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. Our method shows reduced 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 $\ce{H10}$-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 wavefunction methods such as Coupled Clusters (CC) or Density Matrix Renormalization Group (DMRG), while offering significantly improved scaling.

Figures (4)

• Figure 1: Imaginary-time propagation procedure for the extended-basis AFQMC method.
• Figure 2: (a) Convergence of the AFQMC simulation energy of the $\ce{H10}$-chain using the standard AFQMC method (red) and our method (blue). The HF ground-state energy is shown as a black dotted line. The FCI benchmark is shown as a black line with the shaded area representing the range of chemical accuracy ($\pm 1.6~mE_h$). A close-up of the FCI benchmark is shown in (b), with the averages of both methods.
• Figure 3: Comparison of GPU performance of propagation time (left) and estimator time (right) between our method (blue) and the standard method found in ipie (red) for different lengths of the hydrogen chain.
• Figure 4: Average value of the correlation energy of benzene calculated using our extended method with different time steps $\Delta \tau$. The error bars indicate the standard deviation, and the linear regression fit is shown as a red dotted line. The extrapolated value for $\Delta \tau=0$ is $-861(1) mE_h$.