Ab-initio Approaches to Correlated Materials

Markus Aichhorn

Oleg V. Prezhdo

Zhi‐Hao Cui, Huanchen Zhai, Xing Zhang +1 more

The quantitative description of correlated electron materials remains a modern computational challenge. We demonstrate a numerical strategy to simulate correlated materials at the fully ab initio level beyond the solution of effective low-energy models and apply it to gain a detailed microscopic understanding across a family of cuprate superconducting materials in their parent undoped states. We uncover microscopic trends in the electron correlations and reveal the link between the material composition and magnetic energy scales through a many-body picture of excitation processes involving the buffer layers. Our work illustrates a path toward a quantitative and reliable understanding of more complex states of correlated materials at the ab initio many-body level.

Sergey Yu. Savrasov

Antonios M. Alvertis, Abid Khan, Norm M. Tubman

The accurate first-principles description of strongly correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that maintain the essential physics of strongly correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here, we demonstrate that using quantum algorithms to obtain the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate ${\mathrm{Ca}}_{2}{\mathrm{Cu}\mathrm{O}}_{3}$, the excitonic ground state of monolayer ${\mathrm{W}\mathrm{Te}}_{2}$, and the charge-ordered state of correlated metal ${\mathrm{Sr}\mathrm{VO}}_{3}$. Numerical simulations using a classical tensor network implementation of variational quantum eigensolvers allow us to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address. Through these methods we demonstrate the potential of classical preoptimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.

A. Toschi, G. Rohringer, A. A. Katanin +1 more

Abstract We propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb interaction. It includes the so‐called GW and dynamical mean field theory and important non‐local correlations beyond, with a computational effort estimated to be still manageable.