Hidden Mott transition and large-$U$ superconductivity in the two-dimensional Hubbard model

TL;DR

This study reveals a hidden Mott transition in the 2D Hubbard model, showing how superconductivity and phase separation depend on the interaction strength and doping, with implications for understanding correlated electron systems.

Contribution

The paper identifies a hidden critical point U_Mott in the 2D Hubbard model, linking Mott physics to superconductivity and phase separation phenomena.

Findings

Existence of a hidden critical point U_Mott separating Slater and Mott insulators.

Superconducting correlations form a dome structure above U_Mott.

Doping behavior differs between Slater and Mott insulators, affecting phase separation.

Abstract

We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction $U$, we can identify a hidden critical point $U_{\rm Mott}$, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Slater insulator (at small values of $U$), where magnetism induces a potential energy gain, and a Mott insulator (at large values of $U$), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of $U_{\rm Mott}$ has crucial consequences when doping the system: We observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Slater insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above $U_{\rm Mott}$, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above $U_{\rm Mott}$ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.