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arXiv:cond-mat/9803314 · Physical review. B, Condensed matter

Hole pairs in a spin liquid: Influence of electrostatic hole-hole repulsion

C. J. Gazza, George Balster Martins, José A. Riera, Elbio R. Dagotto

Published Jan 1, 1999• 18 citations
arXivHTMLPDF

Abstract

The stability of hole bound states in the $t\ensuremath{-}J$ model including short-range Coulomb interactions is analyzed using computational techniques on ladders with up to $2\ifmmode\times\else\texttimes\fi{}30$ sites. For a nearest-neighbor (NN) hole-hole repulsion, the two-holes bound state is surprisingly robust and breaks only when the repulsion is several times the exchange $J.$ At $\ensuremath{\sim}10%$ hole doping the pairs break only for a NN repulsion as large as $V\ensuremath{\sim}4J.$ Pair-pair correlations remain robust in the regime of hole binding. The results support electronic hole-pairing mechanisms on ladders based on holes moving in spin-liquid backgrounds. Implications in two dimensions are also presented. The need for better estimations of the range and strength of the Coulomb interaction in copper oxides is remarked.

DOI
10.1103/physrevb.59.r709

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The stability of hole bound states in the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model including short-range Coulomb interactions is analyzed using computational techniques on ladders with up to 2\ifmmode×\else\texttimes\fi302\ifmmode\times\else\texttimes\fi{}302\ifmmode×\else\texttimes\fi30 sites. For a nearest-neighbor (NN) hole-hole repulsion, the two-holes bound state is surprisingly robust and breaks only when the repulsion is several times the exchange J.J.J. At \ensuremath∼10\ensuremath{\sim}10%\ensuremath∼10 hole doping the pairs break only for a NN repulsion as large as V\ensuremath∼4J.V\ensuremath{\sim}4J.V\ensuremath∼4J. Pair-pair correlations remain robust in the regime of hole binding. The results support electronic hole-pairing mechanisms on ladders based on holes moving in spin-liquid backgrounds. Implications in two dimensions are also presented. The need for better estimations of the range and strength of the Coulomb interaction in copper oxides is remarked.
Recent calculations in the context of ladder systems, but with implications also for high- T c two-dimensional (2D) systems, are described here. In particular, efforts are concentrated on the influence of a hole-hole electrostatic repulsion on holepair binding in the t − J model on ladders. It is concluded that the pairs are very robust because a nearest-neighbor hole-hole repulsion of strength ~5 J is needed to break the pairs. In the second part of the paper, the spectral function of holes is provided on up to 2×20 clusters using a new numerical technique. A gap in the spectrum caused by hole binding is observed, as well as flat regions near (π, 0). Implications for studies of high- T c materials are discussed. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The problem of two holes in the presence of strong antiferromagnetic fluctuations is revisited using computational techniques. Two-dimensional clusters and two-leg ladders are studied with the Lanczos and truncated Lanczos algorithms. Lattices with up to $2\ifmmode\times\else\texttimes\fi{}16$ and $\sqrt{32}\ifmmode\times\else\texttimes\fi{}\sqrt{32}$ sites are studied. The motivation of the paper is the recently discussed spatial distribution of holes in ladders where the maximum probability for the hole-hole distance is obtained at d=2d=\sqrt{2}d=2​ in units of the lattice spacing, a counterintuitive result considering that the overall symmetry of the two-hole bound state is ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$. Here this effect is shown to appear in small ladder clusters that can be addressed exactly, and also in planes. The probability distribution of hole distances ddd was found to be broad with several distances contributing appreciably to the wave function. The existence of holes in the same sublattice is argued to be a consequence of non-negligible retardation effects in the $t\ensuremath{-}J$ model. Effective models with instantaneous interactions nevertheless capture the essence of the hole pairing process in the presence of short-range antiferromagnetic fluctuations (especially regarding the symmetry properties of the condensate), similarly as the (nonretarded) BCS model contains the basic features of the more complicated electron-phonon problem in low-temperature superconductors. The existence of strong spin singlets in the region where the two-hole bound state is located is here confirmed, and a simple explanation for its origin in the case of planes is proposed using the N\'eel state as a background, complementing previous explanations based on a spin-liquid undoped state. It is predicted that these strong singlets should appear regardless of the long distance properties of the spin system under consideration, as long as