In the low-temperature behaviour of quantum systems, we often encounter symmetry breaking and magnetic ordering. In contrast, the fluctuations in many frustrated systems can be so strong that they prevent the onset of magnetic ordering and new, exotic phases of the matter can emerge like quantum spin liquids.

The S=1/2 antiferromagnetic Heisenberg model on the pyrochlore lattice, which is a cubic arrangement of corner-sharing tetrahedra, is one of the most famous systems in this field. Despite several decades’ investigations, the properties of the quantum model remain inconclusive due to the lack of reliable theoretical tools.

In this talk, I will give an overview of my research activities in this area. I am going to show that with the help of large-scale density-matrix renormalization group and numerical linked-cluster expansion significant steps can be made towards the understanding the thermodynamics and ground-state properties of this difficult problem. The experimental relevance of the results and future research directions will be discussed as well.