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

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 $U_{\mathrm{Mott}}$, 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 $U_{\mathrm{Mott}}$ 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 $U_{\mathrm{Mott}}$, 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 $U_{\mathrm{Mott}}$ shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.

10 pages, 7 figures

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• Correlation-induced superconductivity dynamically stabilized and enhanced by laser irradiation
• Effects of interaction strength, doping, and frustration on the antiferromagnetic phase of the two-dimensional Hubbard model
• Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model
• Unified description of cuprate superconductors using four-band $d$-$p$ model
• Local moments versus itinerant antiferromagnetism: magnetic phase diagram and spectral properties of the anisotropic square lattice Hubbard model
• Enhancement of superconductivity due to kinetic-energy effect in the strongly correlated phase of the two-dimensional Hubbard model
• Phase diagram of the Hubbard model on a square lattice: A cluster slave-spin study
• Ferromagnetic diagonal stripe states in the two-dimensional Hubbard model with $U\lesssim \infty$