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Physical Review B

Electron correlation effects on Lehmann spectra of one-body Green functions for insulating states caused by the Coulomb repulsion

Norikazu Tomita, Keiichirō Nasu

Published Mar 30, 2007• 0 citations
Publisher

Abstract

Electron correlation effects on the Lehmann spectra of the one-body Green functions are clarified by using the quantum Monte Carlo simulation of path-integral form. Through the analysis of the Lehmann spectrum, we also show that the electron states of the insulating systems caused by the Coulomb repulsion (Mott-type insulators) significantly depend on the strength of the Coulomb interaction. Specifically, it is shown that in the weak interaction regime, the momentum-specified Lehmann spectrum is qualitatively explained by the second order perturbation theory from the unrestricted Hartree-Fock state, especially near the Fermi energy. This means that the Lehmann spectrum still has a dominant one-body component. On the other hand, in the strong interaction regime, the Lehmann spectrum loses such a one-body component almost completely even near the Fermi energy, and is constituted of the many-body component caused by the coupling between the charge and magnetic excitations. These results indicate that in the weak interaction regime, the electron state of the Mott-type insulator can be described by the one-body picture near the Fermi energy, while in the strong interaction regime, such a one-body picture no longer works even near the Fermi energy. For these two cases, the Lehmann spectra have clearly different peak structures. Since the Lehmann spectrum corresponds to the photoemission spectrum in experiment, we conclude that photoemission spectroscopy can be a valuable tool to obtain direct information on the strength of the Coulomb interaction.

