Metal-insulator transition and strong-coupling spin liquid in the $t{-}t^\prime$ Hubbard model

TL;DR

This paper investigates the phase diagram of the frustrated $t{-}t^\prime$ Hubbard model on a square lattice, revealing a transition to an insulating, non-magnetic phase at strong coupling and high frustration using a novel variational wave function.

Contribution

The study introduces a new variational wave function incorporating backflow correlations to accurately analyze the ground state of the frustrated Hubbard model on the lattice.

Findings

Identification of an insulating, non-magnetic phase at strong coupling and high frustration.

Validation of the variational wave function's accuracy across weak and strong coupling regimes.

Evidence supporting a metal-insulator transition driven by frustration and interaction strength.

Abstract

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 $t^\prime/t$.