Qualitative understanding of the sign of t′ asymmetry in the extended t-J model and relevance for pairing properties -: art. no. 180513

Numerical calculations illustrate the effect of the sign of the next-nearest-neighbor hopping term t' on the two-hole properties of the t-t'-J model. Working mainly on two-leg ladders, in the -1.0 less than or equal to t'/t less than or equal to 1.0 regime, it is shown that introducing t' in the t-J model is equivalent to effectively renormalizing J, namely t' negative (positive) is equivalent to an effective t-J model with smaller (bigger) J. This effect is present even at the level of a 2 x 2 plaquette toy model. and was observed also in calculations on small square clusters. Analyzing the transition probabilities of a hole pair in the plaquette toy model, it is argued that the coherent propagation of such hole pair is enhanced by a constructive interference between both t and t' for t' > 0. This interference is destructive for t' < 0.