From Random Slater Determinants to the Ground State

We introduce a new algorithm for obtaining the ground state of quantum many-body systems by systematically trimming unimportant basis states from a dynamically expanded space. The method, termed Trimmed Configuration Interaction (TrimCI), operates within the space of Slater determinants and alternates between two key stages: expansion and trimming. Starting from an initial core of randomly generated determinants, rather than a Hartree-Fock reference, the algorithm expands the space by incorporating all determinants connected to the core through the Hamiltonian matrix. Trimming procedures are then applied to remove unimportant determinants according to their contributions to the approximate ground state within the subspace. These expansion-trimming cycles are iterated until convergence. Benchmarks on challenging molecular systems demonstrate that TrimCI outperforms state-of-the-art selected configuration-interaction methods by several orders of magnitude in efficiency, for example, achieving the same accuracy on systems with 73 spatial orbitals and 114 electrons using 10^4 times fewer determinants. For the two-dimensional Hubbard model at half-filling, TrimCI attains ground-state energies within 1% of numerically exact AFQMC results for lattices up to 8×8, yielding an explicitly compact wavefunction (fewer than 10^9 determinants) that enables direct and rapid evaluation of physical observables.