2025-07-24 –, Main Room 6
We present a demonstration of applying tensor network methods with gausslets as a basis set. The locality of gausslets promotes sparsity in the molecular Hamiltonian, which is important for numerical scaling. We first use Quiqbox.jl to discretize molecular Hamiltonians with gausslets, then use iTensor.jl to approximate the ground-state energies. This pipeline demonstrates the potential of studying the application of novel basis sets for tensor network methods in electronic structure problems.
Discretization of molecular Hamiltonians using a basis set is an important first step for numerically solving electronic structure problems in quantum chemistry. First proposed by Steven White, gausslets are constructed from wavelet transformations on gaussian functions. Compared to atomic basis sets, gausslets are highly localized. Due to their locality, they increase the sparsity of molecular Hamiltonians, which improves the computational scalability of tensor network methods in quantum chemistry. Specifically, they diagonalize the two-body interactions in the Hamiltonian, reducing the number of non-zero terms from O(N^4) to O(N^2). However, many more basis functions may be required to reach an accuracy comparable to atomic basis sets.
We will show how Quiqbox.jl can both construct gausslets and augment them with atomic basis sets to reduce the overall basis set size while maintaining accuracy and two-body diagonalization. Since gausslets are constructed from gaussian functions, the analytical integral engine in Quiqbox.jl can still be utilized. By using Quiqbox.jl and iTensor.jl, we hope to demonstrate a pathway to exploring novel molecular Hamiltonian discretization methods in conjunction with tensor network methods for electronic structure problems.
I am a PhD mathematics student at Dartmouth college interested in mathematical physics, machine learning, and numerical methods in many-body quantum mechanics.