Non-unitary similarity transformation of the electronic Schrödinger equation via Gutzwiller and Jastrow factorization

Werner DOBRAUTZ
Max Planck Institute for Solid State Research, Stuttgart, Germany
Vendredi 15 Novembre 2019, 11h00
bibliothèque LCT, tour 12 - 13, 4^ème étage

We investigate the utility of non-unitary similarity transformations, based on a Gutzwiller and Jastrow factorization of the electronic wavefunction. Such factorizations generally lead to non-Hermitian effective Hamiltonians which contain three-body interactions. Such Hamiltonians are treatable via the projective FCIQMC [1] technique, which does not suffer from the non-Hermitian characteristic of the Hamiltonian, nor do the 3-body terms present an insuperable obstacle.
In the case of Gutzwiller factorization, we apply this method to the 2D Hubbard model in the strong correlation off-half-filling regime, which is an extremely challenging problem. We show that the similarity transformation results in compact right eigenvectors [2], which can be sampled accurately by the projective FCIQMC method. New benchmark results are provided in the off-half-filling regime, with no severe sign-problem being encountered. In addition, we show that methodology can be used to calculate excited states of the Hubbard model and lay the groundwork for the calculation of observables other than the energy.
For ab-initio systems our approach permits the use of highly flexible Jastrow functions, which we show to be effective in achieving extremely high accuracy, even with small basis sets [3]. Results are presented for the total energies and ionisation potentials of the first-row atoms, achieving accuracy within a mH of the basis-set limit, using modest basis sets and computational effort.
The methodology opens up the prospect to study strongly correlated molecular systems, where much of the dynamical correlation can be captured by the correlation factor, and the strong correlation aspects via the multi-configurational reference function. _________________________________

References :
[1] G. H. Booth, A. J. W. Thom and A. Alavi, J. Chem. Phys. 131 (2009) 054106.
[2] W. Dobrautz, H. Luo, and A. Alavi, Phys. Rev. B 99 (2019) 075119.
[3] A. J. Cohen, H. Luo, K. Guther, W. Dobrautz, David P. Tew, Ali Alavi, J. Chem. Phys. 151 (2019) 061101.