Transfer learning of many-body electronic correlation entropy from local measurements

Characterizing quantum correlations in many-body systems is essential for understanding emergent phenomena in quantum materials. The correlation entropy serves as a key metric for assessing the complexity of a quantum many-body state in interacting electronic systems. However, its determination requires the measurement of all single-particle correlators across a macroscopic sample, which can be impractical. Machine learning methods have been shown to enable the correlation entropy to be learned from a reduced set of measurements, yet these methods assume that the targeted system is contained in the set of training Hamiltonians. Here we show that a transfer learning strategy enables correlation entropy learning from a reduced set of measurements in variants of Hamiltonians never considered in the training set. We demonstrate this transfer learning methodology in a wide variety of interacting models, including local and nonlocal attractive and repulsive many-body interactions, long-range hopping, doping, magnetic field, and spin-orbit coupling. Furthermore, we show that this transfer learning methodology enables the detection of phases in quantum many-body systems beyond those present in the training set. Our results demonstrate that correlation entropy learning can be performed experimentally without requiring training in the experimentally realized Hamiltonian.