Recently, a robust d-wave superconductivity has been unveiled in the ground
state of the 2D t-tβ²-J model -- with both nearest-neighbor (t) and
next-nearest-neighbor (tβ²) hoppings -- through the density matrix
renormalization group calculations in the ground state. In this study, we
exploit the state-of-the-art thermal tensor network approach to accurately
simulate the finite-temperature electron states of the t-tβ²-J model on
cylinders with widths up to W=6. Our analysis suggests that in the dome-like
superconducting phase, the d-wave pairing susceptibility exhibits a divergent
behavior with ΟSCββ1/TΞ± below the onset temperature
Tcββ. Near the optimal doping, Tcββ reaches its highest value of about
0.05t (β‘0.15J). Above Tcββ yet below a higher crossover
temperature Tβ, the magnetic susceptibility is suppressed, and the Fermi
surface also exhibits node-antinode structure, resembling the pseudogap
behaviors observed in cuprates. Our unbiased and accurate thermal tensor
network calculations obtain the phase diagram of the t-tβ²-J model with
tβ²/t>0, shedding light on the d-wave superconducting and pseudogap phases
in the enigmatic cuprate phase diagram.Comment: 7+5 pages, 4+8 figure