# (1) Strongly correlated matter

**[PIs: ****Lippert****, ****Luu****, ****Meißner****, ****Neese****, ****Urbach**** ] **

Dynamics due to strong interactions and correlations leads to fascinating phenomena with rich spectra. The complicated interactions between quarks and gluons lead to the formation of protons and neutrons that form the basic building blocks for nuclei. These nuclei themselves are quantum many-body bound states that exhibit diverse properties. In condensed matter systems, strong correlations of electrons lead to phenomena such as superconductivity and the fractional quantum Hall effect. Lattice stochastic methods are used to calculate the properties of strongly interacting systems. In all cases, a space-time lattice is utilized with appropriate boundary conditions to simulate the system in question. In RU-A, we will investigate various systems using such methods.

*Lattice QCD* is the discretized version of QCD that performs the path integral formalism through Monte Carlo integration. Here, we will investigate multi-hadron interactions that are difficult to constrain from experiments and study their influence on nuclear systems. This will lead to a much deeper understanding of structure formation in QCD. Varying the quark masses and the electromagnetic fine-structure constant gives direct access to topics discussed in the CST, as in this way particular fine-tunings in nature can be studied.

*Nuclear lattice effective field theory* places nucleons on a discrete lattice with interactions derived from chiral perturbation theory. Here, we want to perform ground-breaking calculations in nuclear structure and reactions. Examples are the determination of the lines of stability (drip lines) and the calculation of the Holy Grail of nuclear astrophysics, ^{12}C + ^{4}He → ^{16}O + γ at stellar energies. Again, the study of element generation in the early universe and in stars has an immediate link to the CST.

*Strongly correlated electrons* can be simulated via lattice stochastic methods by using the physical ion geometry to define the lattice. The dispersion relation for single and multi-quasiparticle systems can be calculated as a function of lattice momentum and doping. These topics will benefit from the exchange of ideas and methods and in particular from the HPC developments in RU-C, but they will also be driving many of the developments. Furthermore, the ability of combining lattice stochastic methods with deterministic DFT offers potentially new methods for studying the structure of complex matter.