Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach

TL;DR

This paper introduces a novel protocol called Dynamical Block State Selection (DBSS) for the $k$-DMRG method, enabling pre-determination of desired accuracy by dynamically controlling truncation error and block states in quantum chemistry calculations.

Contribution

The paper presents the DBSS protocol that adaptively controls the number of block states and truncation error in $k$-DMRG, improving accuracy management in quantum chemistry applications.

Findings

DBSS effectively controls truncation error and block states.

Successful calculations on molecules with up to 57 orbitals.

Achieved large Hilbert space dimensions with controlled accuracy.

Abstract

We have applied the momentum space version of the Density Matrix Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol which we dubbed Dynamical Block State Selection (DBSS). The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500--2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800.000--1.200.000.