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Siberian Journal of Physics

Investigation Of Anomalies In The Electronic Dispersion Of The Hubbard Model, t–J And t–J* Models Within The Cluster Perturbation Theory In The X-Operator Representation

Valeriy Kuz’min, Sergey V. Nikolaev

Published Mar 1, 2015• 0 citations
Publisher

Abstract

The electronic structure with the spectral line broadening corresponding to the angle-resolved photoemission spectroscopy resolution has been calculated for the Hubbard model, t–J and t–J* models within the norm-conserving cluster perturbation theory. The electronic dispersion anomalies similar to the high-energy kinks observed in the angle-resolved photoemission spectroscopy experiments are obtained at the energy scale of order of the hopping integral t. The doping dependence of the high-energy anomalies for different Coulomb repulsion values is discussed. The influence of the threesite correlated hopping on the results is analyzed.

DOI
10.54362/1818-7919-2015-10-1-50-56

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The electronic structure with the spectral line broadening corresponding to the angle-resolved photoemission spectroscopy resolution has been calculated for the Hubbard model, t–J and t–J* models within the norm-conserving cluster perturbation theory. The electronic dispersion anomalies similar to the high-energy kinks observed in the angle-resolved photoemission spectroscopy experiments are obtained at the energy scale of order of the hopping integral t. The doping dependence of the high-energy anomalies for different Coulomb repulsion values is discussed. The influence of the threesite correlated hopping on the results is analyzed.
Electronic dispersion and density of states (DOS) have been calculated for the Hubbard model and the $t\ensuremath{-}J$ and $t\ensuremath{-}{J}^{*}$ models with three-site correlated hopping by the cluster perturbation theory. We have found a rather strong quantitative difference both in dispersion and DOS at all doping for the Hubbard and $t\ensuremath{-}J$ models at the energy scale $\ensuremath{\omega}\ensuremath{\gtrsim}t$. The three-site correlated hopping addition results in an almost negligible difference for the Hubbard and $t\ensuremath{-}{J}^{*}$ models. Close to the Fermi energy, at the scale $\ensuremath{\omega}\ensuremath{\lesssim}J$, the electronic structure of all three models is similar. We have found the line of zeros of the Green function for the $t\ensuremath{-}J$ model that has been previously obtained for the Hubbard model by cellular dynamical mean-field theory calculations.
The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U . The concentration dependence of the Fermi surface strongly depends on hopping to second ( t ′) and third ( t ″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.
Employing dynamical cluster quantum Monte Carlo calculations we show that the single-particle spectral weight A(k,omega) of the one-band two-dimensional Hubbard model displays a high-energy kink in the quasiparticle dispersion followed by a steep dispersion of a broad peak similar to recent angle-resolved photoemission spectroscopy results reported for the cuprates. Based on the agreement between the Monte Carlo results and a simple calculation which couples the quasiparticle to spin fluctuations, we conclude that the kink and the broad spectral feature in the Hubbard model spectra is due to scattering with damped high-energy spin fluctuations.
It is shown that spectral functions within the extended t-J model, evaluated using the finite-temperature diagonalization of small clusters, exhibit the high-energy kink in single-particle dispersion consistent with recent angle-resolved photoemission results on hole-doped cuprates. The kink and waterfall-like features persist up to large doping and to temperatures beyond J; hence, the origin can be generally attributed to strong correlations and incoherent hole propagation at large binding energies. In contrast, our analysis predicts that electron-doped cuprates do not exhibit these phenomena in photoemission.
Unraveling the nature of the doping-induced transition between a Mott insulator and a weakly correlated metal is crucial to understanding novel emergent phases in strongly correlated materials. For this purpose, we study the evolution of spectral properties upon doping Mott insulating states by utilizing the cluster perturbation theory on the Hubbard and t−−Jt--Jt−−J-like models. Specifically, a quasifree dispersion crossing the Fermi level develops with small doping, and it eventually evolves into the most dominant feature at high doping levels. Although this dispersion is related to the free-electron hopping, our study shows that this spectral feature is, in fact, influenced inherently by both electron-electron correlation and spin-exchange interaction: the correlation destroys coherence, while the coupling between spin and mobile charge restores it in the photoemission spectrum. Due to the persistent impact of correlations and spin physics, the onset of gaps or the high-energy anomaly in the spectral functions can be expected in doped Mott insulators.