Observation of emergent scaling of spin-charge correlations at the onset of the pseudogap

In strongly correlated materials, interacting electrons are entangled and form collective quantum states, resulting in rich low-temperature phase diagrams. Notable examples include cuprate superconductors, in which superconductivity emerges at low doping out of an unusual “pseudogap” metallic state above the critical temperature. The Fermi-Hubbard model, describing a wide range of phenomena associated with strong electron correlations, still offers major computational challenges despite its simple formulation. In this context, ultracold atoms quantum simulators have provided invaluable insights into the microscopic nature of correlated quantum states. Here, we use a quantum gas microscope Fermi-Hubbard simulator to explore a wide range of dopings and temperatures in a regime where a pseudogap is known to develop. By measuring multi-point correlation functions up to fifth order, we uncover a novel universal scaling behaviour in magnetic and higher-order spin-charge correlations characterised by a doping-dependent temperature scale. Accurate comparisons with determinant Quantum Monte Carlo and Minimally Entangled Typical Thermal States simulations confirm that this temperature scale is comparable to the pseudogap temperature T*. Our quantitative findings reveal a novel qualitative behaviour of magnetic properties and spin-charge correlations in an emergent pseudogap and pave the way towards the exploration of charge pairing and collective phenomena expected at lower temperatures.

💡 Research Summary

In this work the authors employ a quantum‑gas‑microscope platform to realize a two‑dimensional Fermi‑Hubbard model with tunable doping and temperature, and they investigate the emergence of the pseudogap regime through high‑order spin‑charge correlation functions. A spin‑balanced gas of ^6Li atoms is loaded into a square optical lattice (t/h≈300 Hz, U/t≈6.5) and a digital micromirror device creates a homogeneous central region of 145 sites surrounded by a low‑density reservoir. By varying the hold time in the lattice they control the temperature in the range T/t≈0.2–1, while the doping δ is tuned from –30 % to +30 % by adjusting the global chemical potential. Over 36 000 site‑resolved snapshots are recorded, each providing spin‑ and charge‑resolved occupation on every lattice site.

The authors first establish a thermometry protocol based on the nearest‑neighbour spin correlator C_ss^(2)(|d|=1). By fitting this observable to determinant Quantum Monte Carlo (dQMC) data they assign a temperature to each experimental dataset. The temperature extraction is cross‑checked with Minimally Entangled Typical Thermal States (METTS) simulations, showing excellent agreement.

Spin correlations are then analysed via the equal‑time spin structure factor S(q), whose peak at the antiferromagnetic wave vector q_AF=(π,π) is denoted S_AFM. Remarkably, S_AFM collapses onto a universal exponential form when plotted as a function of the ratio Θ(δ)/T:

 S_AFM(δ,T) ≈ exp