We investigate the pairing symmetry in the novel superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ under pressure by the nonperturbative variational quantum Monte Carlo. Within the bilayer Hubbard model and extended $t\text{−}J$ model with two orbitals in the $E_g$ doublet, we find the local strong correlation triggers $s_{\pm }$-wave Cooper pairing, with sign change of the gap function among the various Fermi pockets, while the $d_{x^2-y^2}$-wave pairing is generically disfavored. This is in agreement with the results from functional renormalization group applied in the weak up to moderate correlation limit. We find the $3{\mathrm{d}}_{3z^2-r^2}$ orbital plays a leading role in the superconducting pairing. We also demonstrate the finite intraorbital double occupancy even in the strong correlation limit, shedding light on the itinerant versus local moment picture of the electrons in this material.

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• Pairing mechanisms
• Nickelates
• Unconventional superconductors
• Hubbard model
• Monte Carlo methods
• t-J model