Abstract
Quantum embedding methods have become a powerful tool to overcome deficiencies of traditional quantum modelling in materials science. However, while these are systematically improvable in principle, in practice it is rarely possible to achieve rigorous convergence and often necessary to employ empirical parameters. Here, we formulate a quantum embedding theory, building on the methods of density-matrix embedding theory combined with local correlation approaches from quantum chemistry, to ensure the ability to systematically converge properties of real materials with accurate correlated wave~function methods, controlled by a single, rapidly convergent parameter. By expanding supercell size, basis set, and the resolution of the fluctuation space of an embedded fragment, we show that the systematic improvability of the approach yields accurate structural and electronic properties of realistic solids without empirical parameters, even across changes in geometry. Results are presented in insulating, semi-metallic, and more strongly correlated regimes, finding state of the art agreement to experimental data.
Highlights
Computational materials research suffers from a lack of systematic improvability
The quantum embedding of this work combines the strengths from these different perspectives and can be and systematically improved to exactness within the desired quantum-chemical method without requiring an expansion of the fragment space. This builds on the density-matrix embedding theory (DMET), which defines a bath space from the Schmidt decomposition of a meanfield wave function [17,23,37], and augments this bath space with additional states inspired by the pair natural orbital (PNO) approach of local quantum-chemistry methods [16,38,39]
Since the bath is noninteracting in dynamical mean-field theory (DMFT), this expansion does not converge the correlated physics of the fragment, and is — opposed to the approach proposed here—not a route to systematic improvability
Summary
Computational materials research suffers from a lack of systematic improvability. This feature is important to validate and trust each individual prediction with internal checks, without relying on a faithful comparison to experiment which may have other sources of error. The quantum embedding of this work combines the strengths from these different perspectives and can be and systematically improved to exactness within the desired quantum-chemical method without requiring an expansion of the fragment space This builds on the density-matrix embedding theory (DMET), which defines a bath space from the Schmidt decomposition of a meanfield wave function [17,23,37], and augments this (interacting) bath space with additional states inspired by the pair natural orbital (PNO) approach of local quantum-chemistry methods [16,38,39]. This judiciously chosen bath expansion opens up a new single simulation parameter by which results can be systematically improved and avoids the alternative approach to converge the important long-range physics in the embedding via an expansion of the fragment size. We show convergence of properties across a diverse range of electronic characters, demonstrating the advantages of systematic improvability for quantitative accuracy and highlighting qualitative changes to traditional DFT results
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