Quantum materials exhibit a rich variety of phases, each with fascinating properties. The states that spark the most excitement are typically characterized by spontaneous orderings which emerge from low-energy processes, predominant only at low temperatures. These processes, however, also manifest at higher temperatures and can be probed within the normal state. My goal as a scientist is both to improve the characterization and understanding of such exotic states of matter and to develop a first-principles numerical framework that describes and connects the entire spectrum of temperature scales while predicting their behavior. In this talk, I will first present how susceptibilities within a high-temperature normal state can provide crucial information into low temperature ordering. In particular, I will highlight three approaches that attempt to unravel the superconducting state of Sr2RuO4, a material for which the superconductivity is still debated after 30 years [1-3]. I will then discuss future directions and highlight an upcoming implementation of the ghost-Gutzwiller approximation employing matrix product states [4-6].

[1] Gingras et al., Physical Review Letters 123, 217005 (2019).

[2] Gingras et al., Physical Review B 106, 064513 (2022).

[3] Hauck et al., arXiv:2307.10006.

[4] Lanatà et al., Physical Review B 96, 195126 (2017).

[5] Lee et al., arXiv:2305.11128.

[6] Fishman, White and Stoudenmire, SciPost Physics Codebases 4 (2022).