Accelerated quantum Monte Carlo simulations of the attractive Hubbard model on the kagome lattice

Abstract

The recent discovery of several families of kagome materials and experimental realization of optical kagome lattices have stimulated growing numerical studies of interaction-driven correlated states on the kagome lattice. Among the available numerical approaches, determinant quantum Monte Carlo (DQMC) is a powerful method for investigating such strongly correlated states. However, the accessible system sizes of existing DQMC simulations remain limited, preventing reliable finite-size scaling analyses. Here we develop a general acceleration scheme based on fast Fourier transform (FFT) for propagator multiplications on composite lattices and combine it with the delay-update algorithm, enabling simulations on system sizes twice as large as those of previous DQMC studies, allowing reliable finite-size scaling analyses of the attractive kagome-lattice Hubbard model. Our large-scale simulations reveal the interaction-driven zero-temperature superfluid quantum criticality at the Dirac filling and provide reliable estimates of the associated critical exponents. Besides, we find no evidence that the previously proposed triangle-rule charge-density-wave order survives in the thermodynamic limit, suggesting that it is likely a finite-size effect. Moreover, for system sizes accessible in current two-dimensional optical lattice experiments, the combined FFT and delay-update scheme exhibits an effective computational cost scaling as $N^{2.49}$, substantially below the $\mathcal{O}(N^3)$ computational cost of conventional DQMC simulations.