DOI
10.1103/physrevb.75.115132

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Electron correlation effects on the Lehmann spectra of the one-body Green functions are clarified by using the quantum Monte Carlo simulation of path-integral form. Through the analysis of the Lehmann spectrum, we also show that the electron states of the insulating systems caused by the Coulomb repulsion (Mott-type insulators) significantly depend on the strength of the Coulomb interaction. Specifically, it is shown that in the weak interaction regime, the momentum-specified Lehmann spectrum is qualitatively explained by the second order perturbation theory from the unrestricted Hartree-Fock state, especially near the Fermi energy. This means that the Lehmann spectrum still has a dominant one-body component. On the other hand, in the strong interaction regime, the Lehmann spectrum loses such a one-body component almost completely even near the Fermi energy, and is constituted of the many-body component caused by the coupling between the charge and magnetic excitations. These results indicate that in the weak interaction regime, the electron state of the Mott-type insulator can be described by the one-body picture near the Fermi energy, while in the strong interaction regime, such a one-body picture no longer works even near the Fermi energy. For these two cases, the Lehmann spectra have clearly different peak structures. Since the Lehmann spectrum corresponds to the photoemission spectrum in experiment, we conclude that photoemission spectroscopy can be a valuable tool to obtain direct information on the strength of the Coulomb interaction.
We develop a path-integral formulation which is free from Grassmann algebras to calculate absorption spectra of strongly correlated electron systems. The Coulomb repulsions, including not only the short-range part but also a long-range part, are reduced into a time-dependent one-body Hamiltonian with only two kinds of Ising spin variables per site. The sums over these spin configurations are performed according to the quantum Monte Carlo techniques. By this method we disclose the electron correlation effects on absorption spectra. The method is applied to the one-dimensional half-filled electron systems, where the ground state is an insulating state due to the strong long-range Coulomb repulsion and contains large quantum fluctuations by low-energy collective spin excitations. The absorption spectrum shows an infrared divergencelike structure, which seems to arise from the simultaneous excitation of the charge-transfer exciton and collective spin excitations. The spectrum also contains new peaks on the high energy side which correspond to the multiple excitation of electron-hole pairs. Such a multiple excitation is caused by the electron correlation effect, through which the photogenerated electron and hole can excite other electron-hole pairs. Our result clearly shows that charge and spin of the electron are inseparable in a many-body system in an insulating state caused by the strong long-range Coulomb repulsion.
Weights of the multimagnon (incoherent) component and the zero-magnon (coherent) one in the Lehmann's spectral representation of the one-body Green's functions are determined for the one- and the two-dimensional half-filled Hubbard models. The one-body Green's functions with specific momenta are calculated by means of a quantum Monte Carlo simulation. To distinguish the coherent component from the incoherent one in this Lehmann's spectrum, a site-diagonal staggered potential $\ensuremath{\Delta}$ is artificially added to the Hubbard models. Due to this $\ensuremath{\Delta},$ an energy gap opens in the magnon excitation, and as a result, the coherent component is clearly separated from the incoherent one. Systematic analysis on the $\ensuremath{\Delta}$ dependence of these two components shows that the weight of the coherent component is less than a few percent for each dimension in the limit of $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Delta}}0,$ which corresponds with the usual Hubbard model. This means that the incoherent component predominates the spectrum, while the coherent component makes only a minute contribution. In contrast to the widely accepted one-electron band picture, our calculations indicate that the so-called lower Hubbard band peak in the photoemission spectrum of the metal-oxide insulator originates mainly from this incoherent component. It does not correspond with the coherent one that reflects a one-electron state.
In the general frame of a modified many-body perturbation theory, the single-band Hubbard model is treated in the limit of weak electron-electron interaction. In this modification the decomposition of the Hamiltonian into an effective free system and an effective perturbation is rearranged iteratively in each order of the formalism, resulting in a successive reduction of the interaction part. In comparison with conventional perturbation techniques, this means an extended range of validity. Imposing thermodynamic self-consistency, we calculate the wave-vector-dependent electronic self-energy up to second order and analyze the influence of the Coulomb correlations. Several well-known physical properties of the Hubbard model are recovered in characteristic single-particle quantities. Therefore, the effect of the band occupation n and the electron-electron repulsion U on spectral densities, band structures, densities of states, magnetization, etc. is investigated in detail. Some of the most remarkable results are: first, a splitting of the free Bloch band into two quasiparticle subbands when the coupling strength reaches moderate values. These subbands are linked by a small damping-induced background in the density of states and are separated roughly by an energy of the order of U. In addition, the upper subband is shifted to higher energies in the spectrum proportionally to U while the lower one is nearly fixed. Second, we found a paramagnetic-ferromagnetic phase diagram that has a critical coupling strength Uc{U}_{c}Uc​ and exhibits strong indications of a lower critical occupation number nc{n}_{c}nc​. There is no spontaneous magnetization in the system for parameters smaller than these values. Compared with the Stoner model, one thus obtains striking improvements. In many cases our conclusions for the weak-coupling limit are qualitatively in good agreement with well-known results in the strong-correlation regime.
We have theoretically studied various one-dimensional half-filled Hubbard models from weak correlation cases to strong ones, and calculated the Lehmann spectra of the momentum-specified one-body Green's functions, as well as the total density of states (DOS), using the quantum Monte Carlo method. In the region of intermediate correlation strength, we have found the DOS has new characteristic peaks near the Fermi level, in addition to the well-known upper and lower Hubbard-band peaks. We show these new peaks near the Fermi level come from quasi-coherent states, while the upper and lower Hubbard-band peaks come from strongly incoherent ones. This multi-peaked structure, appearing only in the intermediate region, is shown to be quite insensitive to the dimensionality. Finally, we compare our results with the static single impurity model, and give a rough and intuitive explanation for the origin of this newly obtained multi-peaked structure. Our results also qualitatively agree with the recent experiments on CaVO 3 and SrVO 3 crystals.
We theoretically study photoemission spectra for photodoped one-dimensional Mott insulators that can host excitons, and show that their spectral characteristics differ qualitatively from those of photodoped semiconductors. In conventional semiconductors, photoemission spectra are well understood; free charge carriers generate spectral weight near the bottom of the conduction band, while the formation of excitons leads to replica features of the valence band appearing inside the band gap. In one-dimensional Mott insulators, on the other hand, strong correlations give rise to fractionalized elementary excitations-spinons, holons, and doublons-which fundamentally modify the photoemission response. We find that when photodoped carriers, i.e., doublons and holons, remain unbound, the photoemission spectrum directly reflects the dispersion of spinons, i.e., magnetic elementary excitations. In contrast, when a doublon and a holon form an excitonic bound state, replica structures of the lower Hubbard band emerge inside the Mott gap, carrying contributions from both spinon and holon excitations. Importantly, the distribution of the in-gap signal depends sensitively on the degree of doublon-holon binding. The origin of these spectral features is clarified through a combination of exact diagonalization and the slave-particle approach. These results indicate that photoemission from photoinduced carriers and excitons in strongly correlated electron systems can provide information on magnetic properties and carrier-binding properties.
With the hierarchical Green’s function approach, we study a doped Mott insulator described with the Hubbard model by analytically solving the equations of motion of an one-particle Green’s function and related multiple-point correlation functions, and find that the separation of the spin and charge degrees of freedom of the electrons is an intrinsic character of the doped Mott insulator. For enough of large on-site repulsive Coulomb interaction, we show that the spectral weight of the one-particle Green’s function is proportional to the hole doping concentration that is mainly produced by the charge fluctuation of electrons, while the excitation spectrum of the electrons is composed of two parts: One is contributed by the spin fluctuation of the electrons, which is proportional to the hole doping concentration, and another one is coming from the coupling between the charge and spin fluctuations of the electrons that takes the maximum at undoping. All of these low energy/temperature physical properties originate from the strong on-site Coulomb interaction. The present results are consistent with the spectroscopy observations of the cuprate superconductors and the numerical calculations in normal state above the pseudogap regime.