the bound state is ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$. In particular, it is shown that they are present in an Ising spin background. The time retardation in the family of $t\ensuremath{-}J$ models leads naturally to low-energy hole states with nonzero momentum and spin one, providing a possible explanation for apparent SO(5)-symmetric features observed recently in this context. Finally, the influence of a short-range Coulombic repulsion is analyzed. Rough estimations suggest that at a distance of one lattice spacing this repulsion is larger than the exchange JJJ. The hole distribution in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ bound state is reanalyzed in the presence of such repulsion. Very short hole-hole distances lose their relevance in the presence of a realistic hole-hole interaction.
Using numerical results from density matrix renormalization group (DMRG) calculations for the t-J model, on systems as large as 10\ifmmode\times\else\texttimes\fi{}7, we examine the structure of the one and two hole ground states in ladder systems and in two dimensional clusters. A simple theoretical framework is used to explain why holes bind in pairs in two-dimensional antiferromagnets. For the case J/t=0.5, which we have studied, the hole pairs reside predominantly on a 2\ifmmode\times\else\texttimes\fi{}2 core plaquette with the probability that the holes are on diagonal sites greater than nearest-neighbor sites. There is a strong singlet bond connecting the spins on the two remaining sites of the plaquette. We find that a general characteristic of dynamic holes in an antiferromagnet is the presence of frustrating antiferromagnetic bonds connecting next-nearest-neighbor sites across the holes. Pairs of holes bind in order to share the frustrating bonds. At low doping, in addition to hole pairs, there are two additional low-energy structures which spontaneously form on certain finite systems. The first is an undoped L\ifmmode\times\else\texttimes\fi{}2 spin-liquid region, or ladder. The second is a hole moving along a one dimensional chain of sites. At higher doping we expect that hole pairing is always favored.
The recent discovery of superconductivity under high pressure in the ladder compound BaFe2S3{\mathrm{BaFe}}_{2}{\mathrm{S}}_{3}BaFe2​S3​ has opened a new field of research in iron-based superconductors with focus on quasi-one-dimensional geometries. In this publication, using the density matrix renormalization group technique, we study a two-orbital Hubbard model defined in one-dimensional chains. Our main result is the presence of hole binding tendencies at intermediate Hubbard UUU repulsion and robust Hund coupling JH/U=0.25{J}_{H}/U=0.25JH​/U=0.25. Binding does not occur either in weak coupling or at very strong coupling. The pair-pair correlations that are dominant near half-filling, or of similar strength as the charge and spin correlation channels, involve hole-pair operators that are spin singlets, use nearest-neighbor sites, and employ different orbitals for each hole. The Hund coupling strength, presence of robust magnetic moments, and antiferromagnetic correlations among them are important for the binding tendencies found here.
We present numerical results on the role of next-nearest-neighbor (NNN) Coulomb repulsion within t-J-V-Vʹ model using exact diagonalization (ED) technique within an 8 – site tilted square cluster at a hole doping <h>=0.25. Periodic boundary conditions have been applied to obtain complete basis states. It appears that hole-hole correlation is dominant at d = √2. NNN Coulomb repulsion localizes the electrons and cooperates with exchange interaction J. Non-Fermi liquid behavior of the model has been confirmed.
We investigate the binding of holes and the emergence of competing spin-charge order in the simple and extended Hubbard model using exact diagonalization on the 3x4 cylindrical lattice. For the simple Hubbard model (V=0), we find weakly bound hole pairing mediated by magnetic correlations at intermediate repulsive U, without any evidence of phase separation. Introducing nearest-neighbor interaction V reveals a rich phase diagram: attractive V drives multi-hole clustering and phase separation with localized magnetic quenching, while repulsive V stabilizes charge-density-wave (CDW) order that coexists with bound hole pairs within a modulated magnetic background. At strong coupling (U=10), the competition sharpens, with attractive V overcoming on-site repulsion to form magnetically quenched clusters and repulsive V producing robust CDW order that constrains pairing. Real-space analysis of spin and charge correlations provides microscopic evidence of distinct binding mechanisms -- phase separation versus correlation-mediated pairing -- depending on the sign and strength of intersite interaction V . Our results establish a comprehensive picture of how nonlocal Coulomb interactions reshape the landscape of hole-binding and collective order in correlated electron systems.