Abstract
A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we design a computational framework combining quantum-embedding (QE) methods with machine learning. This allows us to bypass altogether the most computationally-expensive components of QE algorithms, making their overall cost comparable to bare Density Functional Theory (DFT). We perform benchmark calculations of a series of actinide systems, where our method describes accurately the correlation effects, reducing by orders of magnitude the computational cost. We argue that, by producing a larger-scale set of training data, it will be possible to apply our method to systems with arbitrary stoichiometries and crystal structures, paving the way to virtually infinite applications in condensed matter physics, chemistry and materials science.
Highlights
The atomic energy scales emerging in “strongly correlated” systems [1,2,3] can induce a broad spectrum of spectacular effects, ranging from arresting the electronic motion [1] to causing high-temperature superconductivity [4], unlocking access to new topological phases and dramatically influencing the potential-energy surfaces (PES) of molecules and solids [5,6,7,8,9,10]
The substantial progress achieved in the past decade in calculating the electronic structure of strongly correlated materials is largely owed to the idea of combining mean-field (MF) theories, such as approximations to density functional theory (DFT) [11,12,13,14,15,16,17] with quantum-embedding (QE) [2,18,19] theoretical frameworks
In this work we proposed a computational framework for simulating strongly correlated electron systems, which offers the possibility of substantially stepping up the accuracy with respect to mean-field theories, at a comparable computational cost
Summary
The atomic energy scales emerging in “strongly correlated” systems [1,2,3] can induce a broad spectrum of spectacular effects, ranging from arresting the electronic motion [1] to causing high-temperature superconductivity [4], unlocking access to new topological phases and dramatically influencing the potential-energy surfaces (PES) of molecules and solids [5,6,7,8,9,10]. Fact that the form of the EH is universal (i.e., it does not depend on the specific stoichiometry and crystal structure of the material considered), we bypass altogether the computationally expensive recursive solution of the EH by “training a machine” to solve this problem once and for all To accomplish this goal, we develop a computational framework combining machine-learning (ML) techniques, such as ‘kernel ridge regression” (KRR), with a mathematical method named “n-mode representation” [46,47]—previously used for effectively reducing the dimensionality of large-scale regression problems (e.g., for reducing the number of points required for constructing high-dimensional PESs in quantum chemistry [48,49]). Utilizing our method, we were able to calculate—at a computational cost comparable to bare DFT—the discontinuous behavior of the equilibrium volumes of the actindes as a function of their atomic number Z (actinide transition) [51], which is a phenomenon originated by a complex interplay between structural degrees of freedom, relativistic effects, atom- and orbital-selective electron correlations [30,52,53,54,55]
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