Short-Range Antiferromagnetic Correlations and the Photoemission Spectrum

SHORT–RANGE ANTIFERROMAGNETIC CORRELATIONS AND THE PHOTOEMISSION SPECTRUM arXiv:cond-mat/9606198v1 26 Jun 1996 N. BULUT Department of Physics, University of California, Santa Barbara, CA 93106–9530, USA We present Quantum Monte Carlo results on the antiferromagnetic correlations and the one–electron excitations of the doped two–dimensional Hubbard model. These results are helpful in interpreting the NMR, neutron scattering and photoemission experiments on the layered cuprates. NMR and neutron scattering experiments have provided clear evidence that the superconducting layered cuprates have short–range and low–frequency antiferromagnetic (AF) correlations. In addition, the photoemission experiments have shown that the one–electron excitations are heavily damped and strongly renormalized. Perhaps, the simplest model to describe these properties is the two–dimensional Hubbard model on a square lattice, X † X † ci↓ ci↓ c†i↑ ci↑ , (1) (ciσ cjσ + c†jσ ciσ ) + U H = −t i hi,ji,σ where t is the hopping matrix element, U is the onsite Coulomb repulsion, and ciσ annihilates an electron of spin σ at site i. Here, we present Quantum Monte Carlo (QMC) results on the magnetic fluctuations and the one–electron properties of the doped 2D Hubbard model. Figure 1: (a) Momentum dependence of the magnetic susceptibility χ(q, ω = 0) along the (1, 1) direction at various temperatures. (b) Frequency dependence of the spin–fluctuation spectral weight Im χ(q, ω) for q = (π, π) at the same temperatures as in Fig. 1(a). Inset: Real–space structure of the equal–time magnetization–magnetization correlation function at T = 0.33t. Using QMC simulations [1] and numerical analytic continuation methods [2] we have calculated the staggered magnetic susceptibility χ(q, ω). The results that we will present here are for U = 8t and 1/8 doping on an 8 × 8 lattice. In addition, we use units such that t = 1 and µB = 1. In Figure 1(a), the momentum dependence of χ(q, ω = 0) is plotted along the (1, 1) direction. Figure 1(b) shows the spectral weight Im χ(q, ω) versus ω for q = (π, π). In the inset of Fig. 1(b), 1 Figure 2: One–electron spectral weight A(p, ω) versus ω at various temperatures for p = (π/2, π/2), (π, 0) and (π, π). the equal–time magnetization–magnetization correlation function is plotted as a function of distance along the (1, 0) direction. These figures show that there are short range AF correlations in the 2D Hubbard model near half–filling. NMR T1−1 and T2−1 measurements and magnetic neutron scattering experiments have shown the existence of short–range AF correlations in the superconducting cuprates. Next, we present results on the one–electron spectral weight A(p, ω) = − π1 Im G(p, ω), where G(p, ω) is the one–electron Green’s function. A(p, ω) is of experimental interest, since, within the sudden approximation, the photoemission intensity is proportional to A(p, ω)f (ω), where f (ω) is the fermi factor. In Figure 2, A(p, ω) versus ω is plotted for three representative points of the Brillouin zone [3,4]. Because of the many–body effects, the quasiparticle peak in A(p, ω) is damped, and the quasiparticle bandwidth is reduced. We also observe that A(p, ω) has significant dependence on temperature in this temperature regime. In this article, we have presented a brief review of the QMC data on the magnetic and one– electron excitations of the 2D Hubbard model near half–filling. In this metallic regime, there exist low–frequency short–range antiferromagnetic fluctuations, and the one–electron excitations are heavily damped and strongly renormalized. Similar electronic features have been observed experimentally for the layered cuprates. Acknowledgments The author would like to thank D.J. Scalapino for many helpful discussions. This review is based on work done in collaboration with D.J. Scalapino and S.R. White. The author also gratefully acknowledges support from the National Science Foundation under Grant No. DMR92– 25027. The numerical calculations reported in this paper were performed at the San Diego Supercomputer Center. References 1. S.R. White, D.J. Scalapino, R.L. Sugar, E.Y. Loh, J.E. Gubernatis and R.T. Scalettar, Phys. Rev. B 40, 506 (1989). 2. S.R. White, Phys. Rev. B 44, 4670 (1991). 3. N. Bulut, D.J. Scalapino and S.R. White, Phys. Rev. Lett. 72, 705 (1994). 2 4. N. Bulut, D.J. Scalapino and S.R. White, Phys. Rev. B 50, 7215 (1994). 3