On Structural and Computational Aspects of Gibbs States 

A central challenge in quantum physics is to understand the structural properties of many-body systems at thermal equilibrium. Directly reasoning about entanglement or clustering of correlations in thermal states is notoriously hard. In this talk, I will discuss the unreasonable effectiveness of the "algorithmic lens" for extracting sharp structural insights. First I will explain the surprising connection between "counting-to-sampling" reductions and the suddent death of entanglement in thermal states above a fixed constant temperature. Next, I will describe how to generalize these techniques to prove that entanglement in thermal states of one-dimensional Hamiltonians is strictly finite at all temperatures, even in the thermodynamic limit. Finally, I'll describe how rapid mixing of a natural Lindbladian dynamics can be used to prove the Global Markovianity conjecture (exponential decay of conditional mutual information) in high-temperature thermal states. Taken together, these results demonstrate that the algorithmic lens turns tractability into structure, leading to unexpected advances in our understanding of quantum and classical correlations in thermal states. I will conclude with some compelling open questions and future directions.