Numerical validation of an ultracold Hubbard quantum simulator

Abstract

We apply the formally exact Diagrammatic Monte Carlo (DiagMC) method to probe the unprecedentedly low-temperature regime recently achieved in an ultracold-atom quantum simulation of the 2D Hubbard model [Xu et al., Nature 642, 909 (2025)]. Computing the experimentally measured observables directly in the thermodynamic limit with a priori control of systematic errors, we find striking agreement with the experimental data across all accessible temperatures -- including the lowest, where existing numerical benchmarks show significant deviations. This validates the quantum simulator's control over systematic errors in this challenging regime and delivers unbiased benchmarks for future method development. Our results demonstrate that classical algorithms remain competitive with state-of-the-art analogue quantum simulators, and emphasise the importance of controlled numerical methods for continuing the development of these experiments.

Figures (4)

• Figure 1: Nearest neighbour spin-spin correlations at $U/t = 8$ and temperatures $T/t=0.1$ and $T/t=0.25$ computed with DiagMC, compared with the experiment of Ref.Xu2025, determinantal quantum Monte Carlo (DQMC), and constrained-path auxiliary field quantum Monte Carlo (CP-AFQMC).
• Figure 2: Next-nearest-neighbour diagonal spin correlations correlations at $U/t = 8$ and temperatures $T/t=0.1$ and $T/t=0.25$ computed with DiagMC, compared with the experiment of Ref.Xu2025, determinantal quantum Monte Carlo (DQMC), and constrained-path auxiliary field quantum Monte Carlo (CP-AFQMC).
• Figure 3: (a) Double occupancy $n_d$ against density $n$ at $U/t=8$ computed by DiagMC and compared with CP-AFQMC data of Ref.Xu2025. For densities $n \geq 0.85$, CP-AFQMC could not be directly applied due to poor convergence, and instead a linear interpolation is performed between $n=0.85$ and half-filling Xu2025, shown as the dashed lines. (b) Temperature dependence of the next-nearest-neighbour spin-spin correlator at doping $\delta = 0.100(14)$ computed by DiagMC and compared with the experimental value at temperature $T/t\lesssim 0.1$ (horizontal band). The apparent slight decrease in $C_S(r)$ with cooling at the lowest temperatures is due to a small increase in the doping. However, the doping of all three points remains within the errorbar of the experimental doping $\delta = 0.100(14)$ to which we are comparing.
• Figure 4: Temperature dependence of spin correlations $C_S(\mathbf{q})$ in momentum space at the $\mathbf{q}=(\pi,\pi)$ point and $\mathbf{q}=(Q,\pi)$, with $Q\approx 2.79$ nearby the predicted spin-stripe wavevector $Q_S$ (see main text).