Tensor decomposition method for strongly correlated few-body systems

Antisymmetrized geminal power (AGP) theory [1], closely related to BCS theory of superconductors, is a mean-field theory of electron pairs (geminals) and provides a basis for a wave function theory. When a many-body wave function is expanded by AGP, resulting AGP-CI series converges much faster than the configuration interaction (CI) series of Slater determinants, thereby enabling a compact representation of correlated wave functions [2,3]. This AGP-CI theory is extended here for further compact representation of the wave function by removing the orthogonality constraint on geminals. When removing the orthogonality constraint, known formula cannot be used to obtain the Hamiltonian matrix elements making the theory numerically intractable. We overcome this problem by using a mathematical theory of tensor decomposition. In this talk, we present the methodology and discuss application to Hubbard models.

[1] A. J. Coleman, J. Math. Phys. 6, 1425 (1965).
[2] W. Uemura, S. Kasamatsu, and O. Sugino, Phys. Rev. A 91, 062504 (2015).
[3] A. Kawasaki and O. Sugino, J. Chem. Phys. 145, 244110 (2016).