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arXiv:2404.11412 · Physical review. B./Physical review. B

Spin and charge dynamics of doped one-dimensional Mott insulators

Takami Tohyama, Hiroki Maeda, Kenji Tsutsui, Shigetoshi Sota, Seiji Yunoki

Published Sep 3, 2024• 2 citations
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Abstract

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.

DOI
10.1103/physrevb.110.125106

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Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator Ba2\ensuremath−xSrxCuO3+\ensuremathδ{\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}Ba2\ensuremath−x​Srx​CuO3+\ensuremathδ​ 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.
We investigate the dynamical spin and charge structure factors and the one-particle spectral function of the one-dimensional extended Hubbard model at half band filling using the dynamical density-matrix renormalization-group method. The influence of the model parameters on these frequency- and momentum-resolved dynamical correlation functions is discussed in detail for the Mott-insulating regime. We find quantitative agreement between our numerical results and experiments for the optical conductivity, resonant inelastic x-ray scattering, neutron scattering, and angle-resolved photoemission spectroscopy in the quasi-one-dimensional Mott insulator SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​.
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Motivated by the recent angle-resolved photoemission spectroscopy (ARPES) measurements on one-dimensional Mott insulators, SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​ and Na0.96V2O5{\mathrm{Na}}_{0.96}{\mathrm{V}}_{2}{\mathrm{O}}_{5}Na0.96​V2​O5​, we examine the single-particle spectral weight of the one-dimensional (1D) Hubbard model at half filling. We are particularly interested in the temperature dependence of the spinon and holon excitations. For this reason, we have performed the dynamical density matrix renormalization group and determinantal quantum Monte Carlo (QMC) calculations for the single-particle spectral weight of the 1D Hubbard model. In the QMC data, the spinon and holon branches become observable at temperatures where the short-range antiferromagnetic correlations develop. At these temperatures, the spinon branch grows rapidly. In the light of the numerical results, we discuss the spinon and holon branches observed by the ARPES experiments on SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​. These numerical results are also in agreement with the temperature dependence of the ARPES results on Na0.96V2O5{\mathrm{Na}}_{0.96}{\mathrm{V}}_{2}{\mathrm{O}}_{5}Na0.96​V2​O5​.
Although charge-spin separation has important consequences for the properties of one-dimensional (1D) Mott-Hubbard insulators, matrix elements in some of its dynamical correlation functions involve the coupling of spin and charge degrees of freedom. The corresponding interplay of the 1D Mott-Hubbard insulator's charge and spin degrees of freedom is an issue of both fundamental and technological interest, for instance, concerning their dynamics at subpicosecond timescales. On the other hand, the up- and down-spin one-particle spectral functions are the simplest dynamical correlation functions that involve excitation of both the charge and spin degrees of freedom. They are thus suitable to extract basic useful physical information on the above interplay at finite magnetic fields. Here the line shape of such functions at and in the $(k,\ensuremath{\omega})$ plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field, they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved nonperturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/21/21/2 atom systems is discussed.
We examine the single-particle excitation spectrum in the one-dimensional Hubbard-Holstein model at half-filling by performing a dynamical density matrix renormalization group calculation. The spin-charge separation is robust against the electron-phonon (EP) coupling, although both spinon and holon branches are affected by phonons. We find that this robustness is in sharp contrast to a rather strong influence of the EP coupling on quasiparticle properties in two dimensions. We discuss the implication of the results of recent angle-resolved photoemission spectroscopy measurements on SrCuO2\mathrm{Sr}\mathrm{Cu}{\mathrm{O}}_{2}SrCuO2​.
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.