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arXiv:cond-mat/9702016 · Physical review. B, Condensed matter

Comparison of 32-site exact-diagonalization results and ARPES spectral functions for the antiferromagnetic insulator Sr2CuO2Cl2

P. W. Leung, Barrett O. Wells, Robert J Gooding

Published Sep 1, 1997• 68 citations
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Abstract

We explore the success of various versions of the one-band $t$-$J$ model in explaining the full spectral functions found in angle-resolved photoemission spectra for the prototypical, quasi-two-dimensional, tetragonal, antiferromagnetic insulator ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}$. After presenting arguments justifying our extraction of $A(\mathbf{k},\ensuremath{\omega})$ from the experimental data, we rely on exact-diagonalization results from studies of a square 32-site lattice, the largest cluster for which such information is presently available, to perform this comparison. Our work leads us to believe that (i) a one-band model that includes hopping out to third-nearest neighbors, as well three-site, spin-dependent hopping, can indeed explain not only the dispersion relation, but also the quasiparticle lifetimes---only in the neighborhood of $\mathbf{k}=(\ensuremath{\pi}/2,0)$ do we find disagreement; (ii) an energy-dependent broadening function, $\ensuremath{\Gamma}(E)={\ensuremath{\Gamma}}_{0}+AE$, is important in accounting for the incoherent contributions to the spectral functions.

DOI
10.1103/physrevb.56.6320

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We explore the success of various versions of the one-band ttt-JJJ model in explaining the full spectral functions found in angle-resolved photoemission spectra for the prototypical, quasi-two-dimensional, tetragonal, antiferromagnetic insulator Sr2CuO2Cl2{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}Sr2​CuO2​Cl2​. After presenting arguments justifying our extraction of A(k,\ensuremathω)A(\mathbf{k},\ensuremath{\omega})A(k,\ensuremathω) from the experimental data, we rely on exact-diagonalization results from studies of a square 32-site lattice, the largest cluster for which such information is presently available, to perform this comparison. Our work leads us to believe that (i) a one-band model that includes hopping out to third-nearest neighbors, as well three-site, spin-dependent hopping, can indeed explain not only the dispersion relation, but also the quasiparticle lifetimes---only in the neighborhood of k=(\ensuremathπ/2,0)\mathbf{k}=(\ensuremath{\pi}/2,0)k=(\ensuremathπ/2,0) do we find disagreement; (ii) an energy-dependent broadening function, \ensuremathΓ(E)=\ensuremathΓ0+AE\ensuremath{\Gamma}(E)={\ensuremath{\Gamma}}_{0}+AE\ensuremathΓ(E)=\ensuremathΓ0​+AE, is important in accounting for the incoherent contributions to the spectral functions.
We present results of an exact diagonalization calculation of the spectral function A(k,\ensuremath{\omega}) for a single hole described by the t-J model propagating on a 32-site square cluster. The minimum energy state is found at a crystal momentum k=(\ensuremath{\pi}/2,\ensuremath{\pi}/2), consistent with theory, and our measured dispersion relation agrees well with that determined using the self-consistent Born approximation. In contrast to smaller cluster studies, our spectra show no evidence of string resonances. We also make a qualitative comparison of the variation of the spectral weight in various regions of the first Brillouin zone with recent angle-resolved-photoemission data.
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Results for the single-particle Green's function for the strong-coupling limit of the single-band Hubbard model ($t\ensuremath{-}J$ model) obtained by numerical and analytical methods are discussed. The numerical calculation of the spectral function is performed for small systems of up to 18 sites using the Lanczos method. A detailed analysis of the spectral functions for the $t\ensuremath{-}J$ model in one and two dimensions is given. We also investigate the effect of the next-nearest-neighbor hopping terms, which appear in order t2U\frac{{t}^{2}}{U}Ut2​ and are omitted in the standard $t\ensuremath{-}J$ model. The role of quantum fluctuations on the shape of the spectra and the fundamental difference between one and two dimensions is elucidated. In 2D we find evidence for a coherent quasiparticle band of width 2J2J2J with dispersion $^{\ensuremath{\omega}}\mathrm{k}\ensuremath{\sim}(\frac{J}{2}){(cos{k}_{x}+cos{k}_{y})}^{2}$ and spin S=12S=\frac{1}{2}S=21​, which emerges at the low-energy edge of the incoherent spectrum. This form of dispersion is due to effective next-nearest-neighbor processes related to spin flips and agrees with our extension of the approach of Brinkman and Rice to finite JJJ.
Angle-resolved photoemission spectroscopy (ARPES) has revealed peculiar properties of mobile dopants in correlated antiferromagnets (AFMs). But, describing them theoretically, even in simplified toy models, remains a challenge. Here, we study ARPES spectra of a single mobile hole in the $t\ensuremath{-}J$ model. Recent progress in the microscopic description of mobile dopants allows us to use a geometric decoupling of spin and charge fluctuations at strong couplings, from which we conjecture a one-to-one relation of the one-dopant spectral function and the spectrum of a constituting spinon in the undoped parent AFM. We thoroughly test this hypothesis for a single hole doped into a two-dimensional Heisenberg AFM by comparing our semianalytical predictions to previous quantum Monte Carlo results and our large-scale time-dependent matrix product state calculations of the spectral function. Our conclusion is supported by a microscopic trial wave function describing spinon-chargon bound states, which captures the momentum and t/Jt/Jt/J dependence of the quasiparticle residue. From our conjecture we speculate that ARPES measurements in the pseudogap phase of cuprates may directly reveal the Dirac-fermion nature of the constituting spinons. Specifically, we demonstrate that our trial wave function provides a microscopic explanation for the sudden drop of spectral weight around the nodal point associated with the formation of Fermi arcs, assuming that additional frustration suppresses long-range AFM ordering. We benchmark our results by studying the crossover from two to one dimension, where spinons and chargons are confined and deconfined, respectively.
We present our theoretical study of the single-particle spectral function in two-dimensional cuprates by using numerically exact diagonalization method on small clusters of the extended t-J model containing long-range hopping matrix elements. For a set of the parameter values, the calculated spectral function systematically explains the angle-resolved photoemission spectroscopy (ARPES) data for Bi2Sr2CaCu2O8+δ. For La2−xSrxCuO4 (LSCO), it is found that slightly smaller values of long-range hoppings are necessary for understanding an observed change of the Fermi surface topology with x. In addition, the dramatic suppression of spectral weight along (0,0)-(π,π) direction observed in under-doped LSCO is found to be explained by introducing an additional potential for holes which stabilizes vertical charge stripes.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for Sr2CuO2Cl2{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}Sr2​CuO2​Cl2​. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation T=t/3T=t/3T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density 〈n〉〈n〉〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from (0,0)(0,0)(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended sss-wave character is found to compete with the ddd wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as 〈n〉〈n〉〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.