Intrinsic dimension of path integrals: data mining quantum criticality and emergent simplicity

Understand

Quantum many-body systems are characterized by patterns of correlations that define highly-non trivial manifolds when interpreted as data structures.

• Physical properties of phases and phase transitions are typically retrieved via simple correlation functions, that are related to observable response functions.
• Recent experiments have demonstrated capabilities to fully characterize quantum many-body systems via wave-function snapshots, opening new possibilities to analyze quantum phenomena.
• Here, we introduce a method to data mine the correlation structure of quantum partition functions via their path integral (or equivalently, stochastic series expansion) manifold.