Efficient Auxiliary-Field Quantum Monte Carlo Using Isometric Tensor Hypercontraction

Abstract

Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel AFQMC method that uses the isometric tensor hypercontraction (ITHC) technique to diagonalize the two-body Coulomb interaction of molecular electronic Hamiltonians by introducing additional fictitious Fermionic modes. While traditional low-rank approximations such as the Tensor Hypercontraction (THC) decomposition have been used in AFQMC in the past, their conventional role has been to provide compact representation of the two-electron interaction, thereby reducing the memory footprint. In comparison, our method not only reduces memory usage but also exhibits lower theoretical complexity and better practical performance for both propagation and local energy evaluation compared to the standard AFQMC method. We demonstrate the efficacy of this approach by computing the ground-state energies of a linear H10-chain and the benzene molecule. Our results show that the extended-basis AFQMC recovers many-body correlations with a precision comparable to that of high-level wave function methods such as Coupled Clusters (CC) or Density Matrix Renormalization Group (DMRG), while offering significantly improved scaling.