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Physical review. B, Condensed matter

Unified theory for photoemission and light absorption spectra of a one-dimensional interacting electron system

Norikazu Tomita, Keiichirō Nasu

Published Sep 11, 2001• 4 citations
Publisher

Abstract

Very recently, the angle-resolved photoemission spectrum (ARPES) of $[\mathrm{Ni}(\mathrm{chxn}{)}_{2}\mathrm{Br}]{\mathrm{Br}}_{2}$ $(\mathrm{chxn}=1R,$ $2R$-cyclohexanediamine), which is a one-dimensional insulator driven by the strong Coulomb repulsion, has been experimentally observed. The experiment has clearly shown that a one-body gap appearing in the ARPES is much smaller than an optical gap observed in the light-absorption spectrum (LAS). The apparent difference between these two gaps indicates the breakdown of a mean-field description of this strongly correlated electron system. In this paper, we show that the ARPES and LAS of $[\mathrm{Ni}(\mathrm{chxn}{)}_{2}\mathrm{Br}]{\mathrm{Br}}_{2}$ are consistently explained within the framework of the one-dimensional extended Hubbard model. Lehmann spectra of the one-body and light-absorption-type two-body Green functions are calculated by a quantum Monte Carlo method. Our numerical results reproduce the experimentally observed ARPES and LAS, confirming the small one-body gap and large optical gap. The apparent difference in the gap structures can be explained by a dynamical Zeeman field induced by quantum fluctuations.

DOI
10.1103/physrevb.64.125118

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In order to understand the effects of electron-phonon coupling and Coulomb interactions in angle-resolved photoemission spectroscopy (ARPES), a spin-1/2 Hubbard-Holstein model at half-filling is theoretically investigated by means of the mean field theory and classical Monte Carlo simulation method. It shows that the spectral shape of the one-dimensional system is significantly modified by the electron-phonon coupling and Coulomb interactions. The suppression of charge-density wave in one-dimensional system has been ascribed to the short-range Coulomb repulsion and thermal lattice fluctuations. The competition between these interactions can induce zero energy gaps in APPES as well as complete cancellation of charge or spin ordering.
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SrCuO 2 has long been considered a near-archetypal realization of a quasi-one-dimensional (1D) system of interacting electrons with short-range interactions. Within this framework, experimental observations — interpreted through the lens of the 1D Hubbard model — suggest that electron and hole excitations decay into two types of (unphysical) collective bosonic modes: “spinons”, which carry the spin degree of freedom, and “holons, which carry the charge degree of freedom. This model, known as spin-charge separation, is most directly evidenced by angle-resolved photoemission spectroscopy (ARPES), where a photo-induced hole decays into a continuum of these excitations. Here we present an alternative perspective grounded in first-principles, self-consistent, and parameter-free many-body perturbation theory. In this revised quasiparticle framework, ARPES can be understood as a one-body effect arising from mild disorder in a long-range antiferromagnetic ground state. the emergence of the so-called spinon branch arises naturally from spin disorder, the anomalous linewidths are accurately captured, and we provide a compelling explanation for the spectral weight observed at the non-magnetic zone boundary. This reinterpretation provides a unified explanation for key experimental signatures previously attributed to spin-charge separation, including features observed in optical conductivity. Additionally, we show that SrCuO 2 exhibits a nontrivial interchain coupling that significantly influences both its one-particle and two-particle spectral functions. By comparing the spectral features of SrCuO 2 with those of La 2 CuO 4 , we argue that SrCuO 2 shares notable similarities with the two-dimensional cuprates—both being rooted in a common CuO 4 plaquette-based molecular orbital framework.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.
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.
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