Hamiltonian learning in quantum field theories

Quantum field theories (QFTs) as relevant for condensed-matter or high-energy physics are formulated in continuous space and time, and typically emerge as effective low-energy descriptions. In atomic physics, an example is given by tunnel-coupled superfluids, which realize the paradigmatic sine-Gordon model, and can act as quantum simulators of continuous QFTs. To quantitatively characterize QFT simulators, or to discover the Hamiltonian governing the dynamics of a continuous many-body quantum system, we discuss Hamiltonian learning as a method to systematically extract the operator content and the coupling constants of Hamiltonians from experimental data. In contrast to Hamiltonian learning for lattice models with a given lattice scale, we learn QFT Hamiltonians on a resolution scale set by the experiment. Varying the resolution scale gives access to QFTs at different energy scales, and allows to learn a flow of Hamiltonians reminiscent of the renormalization group. Applying these techniques to available experimental data from a tunnel-coupled quantum gas experiment allows a definite distinction between a free quadratic theory from an interacting sine-Gordon model, as the underlying QFT description of the system. Published by the American Physical Society 2024