Interaction of holes in a Hubbard antiferromagnet and high-temperature superconductivity

Abstract

The Cu02 planes in the high-temperature superconductors are described by a two-dimensional Hubbard model. The model is investigated for an in6nite system with one and two electrons less than half 6lling. The method used is to diagonalize the Hamiltonian exactly within a retained portion of the Hilbert space. A single hole is found not to be localized by a string potential that increases linearly wreath distance, although it does have a large e6'ective mass. A pair of holes, which naively should be quite mobile, is found instead to be extremely heavy due to a previously unappreciated frustration effect that impedes their motion. This lack of mobility increases the energy of the pair so that they do not bind, contrary to some recently published results using mean6eld theory or intuitive arguments.The energy of one-and two-hole states is calculated as a function of wave vector k. The comparative energy of different angular momentum channels and magnetic polaron e6'ects are discussed.The discovery of high-temperature superconductivity' has stimulated interest in nonphonon pairing mechanisms. The high transition temperature and the small or vanishing isotope effect are evidence that the superconductivity arises primarily from strongly interacting electrons. Further evidence is provided by observations of antiferromagnetic correlations and anomalous normal-state transport propcrtlcs.A number of theoretical models have been proposed to describe nonphonon pairing mechanisms.' Takahashi' has independently done a calculation with some similarities to the present one, and finds that holes in the Hubbard model do not bind. Shraiman and Siggia' have considered this problem by a generalization of the method of nagaoka 2 and Brinkman and Rice. 23 Recent Monte Carlo calculations indicate that the two-dimensional Hubbard model does not support superconductivity. ' There are, however, persuasive qualitative arguments why there should be pairing in the nearly half-filled Hubbard model. These arguments are given below (see also Refs. 9 and 16). It is the purpose of this paper to critically consider these qualitative arguments in the light of a quantitative calculation of the hole interaction. The present calculation is not a mean-field theory, and as such can assess the accuracy of recently published mean-field approximations.The copper-oxygen plane may be described by a Hubbard model, in which the sites represent Wannier functions centered on the copper atoms. The copper d,~2 orbitals are half filled in La2 "Ba"Cu04 when x 0, and are less than half filled as x increases. A similar description of the copper-oxygen planes in YBa2Cu306.9 is also possible. The Hubbard Hamiltonian is HH -t g (c~~,ck, , +H.c.)+Urn, tn, i. &j k&s j The first term connects nearest-neighbor sites on a square lattice. The holes reside primarily on the copper atoms, as found by Martin and Saxe in their cluster calculation. '3 To write a model in which the holes reside on the oxygen atoms, the Wannier functions would be centered on the oxygen p orbitals, which...

Symmetry breaking in the Anderson-Hubbard model

“…Otherwise the perturbed level may cross one corresponding with different quantum numbers. The mentioned k are consistent with numerical calculations done by Trugman [7].…”

“…Only H0-GS with the same S and k are mixed by the perturbation term H'. Looking at table I, one sees that our k are consistent with the k of the GS of the two-hole system, k = (rr, "rr), numerically found by Trugman [7].…”

Spatial structure of spin polarons in thet−Jmodel

“…While the major part of investigations for the t-J model was concerned e.g. with the polaron dispersion and the spectral function using a variety of techniques such as exact diagonalization [2][3][4][5][6][7], selfconsistent Born approximation (SCBA) [8][9][10][11], string theory [12,13] and other methods [14][15][16][17], -our focus here is on the spatial structure of the spin polarization and its asymptotic behaviour. The study of the deformation of the spin system due to spin polaron formation was mainly performed by exact diagonalization techniques [3,18].…”

Hole dynamics in a quantum antiferromagnet: Extension of the retraceable-path approximation

“…In this work, we present a numerical study of the one hole spectral weight by means of the Lanczos iteration scheme, applied directly to the infinite system [9]. We introduce a new method for the calculation of the spectral weight, that we name the Lanczos spectra decoding method (LSD).…”

“…Indeed, in finite dimensions D > 1 several one hole paths exist, allowing for the propagation of the hole [9].…”