Order by Projection in fermionic Hubbard model with finite on-site interaction

In a repulsive Fermi system near or at half-filling, a superconducting pairing channel, not explicitly present in the Hamiltonian, can be enhanced by suppressing another channel with uncertainty principle inequality, such as the extended s-wave pairing can be enhanced by suppressing the s-wave pairing. This phenomenon is referred to as 'Order by Projection' [1], with an exact solution having been obtained for the case of on-site interaction U=0 in the thermodynamic limit [2]. In this study, we systematically investigate this mechanism in the fermionic Hubbard model on a square lattice with finite on-site interactions. We thoroughly explore the behaviors of various pairing channels by suppressing different orders beyond the s-wave channel, utilizing density matrix renormalization groups (DMRG) and exact diagonalization (ED) techniques. Our findings provide numerical evidence supporting the existence of 'Order by Projection' in this system. Additionally, we observe that when one of pairing channels is suppressed, the introduction of the next-nearest neighbor hopping term could result in markedly different performances in other channels, representing a supplementary extension of this mechanism.

[1] Shastry, B.S., 1997. Uncertainty principle enhanced pairing correlations in projected Fermi systems near half filling. Journal of Physics A: Mathematical and General, 30(18), p.L635.

[2] Krishnamurthy, H.R. and Shastry, B.S., 2000. Exact solution of a repulsive Fermi model with enhanced superconducting correlations. Physical Review Letters, 84(21), p.4918.