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arXiv:cond-mat/0204594 · Physical review. B, Condensed matter

Dynamical density correlation function of one-dimensional Mott insulators in a magnetic field

Davide Controzzi, Fabian H. L. Eßler

Published Oct 29, 2002• 18 citations
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Abstract

We consider the one-dimensional extended Hubbard model at half filling in the presence of a magnetic field. Using field theory techniques we calculate the dynamical density-density correlation function ${\ensuremath{\chi}}_{\mathrm{nn}}(\ensuremath{\omega},q)$ in the low-energy limit. When excitons are formed, a singularity appears in ${\ensuremath{\chi}}_{\mathrm{nn}}(\ensuremath{\omega},q)$ at a particular energy and momentum transfer.

DOI
10.1103/physrevb.66.165112

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We consider the one-dimensional extended Hubbard model at half filling in the presence of a magnetic field. Using field theory techniques we calculate the dynamical density-density correlation function \ensuremathχnn(\ensuremathω,q){\ensuremath{\chi}}_{\mathrm{nn}}(\ensuremath{\omega},q)\ensuremathχnn​(\ensuremathω,q) in the low-energy limit. When excitons are formed, a singularity appears in \ensuremathχnn(\ensuremathω,q){\ensuremath{\chi}}_{\mathrm{nn}}(\ensuremath{\omega},q)\ensuremathχnn​(\ensuremathω,q) at a particular energy and momentum transfer.
A modified version of the metallic-phase pseudofermion dynamical theory (PDT) of the 1D Hubbard model is introduced for the spin dynamical correlation functions of the half-filled 1D Hubbard model Mott–Hubbard phase. The Mott–Hubbard insulator phase PDT is applied to the study of the model longitudinal and transverse spin dynamical structure factors at finite magnetic field h , focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. The relation of our theoretical results to both condensed-matter and ultra-cold atom systems is discussed.
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​.
We present a general method for the calculation of correlation functions in the repulsive one-dimensional Hubbard model at less than half-filling in a magnetic field h. We describe the dependence of the critical exponents that drive their long-distance asymptotics on the Coulomb coupling, the density, and h. This dependence can be described in terms of a set of coupled Bethe-Ansatz integral equations. It simplifies significantly in the strong-coupling limit, where we give explicit formulas for the dependence of the critical exponents on the magnetic field. In particular, we find that at small field the functional dependence of the critical exponents on h can be algebraic or logarithmic---depending on the operators involved. In addition, we evaluate the singularities of the Fourier images of the correlation functions. It turns out that switching on a magnetic field gives rise to singularities in the dynamic field-field correlation functions that are absent at h=0.
Critical properties in the dynamical charge correlation function for the one-dimensional Mott insulator are studied. By properly taking into account {\it the final-state interaction} between the charge and spin degrees of freedom, we find that the edge singularity in the charge correlation function is governed by massless spinon excitations, although it is naively expected that spinons do not directly contribute to the charge excitation over the Hubbard gap. We obtain the momentum-dependent anomalous critical exponent by applying the finite-size scaling analysis to the Bethe ansatz solution of the half-filled Hubbard model.
We present a general method for the calculation of correlation functions in the repulsive one-dimensional Hubbard model at less than half-filling in a magnetic field h. We describe the dependence of the critical exponents that drive their long-distance asymptotics on the Coulomb coupling, the density, and h. This dependence can be described in terms of a set of coupled Bethe-Ansatz integral equations. It simplifies significantly in the strong-coupling limit, where we give explicit formulas for the dependence of the critical exponents on the magnetic field. In particular, we find that at small field the functional dependence of the critical exponents on h can be algebraic or logarithmic---depending on the operators involved. In addition, we evaluate the singularities of the Fourier images of the correlation functions. It turns out that switching on a magnetic field gives rise to singularities in the dynamic field-field correlation functions that are absent at h=0.