We study the phase diagram of the frustrated $t{-}t^prime$ Hubbard model on the square lattice by using a novel variational wave function. Taking the clue from the backflow correlations that have been introduced long-time ago by Feynman and Cohen and
have been used for describing various interacting systems on the continuum (like liquid $^3$He, the electron jellium, and metallic Hydrogen), we consider many-body correlations to construct a suitable approximation for the ground state of this correlated model on the lattice. In this way, a very accurate {it ansatz} can be achieved both at weak and strong coupling. We present the evidence that an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^prime/t$.
We study the role of electronic correlation in a disordered two-dimensional model by using a variational wave function that can interpolate between Anderson and Mott insulators. Within this approach, the Anderson-Mott transition can be described both
in the paramagnetic and in the magnetic sectors. In the latter case, we find evidence for the formation of local magnetic moments that order before the Mott transition. The charge gap opening in the Mott insulator is accompanied by the vanishing of the $lim_{qto 0} overline{< n_q>< n_{-q}>}$ (the bar denoting the impurity average), which is related to the compressibility fluctuations. The role of a frustrating (second-neighbor) hopping is also discussed, with a particular emphasis to the formation of metastable spin-glass states.
We introduce an efficient way to improve the accuracy of projected wave functions, widely used to study the two-dimensional Hubbard model. Taking the clue from the backflow contribution, whose relevance has been emphasized for various interacting sys
tems on the continuum, we consider many-body correlations to construct a suitable approximation for the ground state at intermediate and strong couplings. In particular, we study the phase diagram of the frustrated $t{-}t^prime$ Hubbard model on the square lattice and show that, thanks to backflow correlations, an insulating and non-magnetic phase can be stabilized at strong coupling and sufficiently large frustrating ratio $t^prime/t$.
We study the Mott transition occurring for bosonic Hubbard models in one, two, and three spatial dimensions, by means of a variational wave function benchmarked by Greens function Monte Carlo calculations. We show that a very accurate variational wav
e function, constructed by applying a long-range Jastrow factor to the non-interacting boson ground state, can describe the superfluid-insulator transition in any dimensionality. Moreover, by mapping the quantum averages over such a wave function into the the partition function of a classical model, important insights into the insulating phase are uncovered. Finally, the evidence in favor of anomalous scenarios for the Mott transition in two dimensions are reported whenever additional long-range repulsive interactions are added to the Hamiltonian.
We present a systematic study of the phase diagram of the $t{-}t^prime{-}J$ model by using the Greens function Monte Carlo (GFMC) technique, implemented within the fixed-node (FN) approximation and a wave function that contains both antiferromagnetic
and d-wave pairing. This enables us to study the interplay between these two kinds of order and compare the GFMC results with the ones obtained by the simple variational approach. By using a generalization of the forward-walking technique, we are able to calculate true FN ground-state expectation values of the pair-pair correlation functions. In the case of $t^prime=0$, there is a large region with a coexistence of superconductivity and antiferromagnetism, that survives up to $delta_c sim 0.10$ for $J/t=0.2$ and $delta_c sim 0.13$ for $J/t=0.4$. The presence of a finite $t^prime/t<0$ induces a strong suppression of both magnetic (with $delta_c lesssim 0.03$, for $J/t=0.2$ and $t^prime/t=-0.2$) and pairing correlations. In particular, the latter ones are depressed both in the low-doping regime and around $delta sim 0.25$, where strong size effects are present.
