Qualitative understanding of the sign of (formula presented) asymmetry in the extended (formula presented) model and relevance for pairing properties

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 18, 2001, Pages

  Martins, G B ^a   Dagotto, E ^a   Xavier, J C ^b   Arrachea, L ^c  

^a Florida State University   (United States)

^b UNIVERSITY OF CAMPINAS   (Brazil)

^c UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84880324005     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.180513     Document Type: Article

References (26)

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15. It can be shown that changing the sign of t in the (Formula presented) model is equivalent to a shift in momentum by (Formula presented). Thus, by the expression of the dispersion relation of a hole in the (Formula presented) model (Formula presented) it can be concluded that such a change of sign has no effect in the properties of the model. Changing the sign of (Formula presented) in the (Formula presented) model is also irrelevant; this can be concluded by noticing that the (Formula presented) model is equivalent to a (Formula presented) model on a (Formula presented) lattice. Therefore, in the (Formula presented) model, in the limit where either (Formula presented) or (Formula presented), a change of sign in the hopping amplitude is irrelevant.
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22. In previous works by two of the authors (Ref. 5), indications of spin-charge separation were found in the negative (Formula presented) regime. The connection of the ideas discussed here to these previous results is being presently analyzed.
23. Since the objective is to analyze the hole-pair dynamics, a strong coupling regime (Formula presented) (Formula presented) is assumed. In this case the two states with spin singlets in the diagonal of the plaquette are excited configurations (with zero energy) and the four states with spin singlets in the sides of the plaquette form a degenerate ground state (with energy (Formula presented). Therefore, starting from a ground-state configuration (spin singlet on the side), a NN hopping takes it to an excited configuration (spin singlet on the diagonal), being therefore a less probable process, according to standard perturbation theory. Note that the fermionic commutation signs are included in the orientation of the singlets.
24. A previous publication (Ref. 9), discussing differences between hole-doped and electron-doped cuprates, suggested as an explanation for the (Formula presented) sign effect the stabilization of Néel-like configurations (containing NN hole pairs) in the ground state through a diagonal matrix element with value (Formula presented). Such configurations would be energetically favored by a positive (Formula presented), leading to an increase in pairing and AF spin correlations, with the opposite effect for (Formula presented) negative, as compared to the (Formula presented) case. However, this argument does not address an important point: In the limit of (Formula presented) it would still give asymmetric results for positive and negative (Formula presented). It was checked by ED of a (Formula presented) ladder with two holes that the ground state for (Formula presented) and (Formula presented) has (Formula presented), that is a sufficient requirement for the matrix element argument to apply; nevertheless the probability of having the holes in the same rung is quite similar for positive and negative (Formula presented). The spin correlations are also similar, indicating the irrelevance of the sign of (Formula presented) in the (Formula presented) limit. Then, the interference mechanism, that takes into account the interplay of NN and NNN hoppings, supplements their argument, since in the limit (Formula presented) the interference becomes irrelevant. In Ref. 4, the (Formula presented) toy model was used to make an energetic consideration to explain the pair binding dependence on the sign of (Formula presented). The intuitive picture here discussed supplements their discussion and, regarding their assumption about the validity or not of generalizing results obtained in the (Formula presented) plaquette to larger systems, the results shown here (e.g., Fig. 22) give support to such a generalization.
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