A Scalable Configuration-Interaction Impurity Solver via Active Learning

Abstract

Finite-Hamiltonian impurity solvers provide direct real-frequency spectra and a natural route to enlarged impurity Hamiltonians, but their applicability is limited by the rapid Hilbert-space growth with the number of bath or other added one-particle orbitals. We introduce an active-learning extension of adaptive-truncation configuration interaction (AL-ATCI) that identifies the determinant manifold relevant to the correlated state. The approximation is systematically controlled by the query size N_query, which also provides an internal convergence parameter when no external benchmark is available. Over the benchmark range studied here, the computational cost grows only weakly with bath size, because enlarging the bath mainly expands the combinatorial determinant space rather than the physically relevant manifold. In dynamical mean-field-theory benchmarks for the one-dimensional Hubbard model, AL-ATCI reproduces exact-diagonalization accuracy and extends cellular calculations to clusters as large as N_c = 10. For a three-orbital rotationally invariant Sr2RuO4 impurity problem, we demonstrate systematic convergence of dynamical quantities and a highly compressed configuration space as N_b is increased from 9 to 18. These results substantially alleviate the bath-discretization bottleneck of exact-diagonalization- and configuration-interaction-based impurity solvers and make large-bath and enlarged-orbital calculations more practical.