Quantum matter is weakly entangled at low energies

Samuel Garratt presents rigorous upper limits on entanglement entropy for locally interacting quantum many-body states at fixed energy. Ground states usually exhibit an area law, unlike generic states whose entanglement scales with volume, and gapless systems can introduce corrections. The framework constrains ground-state entanglement for gapped and gapless systems in arbitrary spatial dimension, follows the transition toward volume-law behavior as energy increases, and bounds the computational resources needed to calculate response functions at zero temperature. These results connect spectral information with the cost of tensor-network calculations.