Phase Diagram, d-Wave Superconductivity, and Pseudogap of the t−t′−J Model at Finite Temperature

Abstract

Recently, robust d-wave superconductive (SC) order has been unveiled in the ground state of the 2D t−t′−J model—with both nearest-neighbor (t) and next-nearest-neighbor (t′) hoppings—by density matrix renormalization group studies. However, there is currently a debate on whether the d-wave SC holds up strong on both t′/t>0 and t′/t<0 cases for the t−t′−J model, which correspond to the electron- and hole-doped sides of the cuprate phase diagram, respectively. Here, we exploit state-of-the-art thermal tensor network approach to accurately obtain the phase diagram of the t−t′−J model on cylinders with widths up to W=6 and down to low temperature as T/J≃0.06, pushing the boundaries of contemporary finite-T calculations. For t′/t>0, we find a domelike SC regime with a diverging d-wave pairing susceptibility, χSC∝1/Tα below a characteristic temperature Tc*. Near optimal doping, Tc* reaches its highest value of about 0.15J. Above Tc* yet below a higher crossover temperature T*, the magnetic susceptibility becomes suppressed, which can be related to the onset of pseudogap (PG) behaviors. On the other hand, for t′/t<0, we find the pairing correlations are much weaker, although there exhibits a node-antinode structure in the PG regime as observed in the hole-doped cuprates. The thermal tensor network calculations of the t−t′−J model underscore both the similarities and differences in the finite-temperature phase diagram between the fundamental model and cuprates, yielding unique insights into their intricate behaviors.

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