: The Pyrochlore Heisenberg Antiferromagnet: From Finite to Zero Temperature

Frustration provides a fertile ground to explore unconventional forms of quantum matter beyond conventional order. I will discuss significant methodological advancements in various numerical approaches that have been tailored to address an archetypal problem of frustrated magnetism in three dimensions: the pyrochlore Heisenberg antiferromagnet. At finite temperatures, cluster expansion techniques have proven extremely valuable in studying this problem, as they are not affected by the frustrated nature or dimensionality. By pushing the state-of-the-art numerics, we were able to unbiasedly resolve its thermodynamic quantities to a temperature far beyond the scale on which the Schottky anomaly occurs. Moreover, its broad broad applicability has enabled the systematic investigation of various spin-liquid candidate materials, such as the cerium-based pyrochlores Ce$_2$Zr$_2$O$_7$ and Ce$_2$Sn$_2$O$_7$. Zero-temperature properties are even less accessible, and the nature of the ground state or an estimate of its energy is unknown beyond the perturbation regime of quantum spin ice. We used large-scale Density Matrix Renormalization Group (DMRG) calculations pushed to three dimensions to provide the first reliable estimate of its ground-state energy and found robust evidence of a spontaneous inversion symmetry breaking. Continuing the investigation of low-energy states, we propose a new family of valence-bond crystals that are exponentially numerous in the linear system size and visualized as hard-hexagon coverings as potential ground states.