For decades, physicists have been trying to understand what happens when a material that should conduct electricity instead behaves like an insulator—and what changes when electrons are gradually added. Now, a new experiment using ultracold atoms has captured a key transformation predicted in the Hubbard model: the emergence of a pseudogapped metal, a strange state that conducts electricity but loses electronic states near the energy where conduction is most easily expected.
The result addresses one of the most persistent puzzles in condensed-matter physics. In ordinary metals, electrons occupy a broad range of available energy states, allowing them to move freely through a crystal. In a Mott insulator, however, strong repulsion between electrons blocks that motion even when conventional band theory predicts metallic behaviour. Adding carriers, a process known as doping, can eventually produce a metal and, in some real materials such as cuprate superconductors, superconductivity at remarkably high temperatures.
The simplest theoretical framework for this problem is the Hubbard model. It describes particles hopping between sites of a lattice while paying an energetic penalty whenever two particles occupy the same site. The competition between kinetic motion and on-site repulsion can generate insulating, metallic and potentially superconducting phases. Despite its apparent simplicity, the model is notoriously difficult to solve in the regime where interactions are strong and the system is only partially filled, precisely the conditions associated with the unusual metallic states of cuprates.
In the new study, researchers created a highly controlled version of the Hubbard model using a quantum simulator based on ultracold atoms. The atoms were arranged in an artificial lattice that mimics the crystal structure experienced by electrons in a solid. By tuning the interaction strength, density and temperature, the team could explore regions of the phase diagram that are difficult to access in conventional materials, where disorder, chemical complexity and competing effects can obscure the underlying physics.
The experiment benefited from a substantial reduction in achievable temperatures, allowing the atoms to enter a regime where subtle thermodynamic signatures become visible. One of the central measurements was the compressibility, which describes how strongly the density of a system changes when its chemical potential is varied. In practical terms, it reveals how easily particles can be added. The researchers found that, upon cooling, the compressibility develops a maximum at intermediate doping.
That maximum is more than a feature in a graph. It marks an inflection point in the equation of state, meaning that the relationship between particle density and chemical potential changes its curvature. By following the position of this maximum as the interaction strength was varied, the researchers identified a continuous line of thermodynamic anomalies. At strong interactions, this line separates two qualitatively different metallic regimes: an underdoped metal on one side and an overdoped metal on the other.
The team then used lattice modulation spectroscopy to investigate the system’s electronic response at different momenta. In this technique, the artificial lattice is periodically shaken, and the atoms’ response reveals how readily the system can absorb energy. The measurements showed a suppression of low-energy response in the underdoped regime. This loss was particularly pronounced near the antinodal regions of the Brillouin zone, the momentum-space areas associated with directions where the pseudogap is expected to be strongest.
A pseudogap is not a full insulating gap. Instead, it is a partial depletion of available low-energy electronic states. The distinction is crucial: a pseudogapped system may remain metallic, yet its charge carriers do not behave as they would in a conventional metal. The momentum-selective nature of the observed suppression provides an important clue that the phenomenon is linked to strong correlations and collective organization rather than simply to a uniform loss of particles or increased disorder.
By combining thermodynamic measurements with spectroscopic probes, the researchers constructed a pseudogap phase diagram for the Hubbard model as a function of interaction strength and doping. This gives experimental substance to a region of the theoretical phase diagram that has been discussed for decades but has been challenging to isolate in real materials. The observations suggest that the boundary between underdoped and overdoped behaviour is not merely a change in transport properties, but is connected to measurable changes in the system’s thermodynamics and excitation spectrum.
The findings do not yet identify the ultimate microscopic origin of the pseudogap, nor do they demonstrate high-temperature superconductivity in the simulated system. They do, however, establish a powerful platform for testing competing explanations, including possible connections between the pseudogap and charge order. Future experiments may examine whether density patterns, pairing correlations or other forms of hidden organization emerge in the same region. For now, the work shows that cold-atom quantum simulators can reproduce and dissect one of the most enigmatic states in correlated-electron physics, bringing researchers closer to understanding why doped Mott insulators can become both anomalous metals and, in related materials, superconductors.
Subject of Research: Doped Mott insulators, the Hubbard model and the pseudogap metal in strongly correlated quantum systems
Article Title: Pseudogap in a Fermi–Hubbard quantum simulator
Article References: Kendrick, L.H., Kale, A., Gang, Y. et al. “Pseudogap in a Fermi–Hubbard quantum simulator.” Nature (2026). https://doi.org/10.1038/s41586-026-10875-z
Image Credits: AI Generated
DOI: https://doi.org/10.1038/s41586-026-10875-z
Keywords: Fermi–Hubbard model, Mott insulator, pseudogap, quantum simulation, ultracold atoms, strongly correlated matter, anomalous metal, cuprate superconductors, compressibility, lattice modulation spectroscopy
