An efficient relativistic density-matrix renormalization group implementation in a matrix-product formulation

TL;DR

This paper introduces an efficient relativistic DMRG implementation using matrix-product states, enabling accurate calculations of relativistic effects and properties in complex quantum systems.

Contribution

It develops a novel relativistic DMRG method based on matrix-product formalism, integrating scalar-relativistic effects and spin-orbit coupling into wave function optimization.

Findings

Successfully applied to a dysprosium complex, demonstrating accurate ground-state magnetization.

Calculated current density and magnetic properties in a relativistic framework.

Enhanced the capabilities of existing non-relativistic DMRG implementations.

Abstract

We present an implementation of the relativistic quantum-chemical density matrix renormalization group (DMRG) approach based on a matrix-product formalism. Our approach allows us to optimize matrix product state (MPS) wave functions including a variational description of scalar-relativistic effects and spin-orbit coupling from which we can calculate, for example, first-order electric and magnetic properties in a relativistic framework. While complementing our pilot implementation (S. Knecht et al., J. Chem. Phys., 140, 041101 (2014)) this work exploits all features provided by its underlying non-relativistic DMRG implementation based on an matrix product state and operator formalism. We illustrate the capabilities of our relativistic DMRG approach by studying the ground-state magnetization as well as current density of a paramagnetic $f^9$ dysprosium complex as a function of the active orbital space employed in the MPS wave function optimization.