Jastrow and backflow terms to describe correlated electrons on the lattice

I give a review of recent developments on the possibility to describe strongly-interacting systems by variational wave functions obtained by inserting electron-electron correlation on top of Slater determinants. In this regard, both Jastrow and backflow terms are considered [1,2]. The former one is the generalization of the Gutzwiller (soft) projection to include long-range density-density correlations and is nowadays widely used; instead, backflow terms have been defined and introduced only quite recently in strongly-interacting lattice models and make it possible to include electron-electron correlation in the Slater determinant [3]. Remarkably, Jastrow-Slater states may show signatures of long-range order, when all symmetries are preserved in the wave function, thus allowing to describe spontaneous symmetry breaking phenomena [4].

I discuss the accuracy of this approach for both weak and strong couplings and how it is possible to describe the metal-insulator transition, as well as the Mott insulator. Various applications for the single-band Hubbard model on the square and triangular lattices are presented [2,5,6].

Finally, generalizations to multi-band models are straightforward and represent our on-going line of research: the case of the orbital-selective Mott transition in a two-band Hubbard model is discussed [7].

[1] M. Capello, F. Becca, M. Fabrizio, S. Sorella, and E. Tosatti, Phys. Rev. Lett. 94, 026406 (2005).
[2] L.F. Tocchio, F. Becca, A. Parola, and S. Sorella, Phys. Rev. B 78, 041101 (2008).
[3] L.F. Tocchio, F. Becca, and C. Gros, Phys. Rev. B 83, 195138 (2011).
[4] R. Kaneko, L.F. Tocchio, R. Valenti, F. Becca, and C. Gros, arXiv:1510.08653.
[5] L.F. Tocchio, H. Feldner, F. Becca, R. Valenti, and C. Gros, Phys. Rev. B 87, 035143 (2013).
[6] L.F. Tocchio, C. Gros, R. Valenti, and F. Becca, Phys. Rev. B 89, 235107 (2014).
[7] L.F. Tocchio, F. Arrigoni, S. Sorella, and F. Becca, arXiv:1505.07006.