Carlo methods, which not only avoid this problem, but actually turn it into an advantage that results in more efficient algorithms.

Improvements in algorithms and in computer hardware allow us to obtain high precision results for many physical quantities. Precision calculations are very important for the validation of models, as a benchmark to test new methods and experimental setups, and to make predictions for applications and technology. They can also lead to the discovery of new physical phenomena. Such “numerical experiments” are often cheaper and easier to perform their real-world counterparts. But we can also use computational techniques to explain the mechanisms behind physical phenomena. We cannot alter the laws of nature, but we can easily modify a theoretical model. By performing different simulations we can explicitly test which ingredients of a model are necessary to produce certain physical features, and which are irrelevant.

## Ultracold atomic gases

Materials are by nature complicated and messy systems. Many physical forces are present in any material, not to mention that every sample will have its own unique impurities and defects. Such complications hinder or goal of explaining the origin behind different physical phenomena. In other words, theorists prefer simple models and being able to realize such models experimentally would be of great advantage. Fortunately, there is a way to experimentally make simple quantum many-body systems using ultracold atoms.

Atomic gases are dilute systems of many atoms, with densities of four to six orders of magnitude lower than of the air around us. When they are cooled to temperatures very close to zero (typically below 0.000001 Kelvin) quantum mechanical phenomena become apparent. Of course, quantum effects in liquids or solids can be observed at much higher temperatures. But ultracold gases are, due to their diluteness, nearly ideal many-body systems that can be characterized by only few parameters. Their properties can be manipulated in an experiment easily and with great precision. This makes atomic gases a versatile tool for a direct realization of many fundamental models in condensed matter physics. They also give us insight into a wide range of complex real-world systems — from semiconductors to neutron stars — and ultimately contribute to practical applications, such as quantum computers and the development of new materials.