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Journal of Experimental and Theoretical Physics Letters

Calculation of the Fermi surface with complex topology from norm-conserving cluster perturbation theory for doping dependent electronic structure of the Hubbard model

Sergei G. Ovchinnikov, Sergey V. Nikolaev

Published Jul 1, 2011• 6 citations
Publisher

Abstract

The results of recently developed norm-conserving cluster perturbation theory for doping dependent electronic structure of the Hubbard model are reported. We have found that the momentum distribution of the spectral weight strongly depends on the broadening value δ. At δ = 0.1 t , we reproduce the angle-resolved photoemission spectroscopy data, while at δ = 0.01 t we obtain two quantum phase transitions.

DOI
10.1134/s0021364011090116

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Physical review. B, Condensed matter•Aug 15, 2000•2 citations
The results of recently developed norm-conserving cluster perturbation theory for doping dependent electronic structure of the Hubbard model are reported. We have found that the momentum distribution of the spectral weight strongly depends on the broadening value δ. At δ = 0.1 t , we reproduce the angle-resolved photoemission spectroscopy data, while at δ = 0.01 t we obtain two quantum phase transitions.
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 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.
We discuss spectra calculated for the two-dimensional Hubbard model in the intermediate coupling regime with the dynamical cluster approximation, which is a nonperturbative approach. We find a crossover from a normal Fermi liquid with a Fermi surface closed around the Brillouin-zone center at large doping to a non-Fermi liquid for small doping where the Fermi surface is holelike, closed around $M=(\ensuremath{\pi},\ensuremath{\pi}).$ The topology of the Fermi surface at low doping indicates a violation of Luttinger's theorem. We discuss different ways of presenting the spectral data to extract information about the Fermi surface. A comparison to recent experiments is presented.
Angle-resolved photoemission spectra (ARPES) are calculated in the Hubbard model by using cluster perturbation method. It is found that in a cluster of 12 sites, the local density of states displays the phase transition from normal conductor to Mott insulator with the increase of the electron-electron coupling. We show that a pseudogap develops from the metallic phase to the insulating phase. Evidence of spin-charge separation is also verified in the calculated single particle spectral functions.
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.
We calculate the single-particle Green's function for a contact interaction with nearest-neighbor hopping on a square lattice as a function of chemical potential $\ensuremath{\mu}.$ This allows us to investigate the dependence of the leading Fermi-liquid dependencies on the band structure as the Fermi surface evolves from a circle at $\ensuremath{\mu}\ensuremath{\sim}\ensuremath{-}4t$ to a square at $\ensuremath{\mu}=0.$ The form of the single-particle self-energy $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E)$ is determined by the density-density correlation function $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ which develops two peaks for $\ensuremath{\mu}\ensuremath{\gtrsim}\ensuremath{-}2.5t$ unlike the parabolic band case. Near half-filling, $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{q},\ensuremath{\omega})$ becomes independent of $\ensuremath{\omega},$ one-dimensional behavior, at intermediate values of $\ensuremath{\omega},$ which leads to the one-dimensional behavior in $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E).$ However, with $\ensuremath{\mu}<~\ensuremath{-}0.1t$ there is no influence on the Fermi-liquid dependencies from the spin-density wave instability. We find that throughout the doping region $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E)$ remains qualitatively the same as for the isotropic Fermi surface with quantitative differences. The strong $\stackrel{\ensuremath{\rightarrow}}{p}$ and E dependence of the off-shell self-energy $\ensuremath{\Sigma}(p,E)$ found earlier for the parabolic band is recovered for $\ensuremath{\mu}\ensuremath{\lesssim}\ensuremath{-}t$ but deviates from this develop for $\ensuremath{\mu}\ensuremath{\gtrsim}\ensuremath{-}0.1t.$ The resonance peak width of the spectral function $A(\stackrel{\ensuremath{\rightarrow}}{p}E),$ has a linear dependence in ${\ensuremath{\xi}}_{\stackrel{\ensuremath{\rightarrow}}{p}}$ due to the E dependence of the imaginary part of $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E).$ We point out that an accurate detailed form for $\ensuremath{\Sigma}(\stackrel{\ensuremath{\rightarrow}}{p},E)$ would be very difficult to recover from angle-resolved photoemission spectroscopy data for the spectral density. Since the leading corrections are determined by the long wavelength particle-hole excitations, the results found here for the Hubbard model carry over to Hamiltonians with finite range interactions.