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Physical Review B

Comparison of the electronic structure of the Hubbard and t−J models within the cluster perturbation theory

V. I. Kuz’min, Sergey V. Nikolaev, Sergei G. Ovchinnikov

Published Dec 1, 2014• 14 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.90.245104

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Electronic dispersion and density of states (DOS) have been calculated for the Hubbard model and the t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J and t\ensuremath−J∗t\ensuremath{-}{J}^{*}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−Jt\ensuremath{-}Jt\ensuremath−J models at the energy scale \ensuremathω\ensuremath≳t\ensuremath{\omega}\ensuremath{\gtrsim}t\ensuremathω\ensuremath≳t. The three-site correlated hopping addition results in an almost negligible difference for the Hubbard and t\ensuremath−J∗t\ensuremath{-}{J}^{*}t\ensuremath−J∗ models. Close to the Fermi energy, at the scale \ensuremathω\ensuremath≲J\ensuremath{\omega}\ensuremath{\lesssim}J\ensuremathω\ensuremath≲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−Jt\ensuremath{-}Jt\ensuremath−J model that has been previously obtained for the Hubbard model by cellular dynamical mean-field theory calculations.
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.
Cluster perturbation theory is a technique for calculating the spectral weight of Hubbard models of strongly correlated electrons, which combines exact diagonalizations on small clusters with strong-coupling perturbation theory at leading order. It is exact in both the strong- and weak-coupling limits and provides a good approximation to the spectral function at any wave vector. Following the paper by S\'en\'echal et al. [Phys. Rev. Lett. 84,84,84, 522 (2000)], we provide a more complete description and derivation of the method. We illustrate some of its capabilities, in particular regarding the effect of doping, the calculation of ground state energy and double occupancy, the disappearance of the Fermi surface in the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model, and so on. The method is applicable to any model with on-site repulsion only.
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.
The doping and temperature dependencies of the electronic structure and the dynamic spin susceptibility of the Hubbard model on a square lattice are studied within cluster perturbation theory (CPT). The most general features of both electronic and spin spectra qualitatively agree with the experimental data on cuprates. Generalized mean-field calculations of the electronic structure using static short-range magnetic correlations from CPT are also implemented and compared with the results of CPT, allowing us to discuss the role of short-range antiferromagnetism in the formation of the pseudogap.
Cluster perturbation theory is applied to the two-dimensional Hubbard $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{'}\ensuremath{'}}\ensuremath{-}U$ model to obtain doping and temperature-dependent electronic spectral function with $4\ifmmode\times\else\texttimes\fi{}4$ and 12-site clusters. It is shown that evolution of the pseudogap and electronic dispersion with doping and temperature is similar and in both cases it is significantly influenced by spin-spin short-range correlations. When short-range magnetic order is weakened by doping or temperature and Hubbard-I-like electronic dispersion becomes more pronounced, the Fermi arc turns into a large Fermi surface and the pseudogap closes. It is demonstrated how static spin correlations impact the overall dispersion's shape and how accounting for dynamic contributions leads to momentum-dependent spectral weight at the Fermi surface and broadening effects.