Pseudogap in a Fermi-Hubbard quantum simulator

Understanding doped Mott insulators is a fundamental goal in condensed matter physics, relevant to cuprate superconductors and other quantum materials^1-3. The Hubbard model minimally describes such systems and has explicated some of their complex behaviour^4,5. However, many open questions remain concerning the anomalous metallic states that emerge at low temperatures and intermediate doping and which, in cuprates, give rise to high-temperature superconductivity on cooling^2,6,7. Here we observe a crossover between a normal metal and a pseudogapped metal in the Hubbard model using thermodynamic and spectroscopic measurements in a cold-atom quantum simulator, leveraging a recent several-fold reduction in achievable temperatures⁸. On cooling, the compressibility develops a maximum at intermediate doping, signalling an inflection point in the equation of state. We track this maximum versus interaction strength, revealing a line of thermodynamic anomalies in the phase diagram separating an underdoped from an overdoped metal at large interactions. Lattice modulation spectra in the underdoped regime show a loss of low-energy response, especially pronounced in the antinodal regions of the Brillouin zone, indicating a pseudogap. We use this signal to construct a pseudogap phase diagram versus interactions and doping. Our results experimentally establish and characterize the pseudogap metal in the Hubbard model, and suggest connections to charge order that can be studied in future work. Furthermore, this work demonstrates the utility of quantum simulation in addressing frontier problems in correlated electron physics.