Dealing with the exponential wall in electronic structure calculations

Abstract

An alternative to Density Functional Theory are wavefunction based electronic structure calculations for solids. In order to perform them the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an {\it impurity} or {\it fragment} embedded in a {\it bath} which is treated at a much lower level than the former. This is the case in Density Matrix Embedding Theory (DMET) or Density Embedding Theory (DET). The latter are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a $H_{10}$ ring these differences are analyzed with the help of the method of increments.

19 pages, 5 figures

References in corpus (3)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• A practical guide to density matrix embedding theory in quantum chemistry
• Assessment of Multireference Approaches to Explicitly Correlated Full Configuration Interaction Quantum Monte Carlo

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• The Shape of Full Configuration Interaction to Come
• Bypassing the computational bottleneck of quantum-embedding theories for strong electron correlations with machine learning
• Comparative study of the density matrix embedding theory for the Hubbard models
• Ground state of many-electron systems based on the action function
• Ground-state wavefunction of macroscopic electron systems
• Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification
• Local Potential Functional Embedding Theory of Molecular Systems: Localized Orbital-Based Embedding from an Exact Density-Functional Perspective
• Ensemble density functional theory of excited states: Exact N-centered formalism and practical opportunities