# Sliced Basis Density Matrix Renormalization Group for Electronic Structure

## TL;DR

This paper presents a hybrid DMRG method combining grid and Gaussian basis sets for efficient electronic structure calculations of chain-like molecules, achieving near-linear scaling for large systems.

## Contribution

The paper introduces a novel hybrid approach to DMRG that combines grid and Gaussian bases, enabling scalable calculations for long chain molecules.

## Key findings

- Linear scaling of computational time with chain length
- Near-exact results for large hydrogen chains within the basis
- Effective handling of long-range Coulomb interactions

## Abstract

We introduce a hybrid approach to applying the density matrix renormalization group (DMRG) to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set along the remaining two directions. This approach is especially useful for chain-like molecules, where the grid is used in the long direction, and we demonstrate the approach with results for hydrogen chains. The computational time for this system scales approximately linearly with the length of the chain, as we demonstrate with minimal basis set calculations with up to 1000 atoms, which are near-exact within the basis. The linear scaling comes from the combination of localization of the basis and a compression method with controlled accuracy for the long-ranged Coulomb terms in the Hamiltonian.