The accurate simulation of strongly correlated electronic systems is crucial for describing a variety of important chemical phenomenon such as bond breaking and electronic transitions. Although many methods have been proposed to circumvent the exponential complexity of the full configuration interaction solution, there is presently no general, accurate, and computationally affordable approach for describing strongly correlated systems. In order to direct the development of future approaches, we present a study of the compressibility of the full configuration interaction wave function for models of strongly correlated electrons. Five compression schemes are explored: (I) singular value decomposition-based rank reduction of the FCI tensor, (II) removal of determinants that contain at least one unimportant alpha or beta string, (III) a direct elimination of determinants based on cumulative thresholding, (IV) the adaptive configuration interaction, and (V) matrix product states obtained from the density matrix renormalization group. We analyze the effects of orbital localization, dimensionality, and degree of correlation on the properties of these compressed wave functions by studying three H10 systems: a linear chain, a ring, and a pyramidal lattice. Results for the energy error are reported as a function of the number of variational parameters. Orbital localization was found to be beneficial only for one-dimensional systems, with improvements in efficiency equally advantageous for selected configuration interaction methods and the density matrix renormalization group. We found that singular value decomposition-based rank reduction of the FCI tensor and removal of determinants that contain at least one unimportant alpha or beta string are far less efficient at compressing the wave function than selected determinat type approaches or matrix product states. We also found that matrix product states give the most efficient compression for the chain system, and that there is no significant difference between selected determinant approaches and matrix product states for the ring and pyramidal lattice systems.

How compressible are full configuration interaction wave functions for strongly correlated hydrogen systems?

2019 Spring National Meeting

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